{"id":33242,"date":"2023-12-14T00:13:19","date_gmt":"2023-12-13T16:13:19","guid":{"rendered":"https:\/newsletter.sinica.edu.tw\/?p=33242"},"modified":"2023-12-14T04:09:36","modified_gmt":"2023-12-13T20:09:36","slug":"%e3%80%90%e5%b0%88%e6%ac%84%e3%80%91%e4%b8%bb%e6%88%90%e5%88%86%e5%88%86%e6%9e%90%e5%8f%8a%e5%85%b6%e5%9c%a8%e5%bd%b1%e5%83%8f%e8%99%95%e7%90%86%e4%b8%8a%e7%9a%84%e6%87%89%e7%94%a8","status":"publish","type":"post","link":"https:\/newsletter.sinica.edu.tw\/33242\/","title":{"rendered":"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528"},"content":{"rendered":"<div class=\"auth-info\">\n<div class='one_fourth'>\n\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_A.jpg\" alt=\"\u9673\u7d20\u96f2\u7814\u7a76\u54e1\" width=\"150\" height=\"150\" class=\"aligncenter size-full wp-image-33243\" \/>\n\t\t\t\t<\/div>\n<div class='three_fourth et_column_last'>\n\t\t\t\t\t\u9673\u7d20\u96f2\u7562\u696d\u65bc\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\uff0c\u4e26\u65bc 1990 \u5e74\u53d6\u5f97\u7f8e\u570b Purdue University \u7d71\u8a08\u5b78\u535a\u58eb\u5b78\u4f4d\u3002\u66fe\u4efb\u6559\u65bc Wayne State University \u6578\u5b78\u7cfb\uff0c1993 \u5e74\u52a0\u5165\u672c\u9662\uff0c\u76ee\u524d\u64d4\u4efb\u7d71\u8a08\u79d1\u5b78\u7814\u7a76\u6240\u7814\u7a76\u54e1\u3002\u5979\u7684\u4e3b\u8981\u7814\u7a76\u5c08\u9577\u70ba\u9ad8\u7dad\u5ea6\u8cc7\u6599\u5206\u6790\u3001\u7a69\u5065\u7d71\u8a08\u63a8\u8ad6\u53ca\u6a5f\u5668\u5b78\u7fd2\u3002\n\t\t\t\t<\/div><div class='clear'><\/div><\/div>\n<p>&nbsp;<\/p>\n<p>\u96a8\u8457\u5927\u6578\u64da\u6642\u4ee3\u7684\u5230\u4f86\uff0c\u5728\u8a31\u591a\u7814\u7a76\u9818\u57df\u8207\u61c9\u7528\u4e0a\u5f80\u5f80\u9762\u81e8\u5927\u91cf\u9ad8\u7dad\u5ea6\u6578\u64da\u7684\u5206\u6790\u3002\u5927\u91cf\u6578\u64da\u63d0\u4f9b\u66f4\u591a\u7684\u8a0a\u606f\u91cf\uff0c\u4f46\u5176\u4e2d\u53ef\u80fd\u4f34\u96a8\u8457\u4e00\u4e9b\u96dc\u8a0a\uff0c\u6216\u4e0d\u53ef\u4fe1\u8cf4\u7684\u7570\u5e38\u503c\u548c\u96e2\u7fa4\u503c\uff0c\u56e0\u800c\u5c0e\u81f4\u5206\u6790\u504f\u8aa4\uff0c\u9032\u800c\u5f71\u97ff\u5230\u6700\u7d42\u5c0d\u5206\u6790\u7d50\u679c\u7684\u6c7a\u7b56\u53ca\u5224\u65b7\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u5