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",[1116,1195,1197,1211],{"className":1196},[1119],[1116,1198,1200],{"className":1199},[1123],[1125,1201,1202],{"xmlns":1127},[1129,1203,1204,1209],{},[1132,1205,1206],{},[1135,1207,1208],{},"k",[1139,1210,1208],{"encoding":1141},[1116,1212,1214],{"className":1213,"ariaHidden":1146},[1145],[1116,1215,1217,1221],{"className":1216},[1150],[1116,1218],{"className":1219,"style":1220},[1154],"height:0.6944em;",[1116,1222,1208],{"className":1223,"style":1224},[1159,1160],"margin-right:0.0315em;"," 个变量上的差别记为 ",[1116,1227,1229,1258],{"className":1228},[1119],[1116,1230,1232],{"className":1231},[1123],[1125,1233,1234],{"xmlns":1127},[1129,1235,1236,1255],{},[1132,1237,1238,1245,1249],{},[1239,1240,1241,1243],"msub",{},[1135,1242,1137],{},[1135,1244,1208],{},[1246,1247,1248],"mo",{},"−",[1239,1250,1251,1253],{},[1135,1252,1176],{},[1135,1254,1208],{},[1139,1256,1257],{"encoding":1141},"x_k - 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是把这些差别综合起来的一个度量。",[1091,1453,1454,1455,1459],{},"一个合格的",[1456,1457,1458],"strong",{},"距离","要满足三个条件:",[1095,1461,1462,1579,1720],{},[1098,1463,1464,1467,1468,1578],{},[1456,1465,1466],{},"对称性",":",[1116,1469,1471,1510],{"className":1470},[1119],[1116,1472,1474],{"className":1473},[1123],[1125,1475,1476],{"xmlns":1127},[1129,1477,1478,1507],{},[1132,1479,1480,1482,1484,1486,1488,1490,1492,1495,1497,1499,1501,1503,1505],{},[1135,1481,1398],{},[1246,1483,1402],{"stretchy":1401},[1135,1485,1137],{},[1246,1487,1407],{"separator":1146},[1135,1489,1176],{},[1246,1491,1412],{"stretchy":1401},[1246,1493,1494],{},"=",[1135,1496,1398],{},[1246,1498,1402],{"stretchy":1401},[1135,1500,1176],{},[1246,1502,1407],{"separator":1146},[1135,1504,1137],{},[1246,1506,1412],{"stretchy":1401},[1139,1508,1509],{"encoding":1141},"d(x, y) = d(y, x)",[1116,1511,1513,1551],{"className":1512,"ariaHidden":1146},[1145],[1116,1514,1516,1519,1522,1525,1528,1531,1534,1537,1540,1544,1548],{"className":1515},[1150],[1116,1517],{"className":1518,"style":1425},[1154],[1116,1520,1398],{"className":1521},[1159,1160],[1116,1523,1402],{"className":1524},[1432],[1116,1526,1137],{"className":1527},[1159,1160],[1116,1529,1407],{"className":1530},[1439],[1116,1532],{"className":1533,"style":1443},[1327],[1116,1535,1176],{"className":1536,"style":1192},[1159,1160],[1116,1538,1412],{"className":1539},[1450],[1116,1541],{"className":1542,"style":1543},[1327],"margin-right:0.2778em;",[1116,1545,1494],{"className":1546},[1547],"mrel",[1116,1549],{"className":1550,"style":1543},[1327],[1116,1552,1554,1557,1560,1563,1566,1569,1572,1575],{"className":1553},[1150],[1116,1555],{"className":1556,"style":1425},[1154],[1116,1558,1398],{"className":1559},[1159,1160],[1116,1561,1402],{"className":1562},[1432],[1116,1564,1176],{"className":1565,"style":1192},[1159,1160],[1116,1567,1407],{"className":1568},[1439],[1116,1570],{"className":1571,"style":1443},[1327],[1116,1573,1137],{"className":1574},[1159,1160],[1116,1576,1412],{"className":1577},[1450],";",[1098,1580,1581,1467,1584,1667,1668,1719],{},[1456,1582,1583],{},"非负性",[1116,1585,1587,1618],{"className":1586},[1119],[1116,1588,1590],{"className":1589},[1123],[1125,1591,1592],{"xmlns":1127},[1129,1593,1594,1615],{},[1132,1595,1596,1598,1600,1602,1604,1606,1608,1611],{},[1135,1597,1398],{},[1246,1599,1402],{"stretchy":1401},[1135,1601,1137],{},[1246,1603,1407],{"separator":1146},[1135,1605,1176],{},[1246,1607,1412],{"stretchy":1401},[1246,1609,1610],{},"≥",[1612,1613,1614],"mn",{},"0",[1139,1616,1617],{"encoding":1141},"d(x, 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时取等号;",[1098,1721,1722,1467,1725,1886],{},[1456,1723,1724],{},"三角不等式",[1116,1726,1728,1783],{"className":1727},[1119],[1116,1729,1731],{"className":1730},[1123],[1125,1732,1733],{"xmlns":1127},[1129,1734,1735,1780],{},[1132,1736,1737,1739,1741,1743,1745,1748,1750,1753,1755,1757,1759,1761,1763,1765,1768,1770,1772,1774,1776,1778],{},[1135,1738,1398],{},[1246,1740,1402],{"stretchy":1401},[1135,1742,1137],{},[1246,1744,1407],{"separator":1146},[1135,1746,1747],{},"z",[1246,1749,1412],{"stretchy":1401},[1246,1751,1752],{},"≤",[1135,1754,1398],{},[1246,1756,1402],{"stretchy":1401},[1135,1758,1137],{},[1246,1760,1407],{"separator":1146},[1135,1762,1176],{},[1246,1764,1412],{"stretchy":1401},[1246,1766,1767],{},"+",[1135,1769,1398],{},[1246,1771,1402],{"stretchy":1401},[1135,1773,1176],{},[1246,1775,1407],{"separator":1146},[1135,1777,1747],{},[1246,1779,1412],{"stretchy":1401},[1139,1781,1782],{"encoding":1141},"d(x, z) \\le d(x, y) + d(y, z)",[1116,1784,1786,1823,1859],{"className":1785,"ariaHidden":1146},[1145],[1116,1787,1789,1792,1795,1798,1801,1804,1807,1811,1814,1817,1820],{"className":1788},[1150],[1116,1790],{"className":1791,"style":1425},[1154],[1116,1793,1398],{"className":1794},[1159,1160],[1116,1796,1402],{"className":1797},[1432],[1116,1799,1137],{"className":1800},[1159,1160],[1116,1802,1407],{"className":1803},[1439],[1116,1805],{"className":1806,"style":1443},[1327],[1116,1808,1747],{"className":1809,"style":1810},[1159,1160],"margin-right:0.044em;",[1116,1812,1412],{"className":1813},[1450],[1116,1815],{"className":1816,"style":1543},[1327],[1116,1818,1752],{"className":1819},[1547],[1116,1821],{"className":1822,"style":1543},[1327],[1116,1824,1826,1829,1832,1835,1838,1841,1844,1847,1850,1853,1856],{"className":1825},[1150],[1116,1827],{"className":1828,"style":1425},[1154],[1116,1830,1398],{"className":1831},[1159,1160],[1116,1833,1402],{"className":1834},[1432],[1116,1836,1137],{"className":1837},[1159,1160],[1116,1839,1407],{"className":1840},[1439],[1116,1842],{"className":1843,"style":1443},[1327],[1116,1845,1176],{"className":1846,"style":1192},[1159,1160],[1116,1848,1412],{"className":1849},[1450],[1116,1851],{"className":1852,"style":1328},[1327],[1116,1854,1767],{"className":1855},[1332],[1116,1857],{"className":1858,"style":1328},[1327],[1116,1860,1862,1865,1868,1871,1874,1877,1880,1883],{"className":1861},[1150],[1116,1863],{"className":1864,"style":1425},[1154],[1116,1866,1398],{"className":1867},[1159,1160],[1116,1869,1402],{"className":1870},[1432],[1116,1872,1176],{"className":1873,"style":1192},[1159,1160],[1116,1875,1407],{"className":1876},[1439],[1116,1878],{"className":1879,"style":1443},[1327],[1116,1881,1747],{"className":1882,"style":1810},[1159,1160],[1116,1884,1412],{"className":1885},[1450],"。",[1888,1889,1890],"h3",{"id":1890},"常用距离",[1091,1892,1893,1896,1897,1925],{},[1456,1894,1895],{},"数值数据","(设 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个变量):",[1095,1927,1928,2310,2591,2848,3388],{},[1098,1929,1930,1467,1933,1578],{},[1456,1931,1932],{},"欧氏距离",[1116,1934,1936,2008],{"className":1935},[1119],[1116,1937,1939],{"className":1938},[1123],[1125,1940,1941],{"xmlns":1127},[1129,1942,1943,2005],{},[1132,1944,1945,1947,1949,1951,1953,1955,1957,1959],{},[1135,1946,1398],{},[1246,1948,1402],{"stretchy":1401},[1135,1950,1137],{},[1246,1952,1407],{"separator":1146},[1135,1954,1176],{},[1246,1956,1412],{"stretchy":1401},[1246,1958,1494],{},[1960,1961,1962],"msqrt",{},[1132,1963,1964,1981,1983,1989,1991,1997],{},[1965,1966,1967,1970,1979],"msubsup",{},[1246,1968,1969],{},"∑",[1132,1971,1972,1974,1976],{},[1135,1973,1208],{},[1246,1975,1494],{},[1612,1977,1978],{},"1",[1135,1980,1091],{},[1246,1982,1402],{"stretchy":1401},[1239,1984,1985,1987],{},[1135,1986,1137],{},[1135,1988,1208],{},[1246,1990,1248],{},[1239,1992,1993,1995],{},[1135,1994,1176],{},[1135,1996,1208],{},[1998,1999,2000,2002],"msup",{},[1246,2001,1412],{"stretchy":1401},[1612,2003,2004],{},"2",[1139,2006,2007],{"encoding":1141},"d(x,y) = \\sqrt{\\sum_{k=1}^{p}(x_k - y_k)^2}",[1116,2009,2011,2047],{"className":2010,"ariaHidden":1146},[1145],[1116,2012,2014,2017,2020,2023,2026,2029,2032,2035,2038,2041,2044],{"className":2013},[1150],[1116,2015],{"className":2016,"style":1425},[1154],[1116,2018,1398],{"className":2019},[1159,1160],[1116,2021,1402],{"className":2022},[1432],[1116,2024,1137],{"className":2025},[1159,1160],[1116,2027,1407],{"className":2028},[1439],[1116,2030],{"className":2031,"style":1443},[1327],[1116,2033,1176],{"className":2034,"style":1192},[1159,1160],[1116,2036,1412],{"className":2037},[1450],[1116,2039],{"className":2040,"style":1543},[1327],[1116,2042,1494],{"className":2043},[1547],[1116,2045],{"className":2046,"style":1543},[1327],[1116,2048,2050,2054],{"className":2049},[1150],[1116,2051],{"className":2052,"style":2053},[1154],"height:1.24em;vertical-align:-0.3027em;",[1116,2055,2058],{"className":2056},[1159,2057],"sqrt",[1116,2059,2061,2301],{"className":2060},[1281,1282],[1116,2062,2064,2298],{"className":2063},[1286],[1116,2065,2068,2275],{"className":2066,"style":2067},[1290],"height:0.9373em;",[1116,2069,2073,2077],{"className":2070,"style":2072},[2071],"svg-align","top:-3.2em;",[1116,2074],{"className":2075,"style":2076},[1298],"height:3.2em;",[1116,2078,2081,2152,2155,2195,2198,2201,2204,2244],{"className":2079,"style":2080},[1159],"padding-left:1em;",[1116,2082,2085,2091],{"className":2083},[2084],"mop",[1116,2086,1969],{"className":2087,"style":2090},[2084,2088,2089],"op-symbol","small-op","position:relative;top:0em;",[1116,2092,2094],{"className":2093},[1277],[1116,2095,2097,2143],{"className":2096},[1281,1282],[1116,2098,2100,2140],{"className":2099},[1286],[1116,2101,2104,2125],{"className":2102,"style":2103},[1290],"height:0.8043em;",[1116,2105,2107,2110],{"style":2106},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1116,2108],{"className":2109,"style":1299},[1298],[1116,2111,2113],{"className":2112},[1303,1304,1305,1306],[1116,2114,2116,2119,2122],{"className":2115},[1159,1306],[1116,2117,1208],{"className":2118,"style":1224},[1159,1160,1306],[1116,2120,1494],{"className":2121},[1547,1306],[1116,2123,1978],{"className":2124},[1159,1306],[1116,2126,2128,2131],{"style":2127},"top:-3.2029em;margin-right:0.05em;",[1116,2129],{"className":2130,"style":1299},[1298],[1116,2132,2134],{"className":2133},[1303,1304,1305,1306],[1116,2135,2137],{"className":2136},[1159,1306],[1116,2138,1091],{"className":2139},[1159,1160,1306],[1116,2141,1314],{"className":2142},[1313],[1116,2144,2146],{"className":2145},[1286],[1116,2147,2150],{"className":2148,"style":2149},[1290],"height:0.2997em;",[1116,2151],{},[1116,2153,1402],{"className":2154},[1432],[1116,2156,2158,2161],{"className":2157},[1159],[1116,2159,1137],{"className":2160},[1159,1160],[1116,2162,2164],{"className":2163},[1277],[1116,2165,2167,2187],{"className":2166},[1281,1282],[1116,2168,2170,2184],{"className":2169},[1286],[1116,2171,2173],{"className":2172,"style":1291},[1290],[1116,2174,2175,2178],{"style":1294},[1116,2176],{"className":2177,"style":1299},[1298],[1116,2179,2181],{"className":2180},[1303,1304,1305,1306],[1116,2182,1208],{"className":2183,"style":1224},[1159,1160,1306],[1116,2185,1314],{"className":2186},[1313],[1116,2188,2190],{"className":2189},[1286],[1116,2191,2193],{"className":2192,"style":1321},[1290],[1116,2194],{},[1116,2196],{"className":2197,"style":1328},[1327],[1116,2199,1248],{"className":2200},[1332],[1116,2202],{"className":2203,"style":1328},[1327],[1116,2205,2207,2210],{"className":2206},[1159],[1116,2208,1176],{"className":2209,"style":1192},[1159,1160],[1116,2211,2213],{"className":2212},[1277],[1116,2214,2216,2236],{"className":2215},[1281,1282],[1116,2217,2219,2233],{"className":2218},[1286],[1116,2220,2222],{"className":2221,"style":1291},[1290],[1116,2223,2224,2227],{"style":1362},[1116,2225],{"className":2226,"style":1299},[1298],[1116,2228,2230],{"className":2229},[1303,1304,1305,1306],[1116,2231,1208],{"className":2232,"style":1224},[1159,1160,1306],[1116,2234,1314],{"className":2235},[1313],[1116,2237,2239],{"className":2238},[1286],[1116,2240,2242],{"className":2241,"style":1321},[1290],[1116,2243],{},[1116,2245,2247,2250],{"className":2246},[1450],[1116,2248,1412],{"className":2249},[1450],[1116,2251,2253],{"className":2252},[1277],[1116,2254,2256],{"className":2255},[1281],[1116,2257,2259],{"className":2258},[1286],[1116,2260,2263],{"className":2261,"style":2262},[1290],"height:0.7401em;",[1116,2264,2266,2269],{"style":2265},"top:-2.989em;margin-right:0.05em;",[1116,2267],{"className":2268,"style":1299},[1298],[1116,2270,2272],{"className":2271},[1303,1304,1305,1306],[1116,2273,2004],{"className":2274},[1159,1306],[1116,2276,2278,2281],{"style":2277},"top:-2.8973em;",[1116,2279],{"className":2280,"style":2076},[1298],[1116,2282,2286],{"className":2283,"style":2285},[2284],"hide-tail","min-width:1.02em;height:1.28em;",[2287,2288,2294],"svg",{"xmlns":2289,"width":2290,"height":2291,"viewBox":2292,"preserveAspectRatio":2293},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[2295,2296],"path",{"d":2297},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[1116,2299,1314],{"className":2300},[1313],[1116,2302,2304],{"className":2303},[1286],[1116,2305,2308],{"className":2306,"style":2307},[1290],"height:0.3027em;",[1116,2309],{},[1098,2311,2312,1467,2315,1578],{},[1456,2313,2314],{},"绝对距离(曼哈顿距离)",[1116,2316,2318,2378],{"className":2317},[1119],[1116,2319,2321],{"className":2320},[1123],[1125,2322,2323],{"xmlns":1127},[1129,2324,2325,2375],{},[1132,2326,2327,2329,2331,2333,2335,2337,2339,2341,2355,2359,2365,2367,2373],{},[1135,2328,1398],{},[1246,2330,1402],{"stretchy":1401},[1135,2332,1137],{},[1246,2334,1407],{"separator":1146},[1135,2336,1176],{},[1246,2338,1412],{"stretchy":1401},[1246,2340,1494],{},[1965,2342,2343,2345,2353],{},[1246,2344,1969],{},[1132,2346,2347,2349,2351],{},[1135,2348,1208],{},[1246,2350,1494],{},[1612,2352,1978],{},[1135,2354,1091],{},[1135,2356,2358],{"mathvariant":2357},"normal","∣",[1239,2360,2361,2363],{},[1135,2362,1137],{},[1135,2364,1208],{},[1246,2366,1248],{},[1239,2368,2369,2371],{},[1135,2370,1176],{},[1135,2372,1208],{},[1135,2374,2358],{"mathvariant":2357},[1139,2376,2377],{"encoding":1141},"d(x,y) = \\sum_{k=1}^{p}|x_k - y_k|",[1116,2379,2381,2417,2542],{"className":2380,"ariaHidden":1146},[1145],[1116,2382,2384,2387,2390,2393,2396,2399,2402,2405,2408,2411,2414],{"className":2383},[1150],[1116,2385],{"className":2386,"style":1425},[1154],[1116,2388,1398],{"className":2389},[1159,1160],[1116,2391,1402],{"className":2392},[1432],[1116,2394,1137],{"className":2395},[1159,1160],[1116,2397,1407],{"className":2398},[1439],[1116,2400],{"className":2401,"style":1443},[1327],[1116,2403,1176],{"className":2404,"style":1192},[1159,1160],[1116,2406,1412],{"className":2407},[1450],[1116,2409],{"className":2410,"style":1543},[1327],[1116,2412,1494],{"className":2413},[1547],[1116,2415],{"className":2416,"style":1543},[1327],[1116,2418,2420,2424,2487,2490,2493,2533,2536,2539],{"className":2419},[1150],[1116,2421],{"className":2422,"style":2423},[1154],"height:1.104em;vertical-align:-0.2997em;",[1116,2425,2427,2430],{"className":2426},[2084],[1116,2428,1969],{"className":2429,"style":2090},[2084,2088,2089],[1116,2431,2433],{"className":2432},[1277],[1116,2434,2436,2479],{"className":2435},[1281,1282],[1116,2437,2439,2476],{"className":2438},[1286],[1116,2440,2442,2462],{"className":2441,"style":2103},[1290],[1116,2443,2444,2447],{"style":2106},[1116,2445],{"className":2446,"style":1299},[1298],[1116,2448,2450],{"className":2449},[1303,1304,1305,1306],[1116,2451,2453,2456,2459],{"className":2452},[1159,1306],[1116,2454,1208],{"className":2455,"style":1224},[1159,1160,1306],[1116,2457,1494],{"className":2458},[1547,1306],[1116,2460,1978],{"className":2461},[1159,1306],[1116,2463,2464,2467],{"style":2127},[1116,2465],{"className":2466,"style":1299},[1298],[1116,2468,2470],{"className":2469},[1303,1304,1305,1306],[1116,2471,2473],{"className":2472},[1159,1306],[1116,2474,1091],{"className":2475},[1159,1160,1306],[1116,2477,1314],{"className":2478},[1313],[1116,2480,2482],{"className":2481},[1286],[1116,2483,2485],{"className":2484,"style":2149},[1290],[1116,2486],{},[1116,2488],{"className":2489,"style":1443},[1327],[1116,2491,2358],{"className":2492},[1159],[1116,2494,2496,2499],{"className":2495},[1159],[1116,2497,1137],{"className":2498},[1159,1160],[1116,2500,2502],{"className":2501},[1277],[1116,2503,2505,2525],{"className":2504},[1281,1282],[1116,2506,2508,2522],{"className":2507},[1286],[1116,2509,2511],{"className":2510,"style":1291},[1290],[1116,2512,2513,2516],{"style":1294},[1116,2514],{"className":2515,"style":1299},[1298],[1116,2517,2519],{"className":2518},[1303,1304,1305,1306],[1116,2520,1208],{"className":2521,"style":1224},[1159,1160,1306],[1116,2523,1314],{"className":2524},[1313],[1116,2526,2528],{"className":2527},[1286],[1116,2529,2531],{"className":2530,"style":1321},[1290],[1116,2532],{},[1116,2534],{"className":2535,"style":1328},[1327],[1116,2537,1248],{"className":2538},[1332],[1116,2540],{"className":2541,"style":1328},[1327],[1116,2543,2545,2548,2588],{"className":2544},[1150],[1116,2546],{"className":2547,"style":1425},[1154],[1116,2549,2551,2554],{"className":2550},[1159],[1116,2552,1176],{"className":2553,"style":1192},[1159,1160],[1116,2555,2557],{"className":2556},[1277],[1116,2558,2560,2580],{"className":2559},[1281,1282],[1116,2561,2563,2577],{"className":2562},[1286],[1116,2564,2566],{"className":2565,"style":1291},[1290],[1116,2567,2568,2571],{"style":1362},[1116,2569],{"className":2570,"style":1299},[1298],[1116,2572,2574],{"className":2573},[1303,1304,1305,1306],[1116,2575,1208],{"className":2576,"style":1224},[1159,1160,1306],[1116,2578,1314],{"className":2579},[1313],[1116,2581,2583],{"className":2582},[1286],[1116,2584,2586],{"className":2585,"style":1321},[1290],[1116,2587],{},[1116,2589,2358],{"className":2590},[1159],[1098,2592,2593,1467,2596,1578],{},[1456,2594,2595],{},"切氏距离(切比雪夫距离)",[1116,2597,2599,2655],{"className":2598},[1119],[1116,2600,2602],{"className":2601},[1123],[1125,2603,2604],{"xmlns":1127},[1129,2605,2606,2652],{},[1132,2607,2608,2610,2612,2614,2616,2618,2620,2622,2634,2636,2642,2644,2650],{},[1135,2609,1398],{},[1246,2611,1402],{"stretchy":1401},[1135,2613,1137],{},[1246,2615,1407],{"separator":1146},[1135,2617,1176],{},[1246,2619,1412],{"stretchy":1401},[1246,2621,1494],{},[1239,2623,2624,2632],{},[1132,2625,2626,2629],{},[1135,2627,2628],{},"max",[1246,2630,2631],{},"⁡",[1135,2633,1208],{},[1135,2635,2358],{"mathvariant":2357},[1239,2637,2638,2640],{},[1135,2639,1137],{},[1135,2641,1208],{},[1246,2643,1248],{},[1239,2645,2646,2648],{},[1135,2647,1176],{},[1135,2649,1208],{},[1135,2651,2358],{"mathvariant":2357},[1139,2653,2654],{"encoding":1141},"d(x,y) = \\max_{k}|x_k - y_k|",[1116,2656,2658,2694,2799],{"className":2657,"ariaHidden":1146},[1145],[1116,2659,2661,2664,2667,2670,2673,2676,2679,2682,2685,2688,2691],{"className":2660},[1150],[1116,2662],{"className":2663,"style":1425},[1154],[1116,2665,1398],{"className":2666},[1159,1160],[1116,2668,1402],{"className":2669},[1432],[1116,2671,1137],{"className":2672},[1159,1160],[1116,2674,1407],{"className":2675},[1439],[1116,2677],{"className":2678,"style":1443},[1327],[1116,2680,1176],{"className":2681,"style":1192},[1159,1160],[1116,2683,1412],{"className":2684},[1450],[1116,2686],{"className":2687,"style":1543},[1327],[1116,2689,1494],{"className":2690},[1547],[1116,2692],{"className":2693,"style":1543},[1327],[1116,2695,2697,2700,2744,2747,2750,2790,2793,2796],{"className":2696},[1150],[1116,2698],{"className":2699,"style":1425},[1154],[1116,2701,2703,2706],{"className":2702},[2084],[1116,2704,2628],{"className":2705},[2084],[1116,2707,2709],{"className":2708},[1277],[1116,2710,2712,2736],{"className":2711},[1281,1282],[1116,2713,2715,2733],{"className":2714},[1286],[1116,2716,2718],{"className":2717,"style":1291},[1290],[1116,2719,2721,2724],{"style":2720},"top:-2.55em;margin-right:0.05em;",[1116,2722],{"className":2723,"style":1299},[1298],[1116,2725,2727],{"className":2726},[1303,1304,1305,1306],[1116,2728,2730],{"className":2729},[1159,1306],[1116,2731,1208],{"className":2732,"style":1224},[1159,1160,1306],[1116,2734,1314],{"className":2735},[1313],[1116,2737,2739],{"className":2738},[1286],[1116,2740,2742],{"className":2741,"style":1321},[1290],[1116,2743],{},[1116,2745],{"className":2746,"style":1443},[1327],[1116,2748,2358],{"className":2749},[1159],[1116,2751,2753,2756],{"className":2752},[1159],[1116,2754,1137],{"className":2755},[1159,1160],[1116,2757,2759],{"className":2758},[1277],[1116,2760,2762,2782],{"className":2761},[1281,1282],[1116,2763,2765,2779],{"className":2764},[1286],[1116,2766,2768],{"className":2767,"style":1291},[1290],[1116,2769,2770,2773],{"style":1294},[1116,2771],{"className":2772,"style":1299},[1298],[1116,2774,2776],{"className":2775},[1303,1304,1305,1306],[1116,2777,1208],{"className":2778,"style":1224},[1159,1160,1306],[1116,2780,1314],{"className":2781},[1313],[1116,2783,2785],{"className":2784},[1286],[1116,2786,2788],{"className":2787,"style":1321},[1290],[1116,2789],{},[1116,2791],{"className":2792,"style":1328},[1327],[1116,2794,1248],{"className":2795},[1332],[1116,2797],{"className":2798,"style":1328},[1327],[1116,2800,2802,2805,2845],{"className":2801},[1150],[1116,2803],{"className":2804,"style":1425},[1154],[1116,2806,2808,2811],{"className":2807},[1159],[1116,2809,1176],{"className":2810,"style":1192},[1159,1160],[1116,2812,2814],{"className":2813},[1277],[1116,2815,2817,2837],{"className":2816},[1281,1282],[1116,2818,2820,2834],{"className":2819},[1286],[1116,2821,2823],{"className":2822,"style":1291},[1290],[1116,2824,2825,2828],{"style":1362},[1116,2826],{"className":2827,"style":1299},[1298],[1116,2829,2831],{"className":2830},[1303,1304,1305,1306],[1116,2832,1208],{"className":2833,"style":1224},[1159,1160,1306],[1116,2835,1314],{"className":2836},[1313],[1116,2838,2840],{"className":2839},[1286],[1116,2841,2843],{"className":2842,"style":1321},[1290],[1116,2844],{},[1116,2846,2358],{"className":2847},[1159],[1098,2849,2850,1467,2853,3229,3230,3281,3282,3333,3334,3387],{},[1456,2851,2852],{},"明氏距离(闵可夫斯基距离)",[1116,2854,2856,2935],{"className":2855},[1119],[1116,2857,2859],{"className":2858},[1123],[1125,2860,2861],{"xmlns":1127},[1129,2862,2863,2932],{},[1132,2864,2865,2867,2869,2871,2873,2875,2877,2879,2882,2896,2898,2904,2906,2912,2919],{},[1135,2866,1398],{},[1246,2868,1402],{"stretchy":1401},[1135,2870,1137],{},[1246,2872,1407],{"separator":1146},[1135,2874,1176],{},[1246,2876,1412],{"stretchy":1401},[1246,2878,1494],{},[1246,2880,1402],{"fence":1401,"stretchy":1146,"minsize":2881,"maxsize":2881},"1.8em",[1965,2883,2884,2886,2894],{},[1246,2885,1969],{},[1132,2887,2888,2890,2892],{},[1135,2889,1208],{},[1246,2891,1494],{},[1612,2893,1978],{},[1135,2895,1091],{},[1135,2897,2358],{"mathvariant":2357},[1239,2899,2900,2902],{},[1135,2901,1137],{},[1135,2903,1208],{},[1246,2905,1248],{},[1239,2907,2908,2910],{},[1135,2909,1176],{},[1135,2911,1208],{},[1998,2913,2914,2916],{},[1135,2915,2358],{"mathvariant":2357},[1135,2917,2918],{},"q",[1998,2920,2921,2923],{},[1246,2922,1412],{"fence":1401,"stretchy":1146,"minsize":2881,"maxsize":2881},[1132,2924,2925,2927,2930],{},[1612,2926,1978],{},[1135,2928,2929],{"mathvariant":2357},"\u002F",[1135,2931,2918],{},[1139,2933,2934],{"encoding":1141},"d(x,y) = \\Big(\\sum_{k=1}^{p}|x_k - y_k|^q\\Big)^{1\u002Fq}",[1116,2936,2938,2974,3110],{"className":2937,"ariaHidden":1146},[1145],[1116,2939,2941,2944,2947,2950,2953,2956,2959,2962,2965,2968,2971],{"className":2940},[1150],[1116,2942],{"className":2943,"style":1425},[1154],[1116,2945,1398],{"className":2946},[1159,1160],[1116,2948,1402],{"className":2949},[1432],[1116,2951,1137],{"className":2952},[1159,1160],[1116,2954,1407],{"className":2955},[1439],[1116,2957],{"className":2958,"style":1443},[1327],[1116,2960,1176],{"className":2961,"style":1192},[1159,1160],[1116,2963,1412],{"className":2964},[1450],[1116,2966],{"className":2967,"style":1543},[1327],[1116,2969,1494],{"className":2970},[1547],[1116,2972],{"className":2973,"style":1543},[1327],[1116,2975,2977,2981,2989,2992,3055,3058,3061,3101,3104,3107],{"className":2976},[1150],[1116,2978],{"className":2979,"style":2980},[1154],"height:1.8em;vertical-align:-0.65em;",[1116,2982,2984],{"className":2983},[1159],[1116,2985,1402],{"className":2986},[2987,2988],"delimsizing","size2",[1116,2990],{"className":2991,"style":1443},[1327],[1116,2993,2995,2998],{"className":2994},[2084],[1116,2996,1969],{"className":2997,"style":2090},[2084,2088,2089],[1116,2999,3001],{"className":3000},[1277],[1116,3002,3004,3047],{"className":3003},[1281,1282],[1116,3005,3007,3044],{"className":3006},[1286],[1116,3008,3010,3030],{"className":3009,"style":2103},[1290],[1116,3011,3012,3015],{"style":2106},[1116,3013],{"className":3014,"style":1299},[1298],[1116,3016,3018],{"className":3017},[1303,1304,1305,1306],[1116,3019,3021,3024,3027],{"className":3020},[1159,1306],[1116,3022,1208],{"className":3023,"style":1224},[1159,1160,1306],[1116,3025,1494],{"className":3026},[1547,1306],[1116,3028,1978],{"className":3029},[1159,1306],[1116,3031,3032,3035],{"style":2127},[1116,3033],{"className":3034,"style":1299},[1298],[1116,3036,3038],{"className":3037},[1303,1304,1305,1306],[1116,3039,3041],{"className":3040},[1159,1306],[1116,3042,1091],{"className":3043},[1159,1160,1306],[1116,3045,1314],{"className":3046},[1313],[1116,3048,3050],{"className":3049},[1286],[1116,3051,3053],{"className":3052,"style":2149},[1290],[1116,3054],{},[1116,3056],{"className":3057,"style":1443},[1327],[1116,3059,2358],{"className":3060},[1159],[1116,3062,3064,3067],{"className":3063},[1159],[1116,3065,1137],{"className":3066},[1159,1160],[1116,3068,3070],{"className":3069},[1277],[1116,3071,3073,3093],{"className":3072},[1281,1282],[1116,3074,3076,3090],{"className":3075},[1286],[1116,3077,3079],{"className":3078,"style":1291},[1290],[1116,3080,3081,3084],{"style":1294},[1116,3082],{"className":3083,"style":1299},[1298],[1116,3085,3087],{"className":3086},[1303,1304,1305,1306],[1116,3088,1208],{"className":3089,"style":1224},[1159,1160,1306],[1116,3091,1314],{"className":3092},[1313],[1116,3094,3096],{"className":3095},[1286],[1116,3097,3099],{"className":3098,"style":1321},[1290],[1116,3100],{},[1116,3102],{"className":3103,"style":1328},[1327],[1116,3105,1248],{"className":3106},[1332],[1116,3108],{"className":3109,"style":1328},[1327],[1116,3111,3113,3117,3157,3188],{"className":3112},[1150],[1116,3114],{"className":3115,"style":3116},[1154],"height:2.0779em;vertical-align:-0.65em;",[1116,3118,3120,3123],{"className":3119},[1159],[1116,3121,1176],{"className":3122,"style":1192},[1159,1160],[1116,3124,3126],{"className":3125},[1277],[1116,3127,3129,3149],{"className":3128},[1281,1282],[1116,3130,3132,3146],{"className":3131},[1286],[1116,3133,3135],{"className":3134,"style":1291},[1290],[1116,3136,3137,3140],{"style":1362},[1116,3138],{"className":3139,"style":1299},[1298],[1116,3141,3143],{"className":3142},[1303,1304,1305,1306],[1116,3144,1208],{"className":3145,"style":1224},[1159,1160,1306],[1116,3147,1314],{"className":3148},[1313],[1116,3150,3152],{"className":3151},[1286],[1116,3153,3155],{"className":3154,"style":1321},[1290],[1116,3156],{},[1116,3158,3160,3163],{"className":3159},[1159],[1116,3161,2358],{"className":3162},[1159],[1116,3164,3166],{"className":3165},[1277],[1116,3167,3169],{"className":3168},[1281],[1116,3170,3172],{"className":3171},[1286],[1116,3173,3176],{"className":3174,"style":3175},[1290],"height:0.6644em;",[1116,3177,3179,3182],{"style":3178},"top:-3.063em;margin-right:0.05em;",[1116,3180],{"className":3181,"style":1299},[1298],[1116,3183,3185],{"className":3184},[1303,1304,1305,1306],[1116,3186,2918],{"className":3187,"style":1192},[1159,1160,1306],[1116,3189,3191,3197],{"className":3190},[1159],[1116,3192,3194],{"className":3193},[1159],[1116,3195,1412],{"className":3196},[2987,2988],[1116,3198,3200],{"className":3199},[1277],[1116,3201,3203],{"className":3202},[1281],[1116,3204,3206],{"className":3205},[1286],[1116,3207,3210],{"className":3208,"style":3209},[1290],"height:1.4279em;",[1116,3211,3213,3216],{"style":3212},"top:-3.6029em;margin-right:0.05em;",[1116,3214],{"className":3215,"style":1299},[1298],[1116,3217,3219],{"className":3218},[1303,1304,1305,1306],[1116,3220,3222,3226],{"className":3221},[1159,1306],[1116,3223,3225],{"className":3224},[1159,1306],"1\u002F",[1116,3227,2918],{"className":3228,"style":1192},[1159,1160,1306],",是前三者的统一形式(",[1116,3231,3233,3251],{"className":3232},[1119],[1116,3234,3236],{"className":3235},[1123],[1125,3237,3238],{"xmlns":1127},[1129,3239,3240,3248],{},[1132,3241,3242,3244,3246],{},[1135,3243,2918],{},[1246,3245,1494],{},[1612,3247,2004],{},[1139,3249,3250],{"encoding":1141},"q=2",[1116,3252,3254,3272],{"className":3253,"ariaHidden":1146},[1145],[1116,3255,3257,3260,3263,3266,3269],{"className":3256},[1150],[1116,3258],{"className":3259,"style":1188},[1154],[1116,3261,2918],{"className":3262,"style":1192},[1159,1160],[1116,3264],{"className":3265,"style":1543},[1327],[1116,3267,1494],{"className":3268},[1547],[1116,3270],{"className":3271,"style":1543},[1327],[1116,3273,3275,3278],{"className":3274},[1150],[1116,3276],{"className":3277,"style":1663},[1154],[1116,3279,2004],{"className":3280},[1159]," 为欧氏、",[1116,3283,3285,3303],{"className":3284},[1119],[1116,3286,3288],{"className":3287},[1123],[1125,3289,3290],{"xmlns":1127},[1129,3291,3292,3300],{},[1132,3293,3294,3296,3298],{},[1135,3295,2918],{},[1246,3297,1494],{},[1612,3299,1978],{},[1139,3301,3302],{"encoding":1141},"q=1",[1116,3304,3306,3324],{"className":3305,"ariaHidden":1146},[1145],[1116,3307,3309,3312,3315,3318,3321],{"className":3308},[1150],[1116,3310],{"className":3311,"style":1188},[1154],[1116,3313,2918],{"className":3314,"style":1192},[1159,1160],[1116,3316],{"className":3317,"style":1543},[1327],[1116,3319,1494],{"className":3320},[1547],[1116,3322],{"className":3323,"style":1543},[1327],[1116,3325,3327,3330],{"className":3326},[1150],[1116,3328],{"className":3329,"style":1663},[1154],[1116,3331,1978],{"className":3332},[1159]," 为绝对、",[1116,3335,3337,3357],{"className":3336},[1119],[1116,3338,3340],{"className":3339},[1123],[1125,3341,3342],{"xmlns":1127},[1129,3343,3344,3354],{},[1132,3345,3346,3348,3351],{},[1135,3347,2918],{},[1246,3349,3350],{},"→",[1135,3352,3353],{"mathvariant":2357},"∞",[1139,3355,3356],{"encoding":1141},"q\\to\\infty",[1116,3358,3360,3378],{"className":3359,"ariaHidden":1146},[1145],[1116,3361,3363,3366,3369,3372,3375],{"className":3362},[1150],[1116,3364],{"className":3365,"style":1188},[1154],[1116,3367,2918],{"className":3368,"style":1192},[1159,1160],[1116,3370],{"className":3371,"style":1543},[1327],[1116,3373,3350],{"className":3374},[1547],[1116,3376],{"className":3377,"style":1543},[1327],[1116,3379,3381,3384],{"className":3380},[1150],[1116,3382],{"className":3383,"style":1155},[1154],[1116,3385,3353],{"className":3386},[1159]," 为切氏);",[1098,3389,3390,1467,3393,3662,3663,3693],{},[1456,3391,3392],{},"马氏距离(马哈拉诺比斯距离)",[1116,3394,3396,3462],{"className":3395},[1119],[1116,3397,3399],{"className":3398},[1123],[1125,3400,3401],{"xmlns":1127},[1129,3402,3403,3459],{},[1132,3404,3405,3407,3409,3411,3413,3415,3417,3419],{},[1135,3406,1398],{},[1246,3408,1402],{"stretchy":1401},[1135,3410,1137],{},[1246,3412,1407],{"separator":1146},[1135,3414,1176],{},[1246,3416,1412],{"stretchy":1401},[1246,3418,1494],{},[1960,3420,3421],{},[1132,3422,3423,3425,3427,3429,3431,3438,3449,3451,3453,3455,3457],{},[1246,3424,1402],{"stretchy":1401},[1135,3426,1137],{},[1246,3428,1248],{},[1135,3430,1176],{},[1998,3432,3433,3435],{},[1246,3434,1412],{"stretchy":1401},[1135,3436,3437],{"mathvariant":2357},"⊤",[1998,3439,3440,3443],{},[1135,3441,3442],{"mathvariant":2357},"Σ",[1132,3444,3445,3447],{},[1246,3446,1248],{},[1612,3448,1978],{},[1246,3450,1402],{"stretchy":1401},[1135,3452,1137],{},[1246,3454,1248],{},[1135,3456,1176],{},[1246,3458,1412],{"stretchy":1401},[1139,3460,3461],{"encoding":1141},"d(x,y) = \\sqrt{(x-y)^{\\top}\\Sigma^{-1}(x-y)}",[1116,3463,3465,3501],{"className":3464,"ariaHidden":1146},[1145],[1116,3466,3468,3471,3474,3477,3480,3483,3486,3489,3492,3495,3498],{"className":3467},[1150],[1116,3469],{"className":3470,"style":1425},[1154],[1116,3472,1398],{"className":3473},[1159,1160],[1116,3475,1402],{"className":3476},[1432],[1116,3478,1137],{"className":3479},[1159,1160],[1116,3481,1407],{"className":3482},[1439],[1116,3484],{"className":3485,"style":1443},[1327],[1116,3487,1176],{"className":3488,"style":1192},[1159,1160],[1116,3490,1412],{"className":3491},[1450],[1116,3493],{"className":3494,"style":1543},[1327],[1116,3496,1494],{"className":3497},[1547],[1116,3499],{"className":3500,"style":1543},[1327],[1116,3502,3504,3508],{"className":3503},[1150],[1116,3505],{"className":3506,"style":3507},[1154],"height:1.24em;vertical-align:-0.2924em;",[1116,3509,3511],{"className":3510},[1159,2057],[1116,3512,3514,3653],{"className":3513},[1281,1282],[1116,3515,3517,3650],{"className":3516},[1286],[1116,3518,3521,3637],{"className":3519,"style":3520},[1290],"height:0.9476em;",[1116,3522,3524,3527],{"className":3523,"style":2072},[2071],[1116,3525],{"className":3526,"style":2076},[1298],[1116,3528,3530,3533,3536,3539,3542,3545,3548,3581,3616,3619,3622,3625,3628,3631,3634],{"className":3529,"style":2080},[1159],[1116,3531,1402],{"className":3532},[1432],[1116,3534,1137],{"className":3535},[1159,1160],[1116,3537],{"className":3538,"style":1328},[1327],[1116,3540,1248],{"className":3541},[1332],[1116,3543],{"className":3544,"style":1328},[1327],[1116,3546,1176],{"className":3547,"style":1192},[1159,1160],[1116,3549,3551,3554],{"className":3550},[1450],[1116,3552,1412],{"className":3553},[1450],[1116,3555,3557],{"className":3556},[1277],[1116,3558,3560],{"className":3559},[1281],[1116,3561,3563],{"className":3562},[1286],[1116,3564,3567],{"className":3565,"style":3566},[1290],"height:0.7751em;",[1116,3568,3569,3572],{"style":2265},[1116,3570],{"className":3571,"style":1299},[1298],[1116,3573,3575],{"className":3574},[1303,1304,1305,1306],[1116,3576,3578],{"className":3577},[1159,1306],[1116,3579,3437],{"className":3580},[1159,1306],[1116,3582,3584,3587],{"className":3583},[1159],[1116,3585,3442],{"className":3586},[1159],[1116,3588,3590],{"className":3589},[1277],[1116,3591,3593],{"className":3592},[1281],[1116,3594,3596],{"className":3595},[1286],[1116,3597,3599],{"className":3598,"style":2262},[1290],[1116,3600,3601,3604],{"style":2265},[1116,3602],{"className":3603,"style":1299},[1298],[1116,3605,3607],{"className":3606},[1303,1304,1305,1306],[1116,3608,3610,3613],{"className":3609},[1159,1306],[1116,3611,1248],{"className":3612},[1159,1306],[1116,3614,1978],{"className":3615},[1159,1306],[1116,3617,1402],{"className":3618},[1432],[1116,3620,1137],{"className":3621},[1159,1160],[1116,3623],{"className":3624,"style":1328},[1327],[1116,3626,1248],{"className":3627},[1332],[1116,3629],{"className":3630,"style":1328},[1327],[1116,3632,1176],{"className":3633,"style":1192},[1159,1160],[1116,3635,1412],{"className":3636},[1450],[1116,3638,3640,3643],{"style":3639},"top:-2.9076em;",[1116,3641],{"className":3642,"style":2076},[1298],[1116,3644,3646],{"className":3645,"style":2285},[2284],[2287,3647,3648],{"xmlns":2289,"width":2290,"height":2291,"viewBox":2292,"preserveAspectRatio":2293},[2295,3649],{"d":2297},[1116,3651,1314],{"className":3652},[1313],[1116,3654,3656],{"className":3655},[1286],[1116,3657,3660],{"className":3658,"style":3659},[1290],"height:0.2924em;",[1116,3661],{},",用协方差矩阵 ",[1116,3664,3666,3680],{"className":3665},[1119],[1116,3667,3669],{"className":3668},[1123],[1125,3670,3671],{"xmlns":1127},[1129,3672,3673,3677],{},[1132,3674,3675],{},[1135,3676,3442],{"mathvariant":2357},[1139,3678,3679],{"encoding":1141},"\\Sigma",[1116,3681,3683],{"className":3682,"ariaHidden":1146},[1145],[1116,3684,3686,3690],{"className":3685},[1150],[1116,3687],{"className":3688,"style":3689},[1154],"height:0.6833em;",[1116,3691,3442],{"className":3692},[1159]," 消除量纲和相关性影响。",[1091,3695,3696,3699,3700,3703,3704,3707],{},[1456,3697,3698],{},"次序数据",":观察值虽用文本或数字表示,但只有",[1456,3701,3702],{},"次序","有用(如成绩 A、B、C)。此时先把数据",[1456,3705,3706],{},"量化","(如 A=1、B=2、C=3),再套用数值距离。",[1091,3709,3710,3713,3714,3717],{},[1456,3711,3712],{},"属性数据(分类数据)",":观察值只有分类意义、不存在任何次序时,可以定义",[1456,3715,3716],{},"简单匹配距离","——按两个观测取值不同的变量个数占比来算:",[1091,3719,3720],{},[1116,3721,3723,3758],{"className":3722},[1119],[1116,3724,3726],{"className":3725},[1123],[1125,3727,3728],{"xmlns":1127},[1129,3729,3730,3755],{},[1132,3731,3732,3734,3736,3738,3740,3742,3744,3746],{},[1135,3733,1398],{},[1246,3735,1402],{"stretchy":1401},[1135,3737,1137],{},[1246,3739,1407],{"separator":1146},[1135,3741,1176],{},[1246,3743,1412],{"stretchy":1401},[1246,3745,1494],{},[3747,3748,3749,3753],"mfrac",{},[3750,3751,3752],"mtext",{},"取值不同的变量个数",[1135,3754,1091],{},[1139,3756,3757],{"encoding":1141},"d(x, y) = \\frac{\\text{取值不同的变量个数}}{p}",[1116,3759,3761,3797],{"className":3760,"ariaHidden":1146},[1145],[1116,3762,3764,3767,3770,3773,3776,3779,3782,3785,3788,3791,3794],{"className":3763},[1150],[1116,3765],{"className":3766,"style":1425},[1154],[1116,3768,1398],{"className":3769},[1159,1160],[1116,3771,1402],{"className":3772},[1432],[1116,3774,1137],{"className":3775},[1159,1160],[1116,3777,1407],{"className":3778},[1439],[1116,3780],{"className":3781,"style":1443},[1327],[1116,3783,1176],{"className":3784,"style":1192},[1159,1160],[1116,3786,1412],{"className":3787},[1450],[1116,3789],{"className":3790,"style":1543},[1327],[1116,3792,1494],{"className":3793},[1547],[1116,3795],{"className":3796,"style":1543},[1327],[1116,3798,3800,3804],{"className":3799},[1150],[1116,3801],{"className":3802,"style":3803},[1154],"height:1.3534em;vertical-align:-0.4811em;",[1116,3805,3807,3811,3883],{"className":3806},[1159],[1116,3808],{"className":3809},[1432,3810],"nulldelimiter",[1116,3812,3814],{"className":3813},[3747],[1116,3815,3817,3874],{"className":3816},[1281,1282],[1116,3818,3820,3871],{"className":3819},[1286],[1116,3821,3824,3840,3851],{"className":3822,"style":3823},[1290],"height:0.8723em;",[1116,3825,3827,3831],{"style":3826},"top:-2.655em;",[1116,3828],{"className":3829,"style":3830},[1298],"height:3em;",[1116,3832,3834],{"className":3833},[1303,1304,1305,1306],[1116,3835,3837],{"className":3836},[1159,1306],[1116,3838,1091],{"className":3839},[1159,1160,1306],[1116,3841,3843,3846],{"style":3842},"top:-3.23em;",[1116,3844],{"className":3845,"style":3830},[1298],[1116,3847],{"className":3848,"style":3850},[3849],"frac-line","border-bottom-width:0.04em;",[1116,3852,3854,3857],{"style":3853},"top:-3.394em;",[1116,3855],{"className":3856,"style":3830},[1298],[1116,3858,3860],{"className":3859},[1303,1304,1305,1306],[1116,3861,3863],{"className":3862},[1159,1306],[1116,3864,3867],{"className":3865},[1159,3866,1306],"text",[1116,3868,3752],{"className":3869},[1159,3870,1306],"cjk_fallback",[1116,3872,1314],{"className":3873},[1313],[1116,3875,3877],{"className":3876},[1286],[1116,3878,3881],{"className":3879,"style":3880},[1290],"height:0.4811em;",[1116,3882],{},[1116,3884],{"className":3885},[1450,3810],[3887,3888],"hr",{},[1108,3890,3892],{"id":3891},"二聚类算法","二、聚类算法",[1888,3894,3896],{"id":3895},"系统聚类层次聚类步骤","系统聚类(层次聚类)步骤",[1091,3898,3899,3900,3929,3930,3958,3959,3987,3988,4016],{},"设有 ",[1116,3901,3903,3917],{"className":3902},[1119],[1116,3904,3906],{"className":3905},[1123],[1125,3907,3908],{"xmlns":1127},[1129,3909,3910,3915],{},[1132,3911,3912],{},[1135,3913,3914],{},"n",[1139,3916,3914],{"encoding":1141},[1116,3918,3920],{"className":3919,"ariaHidden":1146},[1145],[1116,3921,3923,3926],{"className":3922},[1150],[1116,3924],{"className":3925,"style":1155},[1154],[1116,3927,3914],{"className":3928},[1159,1160]," 个样品、",[1116,3931,3933,3946],{"className":3932},[1119],[1116,3934,3936],{"className":3935},[1123],[1125,3937,3938],{"xmlns":1127},[1129,3939,3940,3944],{},[1132,3941,3942],{},[1135,3943,1091],{},[1139,3945,1091],{"encoding":1141},[1116,3947,3949],{"className":3948,"ariaHidden":1146},[1145],[1116,3950,3952,3955],{"className":3951},[1150],[1116,3953],{"className":3954,"style":1188},[1154],[1116,3956,1091],{"className":3957},[1159,1160]," 个变量(Q 型聚类对样品分类,",[1116,3960,3962,3975],{"className":3961},[1119],[1116,3963,3965],{"className":3964},[1123],[1125,3966,3967],{"xmlns":1127},[1129,3968,3969,3973],{},[1132,3970,3971],{},[1135,3972,3914],{},[1139,3974,3914],{"encoding":1141},[1116,3976,3978],{"className":3977,"ariaHidden":1146},[1145],[1116,3979,3981,3984],{"className":3980},[1150],[1116,3982],{"className":3983,"style":1155},[1154],[1116,3985,3914],{"className":3986},[1159,1160]," 个个体起步;R 型聚类对变量分类,",[1116,3989,3991,4004],{"className":3990},[1119],[1116,3992,3994],{"className":3993},[1123],[1125,3995,3996],{"xmlns":1127},[1129,3997,3998,4002],{},[1132,3999,4000],{},[1135,4001,1091],{},[1139,4003,1091],{"encoding":1141},[1116,4005,4007],{"className":4006,"ariaHidden":1146},[1145],[1116,4008,4010,4013],{"className":4009},[1150],[1116,4011],{"className":4012,"style":1188},[1154],[1116,4014,1091],{"className":4015},[1159,1160]," 个变量起步):",[4018,4019,4020,4052,4107,4161],"ol",{},[1098,4021,4022,4023,4051],{},"先将每个个体各看成一类,共 ",[1116,4024,4026,4039],{"className":4025},[1119],[1116,4027,4029],{"className":4028},[1123],[1125,4030,4031],{"xmlns":1127},[1129,4032,4033,4037],{},[1132,4034,4035],{},[1135,4036,3914],{},[1139,4038,3914],{"encoding":1141},[1116,4040,4042],{"className":4041,"ariaHidden":1146},[1145],[1116,4043,4045,4048],{"className":4044},[1150],[1116,4046],{"className":4047,"style":1155},[1154],[1116,4049,3914],{"className":4050},[1159,1160]," 类;",[1098,4053,4054,4055,4051],{},"找出最相似(距离最近)的两类,合并成一个新类,得 ",[1116,4056,4058,4076],{"className":4057},[1119],[1116,4059,4061],{"className":4060},[1123],[1125,4062,4063],{"xmlns":1127},[1129,4064,4065,4073],{},[1132,4066,4067,4069,4071],{},[1135,4068,3914],{},[1246,4070,1248],{},[1612,4072,1978],{},[1139,4074,4075],{"encoding":1141},"n-1",[1116,4077,4079,4098],{"className":4078,"ariaHidden":1146},[1145],[1116,4080,4082,4086,4089,4092,4095],{"className":4081},[1150],[1116,4083],{"className":4084,"style":4085},[1154],"height:0.6667em;vertical-align:-0.0833em;",[1116,4087,3914],{"className":4088},[1159,1160],[1116,4090],{"className":4091,"style":1328},[1327],[1116,4093,1248],{"className":4094},[1332],[1116,4096],{"className":4097,"style":1328},[1327],[1116,4099,4101,4104],{"className":4100},[1150],[1116,4102],{"className":4103,"style":1663},[1154],[1116,4105,1978],{"className":4106},[1159],[1098,4108,4109,4110,4051],{},"再找出最相似的两类合并,得 ",[1116,4111,4113,4131],{"className":4112},[1119],[1116,4114,4116],{"className":4115},[1123],[1125,4117,4118],{"xmlns":1127},[1129,4119,4120,4128],{},[1132,4121,4122,4124,4126],{},[1135,4123,3914],{},[1246,4125,1248],{},[1612,4127,2004],{},[1139,4129,4130],{"encoding":1141},"n-2",[1116,4132,4134,4152],{"className":4133,"ariaHidden":1146},[1145],[1116,4135,4137,4140,4143,4146,4149],{"className":4136},[1150],[1116,4138],{"className":4139,"style":4085},[1154],[1116,4141,3914],{"className":4142},[1159,1160],[1116,4144],{"className":4145,"style":1328},[1327],[1116,4147,1248],{"className":4148},[1332],[1116,4150],{"className":4151,"style":1328},[1327],[1116,4153,4155,4158],{"className":4154},[1150],[1116,4156],{"className":4157,"style":1663},[1154],[1116,4159,2004],{"className":4160},[1159],[1098,4162,4163],{},"以此类推,直到把所有类合并成一大类。",[1091,4165,4166,4167,4170],{},"整个过程自底向上逐层合并,可以画成一棵",[1456,4168,4169],{},"谱系图(树状图)",",在任意高度横切就得到相应数目的簇。",[1888,4172,4174],{"id":4173},"k-means-聚类","K-Means 聚类",[1091,4176,4177,1467],{},[1456,4178,4179],{},"算法思想",[4018,4181,4182,4430,4570,4609],{},[1098,4183,4184,4187,4188,4241,4242,4272,4273,1578],{},[1456,4185,4186],{},"初始化",":令迭代次数 ",[1116,4189,4191,4210],{"className":4190},[1119],[1116,4192,4194],{"className":4193},[1123],[1125,4195,4196],{"xmlns":1127},[1129,4197,4198,4207],{},[1132,4199,4200,4203,4205],{},[1135,4201,4202],{},"t",[1246,4204,1494],{},[1612,4206,1614],{},[1139,4208,4209],{"encoding":1141},"t=0",[1116,4211,4213,4232],{"className":4212,"ariaHidden":1146},[1145],[1116,4214,4216,4220,4223,4226,4229],{"className":4215},[1150],[1116,4217],{"className":4218,"style":4219},[1154],"height:0.6151em;",[1116,4221,4202],{"className":4222},[1159,1160],[1116,4224],{"className":4225,"style":1543},[1327],[1116,4227,1494],{"className":4228},[1547],[1116,4230],{"className":4231,"style":1543},[1327],[1116,4233,4235,4238],{"className":4234},[1150],[1116,4236],{"className":4237,"style":1663},[1154],[1116,4239,1614],{"className":4240},[1159],",随机选择 ",[1116,4243,4245,4259],{"className":4244},[1119],[1116,4246,4248],{"className":4247},[1123],[1125,4249,4250],{"xmlns":1127},[1129,4251,4252,4257],{},[1132,4253,4254],{},[1135,4255,4256],{},"K",[1139,4258,4256],{"encoding":1141},[1116,4260,4262],{"className":4261,"ariaHidden":1146},[1145],[1116,4263,4265,4268],{"className":4264},[1150],[1116,4266],{"className":4267,"style":3689},[1154],[1116,4269,4256],{"className":4270,"style":4271},[1159,1160],"margin-right:0.0715em;"," 个样本点作为初始聚类中心 ",[1116,4274,4276,4314],{"className":4275},[1119],[1116,4277,4279],{"className":4278},[1123],[1125,4280,4281],{"xmlns":1127},[1129,4282,4283,4311],{},[1132,4284,4285,4288,4295,4297,4300,4302,4308],{},[1246,4286,4287],{"stretchy":1401},"{",[1239,4289,4290,4293],{},[1135,4291,4292],{},"m",[1612,4294,1978],{},[1246,4296,1407],{"separator":1146},[1246,4298,4299],{},"…",[1246,4301,1407],{"separator":1146},[1239,4303,4304,4306],{},[1135,4305,4292],{},[1135,4307,4256],{},[1246,4309,4310],{"stretchy":1401},"}",[1139,4312,4313],{"encoding":1141},"\\{m_1, \\dots, m_K\\}",[1116,4315,4317],{"className":4316,"ariaHidden":1146},[1145],[1116,4318,4320,4323,4326,4367,4370,4373,4377,4380,4383,4386,4427],{"className":4319},[1150],[1116,4321],{"className":4322,"style":1425},[1154],[1116,4324,4287],{"className":4325},[1432],[1116,4327,4329,4332],{"className":4328},[1159],[1116,4330,4292],{"className":4331},[1159,1160],[1116,4333,4335],{"className":4334},[1277],[1116,4336,4338,4359],{"className":4337},[1281,1282],[1116,4339,4341,4356],{"className":4340},[1286],[1116,4342,4345],{"className":4343,"style":4344},[1290],"height:0.3011em;",[1116,4346,4347,4350],{"style":1294},[1116,4348],{"className":4349,"style":1299},[1298],[1116,4351,4353],{"className":4352},[1303,1304,1305,1306],[1116,4354,1978],{"className":4355},[1159,1306],[1116,4357,1314],{"className":4358},[1313],[1116,4360,4362],{"className":4361},[1286],[1116,4363,4365],{"className":4364,"style":1321},[1290],[1116,4366],{},[1116,4368,1407],{"className":4369},[1439],[1116,4371],{"className":4372,"style":1443},[1327],[1116,4374,4299],{"className":4375},[4376],"minner",[1116,4378],{"className":4379,"style":1443},[1327],[1116,4381,1407],{"className":4382},[1439],[1116,4384],{"className":4385,"style":1443},[1327],[1116,4387,4389,4392],{"className":4388},[1159],[1116,4390,4292],{"className":4391},[1159,1160],[1116,4393,4395],{"className":4394},[1277],[1116,4396,4398,4419],{"className":4397},[1281,1282],[1116,4399,4401,4416],{"className":4400},[1286],[1116,4402,4405],{"className":4403,"style":4404},[1290],"height:0.3283em;",[1116,4406,4407,4410],{"style":1294},[1116,4408],{"className":4409,"style":1299},[1298],[1116,4411,4413],{"className":4412},[1303,1304,1305,1306],[1116,4414,4256],{"className":4415,"style":4271},[1159,1160,1306],[1116,4417,1314],{"className":4418},[1313],[1116,4420,4422],{"className":4421},[1286],[1116,4423,4425],{"className":4424,"style":1321},[1290],[1116,4426],{},[1116,4428,4310],{"className":4429},[1450],[1098,4431,4432,4435,4436,4507,4508,4536,4537,4540,4541,1578],{},[1456,4433,4434],{},"对样本进行聚类",":对固定的类中心 ",[1116,4437,4439,4457],{"className":4438},[1119],[1116,4440,4442],{"className":4441},[1123],[1125,4443,4444],{"xmlns":1127},[1129,4445,4446,4454],{},[1132,4447,4448],{},[1239,4449,4450,4452],{},[1135,4451,4292],{},[1135,4453,1208],{},[1139,4455,4456],{"encoding":1141},"m_k",[1116,4458,4460],{"className":4459,"ariaHidden":1146},[1145],[1116,4461,4463,4467],{"className":4462},[1150],[1116,4464],{"className":4465,"style":4466},[1154],"height:0.5806em;vertical-align:-0.15em;",[1116,4468,4470,4473],{"className":4469},[1159],[1116,4471,4292],{"className":4472},[1159,1160],[1116,4474,4476],{"className":4475},[1277],[1116,4477,4479,4499],{"className":4478},[1281,1282],[1116,4480,4482,4496],{"className":4481},[1286],[1116,4483,4485],{"className":4484,"style":1291},[1290],[1116,4486,4487,4490],{"style":1294},[1116,4488],{"className":4489,"style":1299},[1298],[1116,4491,4493],{"className":4492},[1303,1304,1305,1306],[1116,4494,1208],{"className":4495,"style":1224},[1159,1160,1306],[1116,4497,1314],{"className":4498},[1313],[1116,4500,4502],{"className":4501},[1286],[1116,4503,4505],{"className":4504,"style":1321},[1290],[1116,4506],{},"(第 ",[1116,4509,4511,4524],{"className":4510},[1119],[1116,4512,4514],{"className":4513},[1123],[1125,4515,4516],{"xmlns":1127},[1129,4517,4518,4522],{},[1132,4519,4520],{},[1135,4521,1208],{},[1139,4523,1208],{"encoding":1141},[1116,4525,4527],{"className":4526,"ariaHidden":1146},[1145],[1116,4528,4530,4533],{"className":4529},[1150],[1116,4531],{"className":4532,"style":1220},[1154],[1116,4534,1208],{"className":4535,"style":1224},[1159,1160]," 类的中心),计算每个样本到各类中心的距离,把每个样本",[1456,4538,4539],{},"指派到与其最近的中心所在的类",",构成聚类结果 ",[1116,4542,4544,4558],{"className":4543},[1119],[1116,4545,4547],{"className":4546},[1123],[1125,4548,4549],{"xmlns":1127},[1129,4550,4551,4556],{},[1132,4552,4553],{},[1135,4554,4555],{},"C",[1139,4557,4555],{"encoding":1141},[1116,4559,4561],{"className":4560,"ariaHidden":1146},[1145],[1116,4562,4564,4567],{"className":4563},[1150],[1116,4565],{"className":4566,"style":3689},[1154],[1116,4568,4555],{"className":4569,"style":4271},[1159,1160],[1098,4571,4572,4575,4576,4604,4605,4608],{},[1456,4573,4574],{},"计算新的类中心",":对聚类结果 ",[1116,4577,4579,4592],{"className":4578},[1119],[1116,4580,4582],{"className":4581},[1123],[1125,4583,4584],{"xmlns":1127},[1129,4585,4586,4590],{},[1132,4587,4588],{},[1135,4589,4555],{},[1139,4591,4555],{"encoding":1141},[1116,4593,4595],{"className":4594,"ariaHidden":1146},[1145],[1116,4596,4598,4601],{"className":4597},[1150],[1116,4599],{"className":4600,"style":3689},[1154],[1116,4602,4555],{"className":4603,"style":4271},[1159,1160],",计算当前各类中样本的",[1456,4606,4607],{},"均值",",作为新的类中心;",[1098,4610,4611,4612,4687],{},"如果迭代收敛或符合停止条件,输出结果;否则令 ",[1116,4613,4615,4638],{"className":4614},[1119],[1116,4616,4618],{"className":4617},[1123],[1125,4619,4620],{"xmlns":1127},[1129,4621,4622,4635],{},[1132,4623,4624,4626,4629,4631,4633],{},[1135,4625,4202],{},[1246,4627,4628],{},"←",[1135,4630,4202],{},[1246,4632,1767],{},[1612,4634,1978],{},[1139,4636,4637],{"encoding":1141},"t \\leftarrow t+1",[1116,4639,4641,4659,4678],{"className":4640,"ariaHidden":1146},[1145],[1116,4642,4644,4647,4650,4653,4656],{"className":4643},[1150],[1116,4645],{"className":4646,"style":4219},[1154],[1116,4648,4202],{"className":4649},[1159,1160],[1116,4651],{"className":4652,"style":1543},[1327],[1116,4654,4628],{"className":4655},[1547],[1116,4657],{"className":4658,"style":1543},[1327],[1116,4660,4662,4666,4669,4672,4675],{"className":4661},[1150],[1116,4663],{"className":4664,"style":4665},[1154],"height:0.6984em;vertical-align:-0.0833em;",[1116,4667,4202],{"className":4668},[1159,1160],[1116,4670],{"className":4671,"style":1328},[1327],[1116,4673,1767],{"className":4674},[1332],[1116,4676],{"className":4677,"style":1328},[1327],[1116,4679,4681,4684],{"className":4680},[1150],[1116,4682],{"className":4683,"style":1663},[1154],[1116,4685,1978],{"className":4686},[1159],",返回步骤 2。",[1091,4689,4690,4693,4696,4697,4700],{},[1456,4691,4692],{},"性质",[4694,4695],"k-means",{}," 可以保证在",[1456,4698,4699],{},"有限步数内收敛","(目标函数单调不增且下有界)。",[1091,4702,4703,4706,4707,4735,4736,4805,4806,4834],{},[1456,4704,4705],{},"优化问题",":假设 ",[1116,4708,4710,4723],{"className":4709},[1119],[1116,4711,4713],{"className":4712},[1123],[1125,4714,4715],{"xmlns":1127},[1129,4716,4717,4721],{},[1132,4718,4719],{},[1135,4720,4256],{},[1139,4722,4256],{"encoding":1141},[1116,4724,4726],{"className":4725,"ariaHidden":1146},[1145],[1116,4727,4729,4732],{"className":4728},[1150],[1116,4730],{"className":4731,"style":3689},[1154],[1116,4733,4256],{"className":4734,"style":4271},[1159,1160]," 个中心 ",[1116,4737,4739,4756],{"className":4738},[1119],[1116,4740,4742],{"className":4741},[1123],[1125,4743,4744],{"xmlns":1127},[1129,4745,4746,4754],{},[1132,4747,4748],{},[1239,4749,4750,4752],{},[1135,4751,4292],{},[1135,4753,1208],{},[1139,4755,4456],{"encoding":1141},[1116,4757,4759],{"className":4758,"ariaHidden":1146},[1145],[1116,4760,4762,4765],{"className":4761},[1150],[1116,4763],{"className":4764,"style":4466},[1154],[1116,4766,4768,4771],{"className":4767},[1159],[1116,4769,4292],{"className":4770},[1159,1160],[1116,4772,4774],{"className":4773},[1277],[1116,4775,4777,4797],{"className":4776},[1281,1282],[1116,4778,4780,4794],{"className":4779},[1286],[1116,4781,4783],{"className":4782,"style":1291},[1290],[1116,4784,4785,4788],{"style":1294},[1116,4786],{"className":4787,"style":1299},[1298],[1116,4789,4791],{"className":4790},[1303,1304,1305,1306],[1116,4792,1208],{"className":4793,"style":1224},[1159,1160,1306],[1116,4795,1314],{"className":4796},[1313],[1116,4798,4800],{"className":4799},[1286],[1116,4801,4803],{"className":4802,"style":1321},[1290],[1116,4804],{}," 和指派 ",[1116,4807,4809,4822],{"className":4808},[1119],[1116,4810,4812],{"className":4811},[1123],[1125,4813,4814],{"xmlns":1127},[1129,4815,4816,4820],{},[1132,4817,4818],{},[1135,4819,4555],{},[1139,4821,4555],{"encoding":1141},[1116,4823,4825],{"className":4824,"ariaHidden":1146},[1145],[1116,4826,4828,4831],{"className":4827},[1150],[1116,4829],{"className":4830,"style":3689},[1154],[1116,4832,4555],{"className":4833,"style":4271},[1159,1160],",用欧氏距离考虑",[1091,4836,4837],{},[1116,4838,4840,4939],{"className":4839},[1119],[1116,4841,4843],{"className":4842},[1123],[1125,4844,4845],{"xmlns":1127},[1129,4846,4847,4936],{},[1132,4848,4849,4874,4877,4891,4913,4916,4922,4924,4930],{},[1239,4850,4851,4858],{},[1132,4852,4853,4856],{},[1135,4854,4855],{},"min",[1246,4857,2631],{},[1132,4859,4860,4862,4864,4866,4872],{},[1135,4861,4555],{},[1246,4863,1407],{"separator":1146},[1246,4865,4287],{"stretchy":1401},[1239,4867,4868,4870],{},[1135,4869,4292],{},[1135,4871,1208],{},[1246,4873,4310],{"stretchy":1401},[3750,4875,4876],{}," ",[1965,4878,4879,4881,4889],{},[1246,4880,1969],{},[1132,4882,4883,4885,4887],{},[1135,4884,1208],{},[1246,4886,1494],{},[1612,4888,1978],{},[1135,4890,4256],{},[1239,4892,4893,4895],{},[1246,4894,1969],{},[1132,4896,4897,4904,4907],{},[1239,4898,4899,4901],{},[1135,4900,1137],{},[1135,4902,4903],{},"i",[1246,4905,4906],{},"∈",[1239,4908,4909,4911],{},[1135,4910,4555],{},[1135,4912,1208],{},[1135,4914,4915],{"mathvariant":2357},"∥",[1239,4917,4918,4920],{},[1135,4919,1137],{},[1135,4921,4903],{},[1246,4923,1248],{},[1239,4925,4926,4928],{},[1135,4927,4292],{},[1135,4929,1208],{},[1998,4931,4932,4934],{},[1135,4933,4915],{"mathvariant":2357},[1612,4935,2004],{},[1139,4937,4938],{"encoding":1141},"\\min_{C, \\{m_k\\}}\\ \\sum_{k=1}^{K}\\sum_{x_i \\in C_k}\\|x_i - m_k\\|^2",[1116,4940,4942,5307],{"className":4941,"ariaHidden":1146},[1145],[1116,4943,4945,4949,5049,5052,5055,5119,5122,5251,5254,5257,5298,5301,5304],{"className":4944},[1150],[1116,4946],{"className":4947,"style":4948},[1154],"height:1.3868em;vertical-align:-0.4056em;",[1116,4950,4952,4955],{"className":4951},[2084],[1116,4953,4855],{"className":4954},[2084],[1116,4956,4958],{"className":4957},[1277],[1116,4959,4961,5040],{"className":4960},[1281,1282],[1116,4962,4964,5037],{"className":4963},[1286],[1116,4965,4968],{"className":4966,"style":4967},[1290],"height:0.3448em;",[1116,4969,4971,4974],{"style":4970},"top:-2.5198em;margin-right:0.05em;",[1116,4972],{"className":4973,"style":1299},[1298],[1116,4975,4977],{"className":4976},[1303,1304,1305,1306],[1116,4978,4980,4983,4986,4989,5034],{"className":4979},[1159,1306],[1116,4981,4555],{"className":4982,"style":4271},[1159,1160,1306],[1116,4984,1407],{"className":4985},[1439,1306],[1116,4987,4287],{"className":4988},[1432,1306],[1116,4990,4992,4995],{"className":4991},[1159,1306],[1116,4993,4292],{"className":4994},[1159,1160,1306],[1116,4996,4998],{"className":4997},[1277],[1116,4999,5001,5025],{"className":5000},[1281,1282],[1116,5002,5004,5022],{"className":5003},[1286],[1116,5005,5007],{"className":5006,"style":4967},[1290],[1116,5008,5010,5014],{"style":5009},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[1116,5011],{"className":5012,"style":5013},[1298],"height:2.5em;",[1116,5015,5019],{"className":5016},[1303,5017,5018,1306],"reset-size3","size1",[1116,5020,1208],{"className":5021,"style":1224},[1159,1160,1306],[1116,5023,1314],{"className":5024},[1313],[1116,5026,5028],{"className":5027},[1286],[1116,5029,5032],{"className":5030,"style":5031},[1290],"height:0.1512em;",[1116,5033],{},[1116,5035,4310],{"className":5036},[1450,1306],[1116,5038,1314],{"className":5039},[1313],[1116,5041,5043],{"className":5042},[1286],[1116,5044,5047],{"className":5045,"style":5046},[1290],"height:0.3552em;",[1116,5048],{},[1116,5050,4876],{"className":5051},[1327],[1116,5053],{"className":5054,"style":1443},[1327],[1116,5056,5058,5061],{"className":5057},[2084],[1116,5059,1969],{"className":5060,"style":2090},[2084,2088,2089],[1116,5062,5064],{"className":5063},[1277],[1116,5065,5067,5111],{"className":5066},[1281,1282],[1116,5068,5070,5108],{"className":5069},[1286],[1116,5071,5074,5094],{"className":5072,"style":5073},[1290],"height:0.9812em;",[1116,5075,5076,5079],{"style":2106},[1116,5077],{"className":5078,"style":1299},[1298],[1116,5080,5082],{"className":5081},[1303,1304,1305,1306],[1116,5083,5085,5088,5091],{"className":5084},[1159,1306],[1116,5086,1208],{"className":5087,"style":1224},[1159,1160,1306],[1116,5089,1494],{"className":5090},[1547,1306],[1116,5092,1978],{"className":5093},[1159,1306],[1116,5095,5096,5099],{"style":2127},[1116,5097],{"className":5098,"style":1299},[1298],[1116,5100,5102],{"className":5101},[1303,1304,1305,1306],[1116,5103,5105],{"className":5104},[1159,1306],[1116,5106,4256],{"className":5107,"style":4271},[1159,1160,1306],[1116,5109,1314],{"className":5110},[1313],[1116,5112,5114],{"className":5113},[1286],[1116,5115,5117],{"className":5116,"style":2149},[1290],[1116,5118],{},[1116,5120],{"className":5121,"style":1443},[1327],[1116,5123,5125,5128],{"className":5124},[2084],[1116,5126,1969],{"className":5127,"style":2090},[2084,2088,2089],[1116,5129,5131],{"className":5130},[1277],[1116,5132,5134,5242],{"className":5133},[1281,1282],[1116,5135,5137,5239],{"className":5136},[1286],[1116,5138,5141],{"className":5139,"style":5140},[1290],"height:0.1786em;",[1116,5142,5143,5146],{"style":2106},[1116,5144],{"className":5145,"style":1299},[1298],[1116,5147,5149],{"className":5148},[1303,1304,1305,1306],[1116,5150,5152,5195,5198],{"className":5151},[1159,1306],[1116,5153,5155,5158],{"className":5154},[1159,1306],[1116,5156,1137],{"className":5157},[1159,1160,1306],[1116,5159,5161],{"className":5160},[1277],[1116,5162,5164,5186],{"className":5163},[1281,1282],[1116,5165,5167,5183],{"className":5166},[1286],[1116,5168,5171],{"className":5169,"style":5170},[1290],"height:0.3281em;",[1116,5172,5174,5177],{"style":5173},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1116,5175],{"className":5176,"style":5013},[1298],[1116,5178,5180],{"className":5179},[1303,5017,5018,1306],[1116,5181,4903],{"className":5182},[1159,1160,1306],[1116,5184,1314],{"className":5185},[1313],[1116,5187,5189],{"className":5188},[1286],[1116,5190,5193],{"className":5191,"style":5192},[1290],"height:0.143em;",[1116,5194],{},[1116,5196,4906],{"className":5197},[1547,1306],[1116,5199,5201,5204],{"className":5200},[1159,1306],[1116,5202,4555],{"className":5203,"style":4271},[1159,1160,1306],[1116,5205,5207],{"className":5206},[1277],[1116,5208,5210,5231],{"className":5209},[1281,1282],[1116,5211,5213,5228],{"className":5212},[1286],[1116,5214,5216],{"className":5215,"style":4967},[1290],[1116,5217,5219,5222],{"style":5218},"top:-2.3488em;margin-left:-0.0715em;margin-right:0.0714em;",[1116,5220],{"className":5221,"style":5013},[1298],[1116,5223,5225],{"className":5224},[1303,5017,5018,1306],[1116,5226,1208],{"className":5227,"style":1224},[1159,1160,1306],[1116,5229,1314],{"className":5230},[1313],[1116,5232,5234],{"className":5233},[1286],[1116,5235,5237],{"className":5236,"style":5031},[1290],[1116,5238],{},[1116,5240,1314],{"className":5241},[1313],[1116,5243,5245],{"className":5244},[1286],[1116,5246,5249],{"className":5247,"style":5248},[1290],"height:0.4056em;",[1116,5250],{},[1116,5252],{"className":5253,"style":1443},[1327],[1116,5255,4915],{"className":5256},[1159],[1116,5258,5260,5263],{"className":5259},[1159],[1116,5261,1137],{"className":5262},[1159,1160],[1116,5264,5266],{"className":5265},[1277],[1116,5267,5269,5290],{"className":5268},[1281,1282],[1116,5270,5272,5287],{"className":5271},[1286],[1116,5273,5276],{"className":5274,"style":5275},[1290],"height:0.3117em;",[1116,5277,5278,5281],{"style":1294},[1116,5279],{"className":5280,"style":1299},[1298],[1116,5282,5284],{"className":5283},[1303,1304,1305,1306],[1116,5285,4903],{"className":5286},[1159,1160,1306],[1116,5288,1314],{"className":5289},[1313],[1116,5291,5293],{"className":5292},[1286],[1116,5294,5296],{"className":5295,"style":1321},[1290],[1116,5297],{},[1116,5299],{"className":5300,"style":1328},[1327],[1116,5302,1248],{"className":5303},[1332],[1116,5305],{"className":5306,"style":1328},[1327],[1116,5308,5310,5314,5354],{"className":5309},[1150],[1116,5311],{"className":5312,"style":5313},[1154],"height:1.0641em;vertical-align:-0.25em;",[1116,5315,5317,5320],{"className":5316},[1159],[1116,5318,4292],{"className":5319},[1159,1160],[1116,5321,5323],{"className":5322},[1277],[1116,5324,5326,5346],{"className":5325},[1281,1282],[1116,5327,5329,5343],{"className":5328},[1286],[1116,5330,5332],{"className":5331,"style":1291},[1290],[1116,5333,5334,5337],{"style":1294},[1116,5335],{"className":5336,"style":1299},[1298],[1116,5338,5340],{"className":5339},[1303,1304,1305,1306],[1116,5341,1208],{"className":5342,"style":1224},[1159,1160,1306],[1116,5344,1314],{"className":5345},[1313],[1116,5347,5349],{"className":5348},[1286],[1116,5350,5352],{"className":5351,"style":1321},[1290],[1116,5353],{},[1116,5355,5357,5360],{"className":5356},[1159],[1116,5358,4915],{"className":5359},[1159],[1116,5361,5363],{"className":5362},[1277],[1116,5364,5366],{"className":5365},[1281],[1116,5367,5369],{"className":5368},[1286],[1116,5370,5373],{"className":5371,"style":5372},[1290],"height:0.8141em;",[1116,5374,5375,5378],{"style":3178},[1116,5376],{"className":5377,"style":1299},[1298],[1116,5379,5381],{"className":5380},[1303,1304,1305,1306],[1116,5382,2004],{"className":5383},[1159,1306],[1091,5385,5386,5387,5390],{},"它通过",[1456,5388,5389],{},"交替优化","求解:",[1095,5392,5393,5497],{},[1098,5394,5395,5496],{},[1456,5396,5397,5398,5467,5468],{},"固定中心 ",[1116,5399,5401,5418],{"className":5400},[1119],[1116,5402,5404],{"className":5403},[1123],[1125,5405,5406],{"xmlns":1127},[1129,5407,5408,5416],{},[1132,5409,5410],{},[1239,5411,5412,5414],{},[1135,5413,4292],{},[1135,5415,1208],{},[1139,5417,4456],{"encoding":1141},[1116,5419,5421],{"className":5420,"ariaHidden":1146},[1145],[1116,5422,5424,5427],{"className":5423},[1150],[1116,5425],{"className":5426,"style":4466},[1154],[1116,5428,5430,5433],{"className":5429},[1159],[1116,5431,4292],{"className":5432},[1159,1160],[1116,5434,5436],{"className":5435},[1277],[1116,5437,5439,5459],{"className":5438},[1281,1282],[1116,5440,5442,5456],{"className":5441},[1286],[1116,5443,5445],{"className":5444,"style":1291},[1290],[1116,5446,5447,5450],{"style":1294},[1116,5448],{"className":5449,"style":1299},[1298],[1116,5451,5453],{"className":5452},[1303,1304,1305,1306],[1116,5454,1208],{"className":5455,"style":1224},[1159,1160,1306],[1116,5457,1314],{"className":5458},[1313],[1116,5460,5462],{"className":5461},[1286],[1116,5463,5465],{"className":5464,"style":1321},[1290],[1116,5466],{},",优化指派 ",[1116,5469,5471,5484],{"className":5470},[1119],[1116,5472,5474],{"className":5473},[1123],[1125,5475,5476],{"xmlns":1127},[1129,5477,5478,5482],{},[1132,5479,5480],{},[1135,5481,4555],{},[1139,5483,4555],{"encoding":1141},[1116,5485,5487],{"className":5486,"ariaHidden":1146},[1145],[1116,5488,5490,5493],{"className":5489},[1150],[1116,5491],{"className":5492,"style":3689},[1154],[1116,5494,4555],{"className":5495,"style":4271},[1159,1160],":把每个样本分到最近的中心(第 2 步);",[1098,5498,5499,5600,5601,5670],{},[1456,5500,5501,5502,5530,5531],{},"固定指派 ",[1116,5503,5505,5518],{"className":5504},[1119],[1116,5506,5508],{"className":5507},[1123],[1125,5509,5510],{"xmlns":1127},[1129,5511,5512,5516],{},[1132,5513,5514],{},[1135,5515,4555],{},[1139,5517,4555],{"encoding":1141},[1116,5519,5521],{"className":5520,"ariaHidden":1146},[1145],[1116,5522,5524,5527],{"className":5523},[1150],[1116,5525],{"className":5526,"style":3689},[1154],[1116,5528,4555],{"className":5529,"style":4271},[1159,1160],",优化中心 ",[1116,5532,5534,5551],{"className":5533},[1119],[1116,5535,5537],{"className":5536},[1123],[1125,5538,5539],{"xmlns":1127},[1129,5540,5541,5549],{},[1132,5542,5543],{},[1239,5544,5545,5547],{},[1135,5546,4292],{},[1135,5548,1208],{},[1139,5550,4456],{"encoding":1141},[1116,5552,5554],{"className":5553,"ariaHidden":1146},[1145],[1116,5555,5557,5560],{"className":5556},[1150],[1116,5558],{"className":5559,"style":4466},[1154],[1116,5561,5563,5566],{"className":5562},[1159],[1116,5564,4292],{"className":5565},[1159,1160],[1116,5567,5569],{"className":5568},[1277],[1116,5570,5572,5592],{"className":5571},[1281,1282],[1116,5573,5575,5589],{"className":5574},[1286],[1116,5576,5578],{"className":5577,"style":1291},[1290],[1116,5579,5580,5583],{"style":1294},[1116,5581],{"className":5582,"style":1299},[1298],[1116,5584,5586],{"className":5585},[1303,1304,1305,1306],[1116,5587,1208],{"className":5588,"style":1224},[1159,1160,1306],[1116,5590,1314],{"className":5591},[1313],[1116,5593,5595],{"className":5594},[1286],[1116,5596,5598],{"className":5597,"style":1321},[1290],[1116,5599],{},":令 ",[1116,5602,5604,5621],{"className":5603},[1119],[1116,5605,5607],{"className":5606},[1123],[1125,5608,5609],{"xmlns":1127},[1129,5610,5611,5619],{},[1132,5612,5613],{},[1239,5614,5615,5617],{},[1135,5616,4292],{},[1135,5618,1208],{},[1139,5620,4456],{"encoding":1141},[1116,5622,5624],{"className":5623,"ariaHidden":1146},[1145],[1116,5625,5627,5630],{"className":5626},[1150],[1116,5628],{"className":5629,"style":4466},[1154],[1116,5631,5633,5636],{"className":5632},[1159],[1116,5634,4292],{"className":5635},[1159,1160],[1116,5637,5639],{"className":5638},[1277],[1116,5640,5642,5662],{"className":5641},[1281,1282],[1116,5643,5645,5659],{"className":5644},[1286],[1116,5646,5648],{"className":5647,"style":1291},[1290],[1116,5649,5650,5653],{"style":1294},[1116,5651],{"className":5652,"style":1299},[1298],[1116,5654,5656],{"className":5655},[1303,1304,1305,1306],[1116,5657,1208],{"className":5658,"style":1224},[1159,1160,1306],[1116,5660,1314],{"className":5661},[1313],[1116,5663,5665],{"className":5664},[1286],[1116,5666,5668],{"className":5667,"style":1321},[1290],[1116,5669],{}," 等于该类样本的均值(第 3 步,均值使类内平方和最小)。",[1091,5672,5673,1467],{},[1456,5674,5675],{},"优点",[1095,5677,5678,5685,5691,5698],{},[1098,5679,5680,5681,5684],{},"容易理解,聚类效果不错——虽然只是",[1456,5682,5683],{},"局部最优",",但往往局部最优就够用了;",[1098,5686,5687,5688,1578],{},"处理大数据集时有较好的",[1456,5689,5690],{},"伸缩性",[1098,5692,5693,5694,5697],{},"当簇近似",[1456,5695,5696],{},"高斯分布","时效果非常好;",[1098,5699,5700,1886],{},[1456,5701,5702],{},"算法复杂度低",[3887,5704],{},[1108,5706,5708],{"id":5707},"三隐狄利克雷分布lda模型","三、隐狄利克雷分布(LDA)模型",[1091,5710,5711,5714,5715,5718,5719,5722],{},[1456,5712,5713],{},"*作用",":对给定的文本集合,学习到",[1456,5716,5717],{},"每个文本的话题分布","以及",[1456,5720,5721],{},"每个话题的单词分布","。LDA 是一个典型的三层贝叶斯主题模型。",[1888,5724,5725],{"id":5725},"多项分布",[1091,5727,5728,5729,5904],{},"若多元离散随机变量 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X_k)",[1116,5772,5774,5793],{"className":5773,"ariaHidden":1146},[1145],[1116,5775,5777,5780,5784,5787,5790],{"className":5776},[1150],[1116,5778],{"className":5779,"style":3689},[1154],[1116,5781,5743],{"className":5782,"style":5783},[1159,1160],"margin-right:0.0785em;",[1116,5785],{"className":5786,"style":1543},[1327],[1116,5788,1494],{"className":5789},[1547],[1116,5791],{"className":5792,"style":1543},[1327],[1116,5794,5796,5799,5802,5843,5846,5849,5852,5855,5858,5861,5901],{"className":5795},[1150],[1116,5797],{"className":5798,"style":1425},[1154],[1116,5800,1402],{"className":5801},[1432],[1116,5803,5805,5808],{"className":5804},[1159],[1116,5806,5743],{"className":5807,"style":5783},[1159,1160],[1116,5809,5811],{"className":5810},[1277],[1116,5812,5814,5835],{"className":5813},[1281,1282],[1116,5815,5817,5832],{"className":5816},[1286],[1116,5818,5820],{"className":5819,"style":4344},[1290],[1116,5821,5823,5826],{"style":5822},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1116,5824],{"className":5825,"style":1299},[1298],[1116,5827,5829],{"className":5828},[1303,1304,1305,1306],[1116,5830,1978],{"className":5831},[1159,1306],[1116,5833,1314],{"className":5834},[1313],[1116,5836,5838],{"className":5837},[1286],[1116,5839,5841],{"className":5840,"style":1321},[1290],[1116,5842],{},[1116,5844,1407],{"className":5845},[1439],[1116,5847],{"className":5848,"style":1443},[1327],[1116,5850,4299],{"className":5851},[4376],[1116,5853],{"className":5854,"style":1443},[1327],[1116,5856,1407],{"className":5857},[1439],[1116,5859],{"className":5860,"style":1443},[1327],[1116,5862,5864,5867],{"className":5863},[1159],[1116,5865,5743],{"className":5866,"style":5783},[1159,1160],[1116,5868,5870],{"className":5869},[1277],[1116,5871,5873,5893],{"className":5872},[1281,1282],[1116,5874,5876,5890],{"className":5875},[1286],[1116,5877,5879],{"className":5878,"style":1291},[1290],[1116,5880,5881,5884],{"style":5822},[1116,5882],{"className":5883,"style":1299},[1298],[1116,5885,5887],{"className":5886},[1303,1304,1305,1306],[1116,5888,1208],{"className":5889,"style":1224},[1159,1160,1306],[1116,5891,1314],{"className":5892},[1313],[1116,5894,5896],{"className":5895},[1286],[1116,5897,5899],{"className":5898,"style":1321},[1290],[1116,5900],{},[1116,5902,1412],{"className":5903},[1450]," 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",[1116,8056,8058,8083],{"className":8057},[1119],[1116,8059,8061],{"className":8060},[1123],[1125,8062,8063],{"xmlns":1127},[1129,8064,8065,8080],{},[1132,8066,8067,8069,8071,8074,8076,8078],{},[1135,8068,7258],{},[1246,8070,6959],{},[3750,8072,8073],{},"Dir",[1246,8075,1402],{"stretchy":1401},[1135,8077,7076],{},[1246,8079,1412],{"stretchy":1401},[1139,8081,8082],{"encoding":1141},"\\theta \\sim \\text{Dir}(\\alpha)",[1116,8084,8086,8104],{"className":8085,"ariaHidden":1146},[1145],[1116,8087,8089,8092,8095,8098,8101],{"className":8088},[1150],[1116,8090],{"className":8091,"style":1220},[1154],[1116,8093,7258],{"className":8094,"style":7398},[1159,1160],[1116,8096],{"className":8097,"style":1543},[1327],[1116,8099,6959],{"className":8100},[1547],[1116,8102],{"className":8103,"style":1543},[1327],[1116,8105,8107,8110,8116,8119,8122],{"className":8106},[1150],[1116,8108],{"className":8109,"style":1425},[1154],[1116,8111,8113],{"className":8112},[1159,3866],[1116,8114,8073],{"className":8115},[1159],[1116,8117,1402],{"className":8118},[1432],[1116,8120,7076],{"className":8121,"style":7116},[1159,1160],[1116,8123,1412],{"className":8124},[1450],"。前面那个归一化系数常记作 ",[1116,8127,8129,8156],{"className":8128},[1119],[1116,8130,8132],{"className":8131},[1123],[1125,8133,8134],{"xmlns":1127},[1129,8135,8136,8153],{},[1132,8137,8138],{},[3747,8139,8140,8142],{},[1612,8141,1978],{},[1132,8143,8144,8147,8149,8151],{},[1135,8145,8146],{},"B",[1246,8148,1402],{"stretchy":1401},[1135,8150,7076],{},[1246,8152,1412],{"stretchy":1401},[1139,8154,8155],{"encoding":1141},"\\frac{1}{B(\\alpha)}",[1116,8157,8159],{"className":8158,"ariaHidden":1146},[1145],[1116,8160,8162,8166],{"className":8161},[1150],[1116,8163],{"className":8164,"style":8165},[1154],"height:1.3651em;vertical-align:-0.52em;",[1116,8167,8169,8172,8243],{"className":8168},[1159],[1116,8170],{"className":8171},[1432,3810],[1116,8173,8175],{"className":8174},[3747],[1116,8176,8178,8234],{"className":8177},[1281,1282],[1116,8179,8181,8231],{"className":8180},[1286],[1116,8182,8185,8209,8217],{"className":8183,"style":8184},[1290],"height:0.8451em;",[1116,8186,8187,8190],{"style":3826},[1116,8188],{"className":8189,"style":3830},[1298],[1116,8191,8193],{"className":8192},[1303,1304,1305,1306],[1116,8194,8196,8200,8203,8206],{"className":8195},[1159,1306],[1116,8197,8146],{"className":8198,"style":8199},[1159,1160,1306],"margin-right:0.0502em;",[1116,8201,1402],{"className":8202},[1432,1306],[1116,8204,7076],{"className":8205,"style":7116},[1159,1160,1306],[1116,8207,1412],{"className":8208},[1450,1306],[1116,8210,8211,8214],{"style":3842},[1116,8212],{"className":8213,"style":3830},[1298],[1116,8215],{"className":8216,"style":3850},[3849],[1116,8218,8219,8222],{"style":3853},[1116,8220],{"className":8221,"style":3830},[1298],[1116,8223,8225],{"className":8224},[1303,1304,1305,1306],[1116,8226,8228],{"className":8227},[1159,1306],[1116,8229,1978],{"className":8230},[1159,1306],[1116,8232,1314],{"className":8233},[1313],[1116,8235,8237],{"className":8236},[1286],[1116,8238,8241],{"className":8239,"style":8240},[1290],"height:0.52em;",[1116,8242],{},[1116,8244],{"className":8245},[1450,3810],[1888,8247,8248],{"id":8248},"共轭先验",[1091,8250,8251,8252,8281,8282,8310,8311,8314,8315,8344,8345,8392],{},"把样本数据记为 ",[1116,8253,8255,8269],{"className":8254},[1119],[1116,8256,8258],{"className":8257},[1123],[1125,8259,8260],{"xmlns":1127},[1129,8261,8262,8267],{},[1132,8263,8264],{},[1135,8265,8266],{},"D",[1139,8268,8266],{"encoding":1141},[1116,8270,8272],{"className":8271,"ariaHidden":1146},[1145],[1116,8273,8275,8278],{"className":8274},[1150],[1116,8276],{"className":8277,"style":3689},[1154],[1116,8279,8266],{"className":8280,"style":7398},[1159,1160],",目标是计算在数据 ",[1116,8283,8285,8298],{"className":8284},[1119],[1116,8286,8288],{"className":8287},[1123],[1125,8289,8290],{"xmlns":1127},[1129,8291,8292,8296],{},[1132,8293,8294],{},[1135,8295,8266],{},[1139,8297,8266],{"encoding":1141},[1116,8299,8301],{"className":8300,"ariaHidden":1146},[1145],[1116,8302,8304,8307],{"className":8303},[1150],[1116,8305],{"className":8306,"style":3689},[1154],[1116,8308,8266],{"className":8309,"style":7398},[1159,1160]," 给定条件下参数的",[1456,8312,8313],{},"后验概率","。对于给定样本,似然函数是多项分布形式;假设参数 ",[1116,8316,8318,8332],{"className":8317},[1119],[1116,8319,8321],{"className":8320},[1123],[1125,8322,8323],{"xmlns":1127},[1129,8324,8325,8329],{},[1132,8326,8327],{},[1135,8328,7258],{},[1139,8330,8331],{"encoding":1141},"\\theta",[1116,8333,8335],{"className":8334,"ariaHidden":1146},[1145],[1116,8336,8338,8341],{"className":8337},[1150],[1116,8339],{"className":8340,"style":1220},[1154],[1116,8342,7258],{"className":8343,"style":7398},[1159,1160]," 服从狄利克雷先验 ",[1116,8346,8348,8368],{"className":8347},[1119],[1116,8349,8351],{"className":8350},[1123],[1125,8352,8353],{"xmlns":1127},[1129,8354,8355,8365],{},[1132,8356,8357,8359,8361,8363],{},[3750,8358,8073],{},[1246,8360,1402],{"stretchy":1401},[1135,8362,7076],{},[1246,8364,1412],{"stretchy":1401},[1139,8366,8367],{"encoding":1141},"\\text{Dir}(\\alpha)",[1116,8369,8371],{"className":8370,"ariaHidden":1146},[1145],[1116,8372,8374,8377,8383,8386,8389],{"className":8373},[1150],[1116,8375],{"className":8376,"style":1425},[1154],[1116,8378,8380],{"className":8379},[1159,3866],[1116,8381,8073],{"className":8382},[1159],[1116,8384,1402],{"className":8385},[1432],[1116,8387,7076],{"className":8388,"style":7116},[1159,1160],[1116,8390,1412],{"className":8391},[1450],",根据贝叶斯规则,后验分布是",[1091,8394,8395],{},[1116,8396,8398,8452],{"className":8397},[1119],[1116,8399,8401],{"className":8400},[1123],[1125,8402,8403],{"xmlns":1127},[1129,8404,8405,8449],{},[1132,8406,8407,8409,8411,8413,8415,8417,8419,8422,8424,8426,8428,8430,8432,8434,8437,8439,8441,8443,8445,8447],{},[1135,8408,1091],{},[1246,8410,1402],{"stretchy":1401},[1135,8412,7258],{},[1246,8414,2358],{},[1135,8416,8266],{},[1246,8418,1412],{"stretchy":1401},[1246,8420,8421],{},"∝",[1135,8423,1091],{},[1246,8425,1402],{"stretchy":1401},[1135,8427,8266],{},[1246,8429,2358],{},[1135,8431,7258],{},[1246,8433,1412],{"stretchy":1401},[3750,8435,8436],{}," ",[1135,8438,1091],{},[1246,8440,1402],{"stretchy":1401},[1135,8442,7258],{},[1246,8444,2358],{},[1135,8446,7076],{},[1246,8448,1412],{"stretchy":1401},[1139,8450,8451],{"encoding":1141},"p(\\theta \\mid D) \\propto p(D \\mid \\theta)\\, p(\\theta \\mid \\alpha)",[1116,8453,8455,8479,8500,8524,8557],{"className":8454,"ariaHidden":1146},[1145],[1116,8456,8458,8461,8464,8467,8470,8473,8476],{"className":8457},[1150],[1116,8459],{"className":8460,"style":1425},[1154],[1116,8462,1091],{"className":8463},[1159,1160],[1116,8465,1402],{"className":8466},[1432],[1116,8468,7258],{"className":8469,"style":7398},[1159,1160],[1116,8471],{"className":8472,"style":1543},[1327],[1116,8474,2358],{"className":8475},[1547],[1116,8477],{"className":8478,"style":1543},[1327],[1116,8480,8482,8485,8488,8491,8494,8497],{"className":8481},[1150],[1116,8483],{"className":8484,"style":1425},[1154],[1116,8486,8266],{"className":8487,"style":7398},[1159,1160],[1116,8489,1412],{"className":8490},[1450],[1116,8492],{"className":8493,"style":1543},[1327],[1116,8495,8421],{"className":8496},[1547],[1116,8498],{"className":8499,"style":1543},[1327],[1116,8501,8503,8506,8509,8512,8515,8518,8521],{"className":8502},[1150],[1116,8504],{"className":8505,"style":1425},[1154],[1116,8507,1091],{"className":8508},[1159,1160],[1116,8510,1402],{"className":8511},[1432],[1116,8513,8266],{"className":8514,"style":7398},[1159,1160],[1116,8516],{"className":8517,"style":1543},[1327],[1116,8519,2358],{"className":8520},[1547],[1116,8522],{"className":8523,"style":1543},[1327],[1116,8525,8527,8530,8533,8536,8539,8542,8545,8548,8551,8554],{"className":8526},[1150],[1116,8528],{"className":8529,"style":1425},[1154],[1116,8531,7258],{"className":8532,"style":7398},[1159,1160],[1116,8534,1412],{"className":8535},[1450],[1116,8537],{"className":8538,"style":1443},[1327],[1116,8540,1091],{"className":8541},[1159,1160],[1116,8543,1402],{"className":8544},[1432],[1116,8546,7258],{"className":8547,"style":7398},[1159,1160],[1116,8549],{"className":8550,"style":1543},[1327],[1116,8552,2358],{"className":8553},[1547],[1116,8555],{"className":8556,"style":1543},[1327],[1116,8558,8560,8563,8566],{"className":8559},[1150],[1116,8561],{"className":8562,"style":1425},[1154],[1116,8564,7076],{"className":8565,"style":7116},[1159,1160],[1116,8567,1412],{"className":8568},[1450],[1091,8570,8571,8574,8575,8577,8578,8607,8608,8659],{},[1456,8572,8573],{},"关键结论",":狄利克雷分布是多项分布的",[1456,8576,8248],{},"——先验是狄利克雷、似然是多项,则后验仍是狄利克雷,只是参数从 ",[1116,8579,8581,8595],{"className":8580},[1119],[1116,8582,8584],{"className":8583},[1123],[1125,8585,8586],{"xmlns":1127},[1129,8587,8588,8592],{},[1132,8589,8590],{},[1135,8591,7076],{},[1139,8593,8594],{"encoding":1141},"\\alpha",[1116,8596,8598],{"className":8597,"ariaHidden":1146},[1145],[1116,8599,8601,8604],{"className":8600},[1150],[1116,8602],{"className":8603,"style":1155},[1154],[1116,8605,7076],{"className":8606,"style":7116},[1159,1160]," 更新为 ",[1116,8609,8611,8629],{"className":8610},[1119],[1116,8612,8614],{"className":8613},[1123],[1125,8615,8616],{"xmlns":1127},[1129,8617,8618,8626],{},[1132,8619,8620,8622,8624],{},[1135,8621,7076],{},[1246,8623,1767],{},[1135,8625,3914],{},[1139,8627,8628],{"encoding":1141},"\\alpha + n",[1116,8630,8632,8650],{"className":8631,"ariaHidden":1146},[1145],[1116,8633,8635,8638,8641,8644,8647],{"className":8634},[1150],[1116,8636],{"className":8637,"style":4085},[1154],[1116,8639,7076],{"className":8640,"style":7116},[1159,1160],[1116,8642],{"className":8643,"style":1328},[1327],[1116,8645,1767],{"className":8646},[1332],[1116,8648],{"className":8649,"style":1328},[1327],[1116,8651,8653,8656],{"className":8652},[1150],[1116,8654],{"className":8655,"style":1155},[1154],[1116,8657,3914],{"className":8658},[1159,1160],"(把观测计数加上去)。这个共轭性正是 LDA 能高效推断的原因。",[1888,8661,8663],{"id":8662},"lda-文本生成算法","*LDA 文本生成算法",[1091,8665,8666],{},"LDA 假设每篇文档是这样\"生成\"出来的:",[4018,8668,8669,8820,8969],{},[1098,8670,8671,8702,8703,8816,8817,1578],{},[1456,8672,8673,8674],{},"对于每个话题 ",[1116,8675,8677,8690],{"className":8676},[1119],[1116,8678,8680],{"className":8679},[1123],[1125,8681,8682],{"xmlns":1127},[1129,8683,8684,8688],{},[1132,8685,8686],{},[1135,8687,1208],{},[1139,8689,1208],{"encoding":1141},[1116,8691,8693],{"className":8692,"ariaHidden":1146},[1145],[1116,8694,8696,8699],{"className":8695},[1150],[1116,8697],{"className":8698,"style":1220},[1154],[1116,8700,1208],{"className":8701,"style":1224},[1159,1160],":生成一个多项分布参数 ",[1116,8704,8706,8736],{"className":8705},[1119],[1116,8707,8709],{"className":8708},[1123],[1125,8710,8711],{"xmlns":1127},[1129,8712,8713,8733],{},[1132,8714,8715,8722,8724,8726,8728,8731],{},[1239,8716,8717,8720],{},[1135,8718,8719],{},"φ",[1135,8721,1208],{},[1246,8723,6959],{},[3750,8725,8073],{},[1246,8727,1402],{"stretchy":1401},[1135,8729,8730],{},"β",[1246,8732,1412],{"stretchy":1401},[1139,8734,8735],{"encoding":1141},"\\varphi_k \\sim \\text{Dir}(\\beta)",[1116,8737,8739,8794],{"className":8738,"ariaHidden":1146},[1145],[1116,8740,8742,8745,8785,8788,8791],{"className":8741},[1150],[1116,8743],{"className":8744,"style":1188},[1154],[1116,8746,8748,8751],{"className":8747},[1159],[1116,8749,8719],{"className":8750},[1159,1160],[1116,8752,8754],{"className":8753},[1277],[1116,8755,8757,8777],{"className":8756},[1281,1282],[1116,8758,8760,8774],{"className":8759},[1286],[1116,8761,8763],{"className":8762,"style":1291},[1290],[1116,8764,8765,8768],{"style":1294},[1116,8766],{"className":8767,"style":1299},[1298],[1116,8769,8771],{"className":8770},[1303,1304,1305,1306],[1116,8772,1208],{"className":8773,"style":1224},[1159,1160,1306],[1116,8775,1314],{"className":8776},[1313],[1116,8778,8780],{"className":8779},[1286],[1116,8781,8783],{"className":8782,"style":1321},[1290],[1116,8784],{},[1116,8786],{"className":8787,"style":1543},[1327],[1116,8789,6959],{"className":8790},[1547],[1116,8792],{"className":8793,"style":1543},[1327],[1116,8795,8797,8800,8806,8809,8813],{"className":8796},[1150],[1116,8798],{"className":8799,"style":1425},[1154],[1116,8801,8803],{"className":8802},[1159,3866],[1116,8804,8073],{"className":8805},[1159],[1116,8807,1402],{"className":8808},[1432],[1116,8810,8730],{"className":8811,"style":8812},[1159,1160],"margin-right:0.0528em;",[1116,8814,1412],{"className":8815},[1450],",作为该话题的",[1456,8818,8819],{},"单词分布",[1098,8821,8822,8702,8853,8965,8966,1578],{},[1456,8823,8824,8825],{},"对于每篇文本 ",[1116,8826,8828,8841],{"className":8827},[1119],[1116,8829,8831],{"className":8830},[1123],[1125,8832,8833],{"xmlns":1127},[1129,8834,8835,8839],{},[1132,8836,8837],{},[1135,8838,4292],{},[1139,8840,4292],{"encoding":1141},[1116,8842,8844],{"className":8843,"ariaHidden":1146},[1145],[1116,8845,8847,8850],{"className":8846},[1150],[1116,8848],{"className":8849,"style":1155},[1154],[1116,8851,4292],{"className":8852},[1159,1160],[1116,8854,8856,8884],{"className":8855},[1119],[1116,8857,8859],{"className":8858},[1123],[1125,8860,8861],{"xmlns":1127},[1129,8862,8863,8881],{},[1132,8864,8865,8871,8873,8875,8877,8879],{},[1239,8866,8867,8869],{},[1135,8868,7258],{},[1135,8870,4292],{},[1246,8872,6959],{},[3750,8874,8073],{},[1246,8876,1402],{"stretchy":1401},[1135,8878,7076],{},[1246,8880,1412],{"stretchy":1401},[1139,8882,8883],{"encoding":1141},"\\theta_m \\sim \\text{Dir}(\\alpha)",[1116,8885,8887,8944],{"className":8886,"ariaHidden":1146},[1145],[1116,8888,8890,8894,8935,8938,8941],{"className":8889},[1150],[1116,8891],{"className":8892,"style":8893},[1154],"height:0.8444em;vertical-align:-0.15em;",[1116,8895,8897,8900],{"className":8896},[1159],[1116,8898,7258],{"className":8899,"style":7398},[1159,1160],[1116,8901,8903],{"className":8902},[1277],[1116,8904,8906,8927],{"className":8905},[1281,1282],[1116,8907,8909,8924],{"className":8908},[1286],[1116,8910,8913],{"className":8911,"style":8912},[1290],"height:0.1514em;",[1116,8914,8915,8918],{"style":7903},[1116,8916],{"className":8917,"style":1299},[1298],[1116,8919,8921],{"className":8920},[1303,1304,1305,1306],[1116,8922,4292],{"className":8923},[1159,1160,1306],[1116,8925,1314],{"className":8926},[1313],[1116,8928,8930],{"className":8929},[1286],[1116,8931,8933],{"className":8932,"style":1321},[1290],[1116,8934],{},[1116,8936],{"className":8937,"style":1543},[1327],[1116,8939,6959],{"className":8940},[1547],[1116,8942],{"className":8943,"style":1543},[1327],[1116,8945,8947,8950,8956,8959,8962],{"className":8946},[1150],[1116,8948],{"className":8949,"style":1425},[1154],[1116,8951,8953],{"className":8952},[1159,3866],[1116,8954,8073],{"className":8955},[1159],[1116,8957,1402],{"className":8958},[1432],[1116,8960,7076],{"className":8961,"style":7116},[1159,1160],[1116,8963,1412],{"className":8964},[1450],",作为该文本的",[1456,8967,8968],{},"话题分布",[1098,8970,8971,9031,9032],{},[1456,8972,8973,8974,9002,9003],{},"对于文本 ",[1116,8975,8977,8990],{"className":8976},[1119],[1116,8978,8980],{"className":8979},[1123],[1125,8981,8982],{"xmlns":1127},[1129,8983,8984,8988],{},[1132,8985,8986],{},[1135,8987,4292],{},[1139,8989,4292],{"encoding":1141},[1116,8991,8993],{"className":8992,"ariaHidden":1146},[1145],[1116,8994,8996,8999],{"className":8995},[1150],[1116,8997],{"className":8998,"style":1155},[1154],[1116,9000,4292],{"className":9001},[1159,1160]," 中的每个单词位置 ",[1116,9004,9006,9019],{"className":9005},[1119],[1116,9007,9009],{"className":9008},[1123],[1125,9010,9011],{"xmlns":1127},[1129,9012,9013,9017],{},[1132,9014,9015],{},[1135,9016,3914],{},[1139,9018,3914],{"encoding":1141},[1116,9020,9022],{"className":9021,"ariaHidden":1146},[1145],[1116,9023,9025,9028],{"className":9024},[1150],[1116,9026],{"className":9027,"style":1155},[1154],[1116,9029,3914],{"className":9030},[1159,1160],":\n",[4018,9033,9034,9207],{},[1098,9035,9036,9037,9206],{},"先从文档的话题分布中抽一个话题 ",[1116,9038,9040,9078],{"className":9039},[1119],[1116,9041,9043],{"className":9042},[1123],[1125,9044,9045],{"xmlns":1127},[1129,9046,9047,9075],{},[1132,9048,9049,9061,9063,9065,9067,9073],{},[1239,9050,9051,9053],{},[1135,9052,1747],{},[1132,9054,9055,9057,9059],{},[1135,9056,4292],{},[1246,9058,1407],{"separator":1146},[1135,9060,3914],{},[1246,9062,6959],{},[3750,9064,6962],{},[1246,9066,1402],{"stretchy":1401},[1239,9068,9069,9071],{},[1135,9070,7258],{},[1135,9072,4292],{},[1246,9074,1412],{"stretchy":1401},[1139,9076,9077],{"encoding":1141},"z_{m,n} \\sim \\text{Mult}(\\theta_m)",[1116,9079,9081,9148],{"className":9080,"ariaHidden":1146},[1145],[1116,9082,9084,9088,9139,9142,9145],{"className":9083},[1150],[1116,9085],{"className":9086,"style":9087},[1154],"height:0.7167em;vertical-align:-0.2861em;",[1116,9089,9091,9094],{"className":9090},[1159],[1116,9092,1747],{"className":9093,"style":1810},[1159,1160],[1116,9095,9097],{"className":9096},[1277],[1116,9098,9100,9130],{"className":9099},[1281,1282],[1116,9101,9103,9127],{"className":9102},[1286],[1116,9104,9106],{"className":9105,"style":8912},[1290],[1116,9107,9109,9112],{"style":9108},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[1116,9110],{"className":9111,"style":1299},[1298],[1116,9113,9115],{"className":9114},[1303,1304,1305,1306],[1116,9116,9118,9121,9124],{"className":9117},[1159,1306],[1116,9119,4292],{"className":9120},[1159,1160,1306],[1116,9122,1407],{"className":9123},[1439,1306],[1116,9125,3914],{"className":9126},[1159,1160,1306],[1116,9128,1314],{"className":9129},[1313],[1116,9131,9133],{"className":9132},[1286],[1116,9134,9137],{"className":9135,"style":9136},[1290],"height:0.2861em;",[1116,9138],{},[1116,9140],{"className":9141,"style":1543},[1327],[1116,9143,6959],{"className":9144},[1547],[1116,9146],{"className":9147,"style":1543},[1327],[1116,9149,9151,9154,9160,9163,9203],{"className":9150},[1150],[1116,9152],{"className":9153,"style":1425},[1154],[1116,9155,9157],{"className":9156},[1159,3866],[1116,9158,6962],{"className":9159},[1159],[1116,9161,1402],{"className":9162},[1432],[1116,9164,9166,9169],{"className":9165},[1159],[1116,9167,7258],{"className":9168,"style":7398},[1159,1160],[1116,9170,9172],{"className":9171},[1277],[1116,9173,9175,9195],{"className":9174},[1281,1282],[1116,9176,9178,9192],{"className":9177},[1286],[1116,9179,9181],{"className":9180,"style":8912},[1290],[1116,9182,9183,9186],{"style":7903},[1116,9184],{"className":9185,"style":1299},[1298],[1116,9187,9189],{"className":9188},[1303,1304,1305,1306],[1116,9190,4292],{"className":9191},[1159,1160,1306],[1116,9193,1314],{"className":9194},[1313],[1116,9196,9198],{"className":9197},[1286],[1116,9199,9201],{"className":9200,"style":1321},[1290],[1116,9202],{},[1116,9204,1412],{"className":9205},[1450],",作为该单词对应的话题;",[1098,9208,9209,9210,1886],{},"再从该话题的单词分布中抽一个单词 ",[1116,9211,9213,9262],{"className":9212},[1119],[1116,9214,9216],{"className":9215},[1123],[1125,9217,9218],{"xmlns":1127},[1129,9219,9220,9259],{},[1132,9221,9222,9235,9237,9239,9241,9257],{},[1239,9223,9224,9227],{},[1135,9225,9226],{},"w",[1132,9228,9229,9231,9233],{},[1135,9230,4292],{},[1246,9232,1407],{"separator":1146},[1135,9234,3914],{},[1246,9236,6959],{},[3750,9238,6962],{},[1246,9240,1402],{"stretchy":1401},[1239,9242,9243,9245],{},[1135,9244,8719],{},[1239,9246,9247,9249],{},[1135,9248,1747],{},[1132,9250,9251,9253,9255],{},[1135,9252,4292],{},[1246,9254,1407],{"separator":1146},[1135,9256,3914],{},[1246,9258,1412],{"stretchy":1401},[1139,9260,9261],{"encoding":1141},"w_{m,n} \\sim \\text{Mult}(\\varphi_{z_{m,n}})",[1116,9263,9265,9331],{"className":9264,"ariaHidden":1146},[1145],[1116,9266,9268,9271,9322,9325,9328],{"className":9267},[1150],[1116,9269],{"className":9270,"style":9087},[1154],[1116,9272,9274,9278],{"className":9273},[1159],[1116,9275,9226],{"className":9276,"style":9277},[1159,1160],"margin-right:0.0269em;",[1116,9279,9281],{"className":9280},[1277],[1116,9282,9284,9314],{"className":9283},[1281,1282],[1116,9285,9287,9311],{"className":9286},[1286],[1116,9288,9290],{"className":9289,"style":8912},[1290],[1116,9291,9293,9296],{"style":9292},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1116,9294],{"className":9295,"style":1299},[1298],[1116,9297,9299],{"className":9298},[1303,1304,1305,1306],[1116,9300,9302,9305,9308],{"className":9301},[1159,1306],[1116,9303,4292],{"className":9304},[1159,1160,1306],[1116,9306,1407],{"className":9307},[1439,1306],[1116,9309,3914],{"className":9310},[1159,1160,1306],[1116,9312,1314],{"className":9313},[1313],[1116,9315,9317],{"className":9316},[1286],[1116,9318,9320],{"className":9319,"style":9136},[1290],[1116,9321],{},[1116,9323],{"className":9324,"style":1543},[1327],[1116,9326,6959],{"className":9327},[1547],[1116,9329],{"className":9330,"style":1543},[1327],[1116,9332,9334,9338,9344,9347,9440],{"className":9333},[1150],[1116,9335],{"className":9336,"style":9337},[1154],"height:1.0973em;vertical-align:-0.3473em;",[1116,9339,9341],{"className":9340},[1159,3866],[1116,9342,6962],{"className":9343},[1159],[1116,9345,1402],{"className":9346},[1432],[1116,9348,9350,9353],{"className":9349},[1159],[1116,9351,8719],{"className":9352},[1159,1160],[1116,9354,9356],{"className":9355},[1277],[1116,9357,9359,9431],{"className":9358},[1281,1282],[1116,9360,9362,9428],{"className":9361},[1286],[1116,9363,9365],{"className":9364,"style":8912},[1290],[1116,9366,9367,9370],{"style":1294},[1116,9368],{"className":9369,"style":1299},[1298],[1116,9371,9373],{"className":9372},[1303,1304,1305,1306],[1116,9374,9376],{"className":9375},[1159,1306],[1116,9377,9379,9382],{"className":9378},[1159,1306],[1116,9380,1747],{"className":9381,"style":1810},[1159,1160,1306],[1116,9383,9385],{"className":9384},[1277],[1116,9386,9388,9419],{"className":9387},[1281,1282],[1116,9389,9391,9416],{"className":9390},[1286],[1116,9392,9395],{"className":9393,"style":9394},[1290],"height:0.1645em;",[1116,9396,9398,9401],{"style":9397},"top:-2.357em;margin-left:-0.044em;margin-right:0.0714em;",[1116,9399],{"className":9400,"style":5013},[1298],[1116,9402,9404],{"className":9403},[1303,5017,5018,1306],[1116,9405,9407,9410,9413],{"className":9406},[1159,1306],[1116,9408,4292],{"className":9409},[1159,1160,1306],[1116,9411,1407],{"className":9412},[1439,1306],[1116,9414,3914],{"className":9415},[1159,1160,1306],[1116,9417,1314],{"className":9418},[1313],[1116,9420,9422],{"className":9421},[1286],[1116,9423,9426],{"className":9424,"style":9425},[1290],"height:0.2819em;",[1116,9427],{},[1116,9429,1314],{"className":9430},[1313],[1116,9432,9434],{"className":9433},[1286],[1116,9435,9438],{"className":9436,"style":9437},[1290],"height:0.3473em;",[1116,9439],{},[1116,9441,1412],{"className":9442},[1450],[1091,9444,9445,9446,9474,9475,9503,9504,9532,9533,1886],{},"也就是\"先按文档选话题、再按话题选词\"两级抽样。观测到的只有单词 ",[1116,9447,9449,9462],{"className":9448},[1119],[1116,9450,9452],{"className":9451},[1123],[1125,9453,9454],{"xmlns":1127},[1129,9455,9456,9460],{},[1132,9457,9458],{},[1135,9459,9226],{},[1139,9461,9226],{"encoding":1141},[1116,9463,9465],{"className":9464,"ariaHidden":1146},[1145],[1116,9466,9468,9471],{"className":9467},[1150],[1116,9469],{"className":9470,"style":1155},[1154],[1116,9472,9226],{"className":9473,"style":9277},[1159,1160],",话题 ",[1116,9476,9478,9491],{"className":9477},[1119],[1116,9479,9481],{"className":9480},[1123],[1125,9482,9483],{"xmlns":1127},[1129,9484,9485,9489],{},[1132,9486,9487],{},[1135,9488,1747],{},[1139,9490,1747],{"encoding":1141},[1116,9492,9494],{"className":9493,"ariaHidden":1146},[1145],[1116,9495,9497,9500],{"className":9496},[1150],[1116,9498],{"className":9499,"style":1155},[1154],[1116,9501,1747],{"className":9502,"style":1810},[1159,1160]," 是隐变量;LDA 的任务就是反过来,根据观测的词推断出各文档的话题分布 ",[1116,9505,9507,9520],{"className":9506},[1119],[1116,9508,9510],{"className":9509},[1123],[1125,9511,9512],{"xmlns":1127},[1129,9513,9514,9518],{},[1132,9515,9516],{},[1135,9517,7258],{},[1139,9519,8331],{"encoding":1141},[1116,9521,9523],{"className":9522,"ariaHidden":1146},[1145],[1116,9524,9526,9529],{"className":9525},[1150],[1116,9527],{"className":9528,"style":1220},[1154],[1116,9530,7258],{"className":9531,"style":7398},[1159,1160]," 和各话题的单词分布 ",[1116,9534,9536,9550],{"className":9535},[1119],[1116,9537,9539],{"className":9538},[1123],[1125,9540,9541],{"xmlns":1127},[1129,9542,9543,9547],{},[1132,9544,9545],{},[1135,9546,8719],{},[1139,9548,9549],{"encoding":1141},"\\varphi",[1116,9551,9553],{"className":9552,"ariaHidden":1146},[1145],[1116,9554,9556,9559],{"className":9555},[1150],[1116,9557],{"className":9558,"style":1188},[1154],[1116,9560,8719],{"className":9561},[1159,1160],[3887,9563],{},[1108,9565,9566],{"id":9566},"总结",[1095,9568,9569,9575,9581,9587,9593,9604,9610],{},[1098,9570,9571,9574],{},[1456,9572,9573],{},"距离三条件",":对称性、非负性(=0 当且仅当同点)、三角不等式。",[1098,9576,9577,9580],{},[1456,9578,9579],{},"常用数值距离",":欧氏(平方和开根)、绝对(绝对值和)、切氏(最大差)、明氏(统一 q 次)、马氏(带 Σ⁻¹ 去量纲\u002F相关)。次序数据先量化,属性数据用匹配距离。",[1098,9582,9583,9586],{},[1456,9584,9585],{},"系统聚类",":每个个体一类起步,反复合并最相似两类,直到并成一大类(谱系图)。",[1098,9588,9589,9592],{},[1456,9590,9591],{},"K-Means 四步",":随机选 K 个中心 → 样本归到最近中心 → 中心更新为类内均值 → 收敛否则迭代;有限步收敛;交替优化(固定中心优化指派 \u002F 固定指派优化中心);优点是简单、伸缩性好、近高斯簇效果佳、复杂度低。",[1098,9594,9595,9598,9599,9601,9602,1886],{},[1456,9596,9597],{},"LDA 作用",":学出每篇文档的",[1456,9600,8968],{},"和每个话题的",[1456,9603,8819],{},[1098,9605,9606,9609],{},[1456,9607,9608],{},"共轭",":狄利克雷是多项分布的共轭先验,后验仍是狄利克雷(参数 α+计数)。",[1098,9611,9612,9615],{},[1456,9613,9614],{},"LDA 生成过程",":每话题一个词分布(Dir(β))、每文档一个话题分布(Dir(α)),每个词位置先选话题再选词。",{"title":9617,"searchDepth":9618,"depth":9618,"links":9619},"",4,[9620,9625,9629,9635],{"id":1110,"depth":9621,"text":1111,"children":9622},2,[9623],{"id":1890,"depth":9624,"text":1890},3,{"id":3891,"depth":9621,"text":3892,"children":9626},[9627,9628],{"id":3895,"depth":9624,"text":3896},{"id":4173,"depth":9624,"text":4174},{"id":5707,"depth":9621,"text":5708,"children":9630},[9631,9632,9633,9634],{"id":5725,"depth":9624,"text":5725},{"id":7029,"depth":9624,"text":7029},{"id":8248,"depth":9624,"text":8248},{"id":8662,"depth":9624,"text":8663},{"id":9566,"depth":9621,"text":9566},"https:\u002F\u002Fpica.zhimg.com\u002Fv2-f3ea0f7d2d672bfef4229fd409cdf8f4_1440w.jpg","常用距离度量、层次聚类与 K-Means 算法","md",true,{"uuid":9641,"slots":9642},"f3561dd0-e86a-11f0-8fd1-914b1152d8ed",{},{"title":1085,"description":9637},"posts\u002F分布式处理与计算\u002F分布式处理与计算：聚类分析",[323,344,345,346],"-h3cqlaC8XKrHeT5qUBAp_MRgh9n3y_NcEZyfBmHkTk",1790443282979]