927\u6578\u64da\u4e5f\u589e\u52a0\u4e86\u5206\u6790\u4e0a\u7684\u8a08\u7b97\u6210\u672c\u3001\u8907\u96dc\u5ea6\uff0c\u9020\u6210\u904b\u7b97\u4e0a\u7684\u8ca0\u64d4\uff0c\u56e0\u6b64\uff0c\u9700\u8981\u627e\u5230\u9069\u7576\u7684\u5206\u6790\u65b9\u6cd5\u53ca\u5de5\u5177\uff0c\u5c07\u6578\u64da\u300c\u5316\u7e41\u70ba\u7c21\u3001\u53bb\u856a\u5b58\u83c1\u300d\u3002\u9019\u4e0d\u50c5\u610f\u5473\u8457\u9664\u53bb\u4e0d\u5fc5\u8981\u7684\u8a0a\u606f\uff0c\u540c\u6642\u76e1\u53ef\u80fd\u5730\u4fdd\u7559\u539f\u59cb\u6578\u64da\u4e2d\u7684\u6709\u7528\u8a0a\u606f\uff0c\u4ee5\u6e1b\u8f15\u5206\u6790\u904e\u7a0b\u4e2d\u7684\u6642\u9593\u548c\u6210\u672c\u8ca0\u64d4\uff0c\u5be6\u73fe\u5c0d\u6578\u64da\u66f4\u5168\u9762\u4e86\u89e3\u7684\u76ee\u6a19\u3002<\/p>\n<p>\u5728\u7d71\u8a08\u5b78\u53ca\u6a5f\u5668\u5b78\u7fd2\u9818\u57df\u4e2d\uff0c\u4e3b\u6210\u5206\u5206\u6790\uff08Principal Component Analysis, PCA\uff09\u5373\u70ba\u4e00\u7a2e\u5e38\u7528\u7684\u964d\u4f4e\u6578\u64da\u7dad\u5ea6\u7684\u624b\u6cd5\u3002\u4e3b\u6210\u5206\u5206\u6790\u7531\u82f1\u570b\u6578\u5b78\u5bb6\u5361\u723e \u2027 \u76ae\u723e\u68ee\uff08Karl Pearson\uff09\u65bc 1901 \u5e74\u63d0\u51fa<sup>1<\/sup>\uff0c\u662f\u4e00\u7a2e\u6b77\u53f2\u60a0\u4e45\u4e14\u76f8\u5c0d\u5bb9\u6613\u904b\u7528\u7684\u964d\u7dad\u5ea6\uff08dimension reduction\uff09\u3001\u53bb\u95dc\u806f\u6027\u7684\u65b9\u6cd5\uff0c\u81f3\u4eca\u5728\u6578\u64da\u5206\u6790\u9818\u57df\u4e2d\u4ecd\u88ab\u5ee3\u6cdb\u5730\u61c9\u7528\u3002\u4e3b\u6210\u5206\u5206\u6790\u662f\u4e00\u7a2e\u975e\u76e3\u7763\u5f0f\u5b78\u7fd2\uff08unsupervised learning\uff09\uff0c\u5176\u4e3b\u8981\u7684\u6838\u5fc3\u6982\u5ff5\u662f\u7528\u6700\u5c11\u7684\u7dad\u5ea6\u4f86\u5448\u73fe\u539f\u672c\u9ad8\u7dad\u5ea6\u6578\u64da\u7684\u8a0a\u606f\uff1a\u5c07\u539f\u672c p \u7dad\u7684\u7279\u5fb5\uff08features\uff09\u4ee5 k \u7dad\u7684\u7dda\u6027\u7d44\u5408\u4f86\u8868\u9054\uff08\u5176\u4e2dk &lt; p\uff09\uff0c\u85c9\u7531\u4e3b\u6210\u5206\uff08Principal Components\uff09\u627e\u5230\u7684 k \u7dad\u65b0\u7279\u5fb5\uff0c\u5176\u80fd\u5920\u6355\u6349\u539f\u672c p \u7dad\u6578\u64da\u4e2d\u7684\u5927\u90e8\u5206\u7684\u7279\u6027\u4f86\u89e3\u91cb\u6578\u64da\u3002\u63db\u8a00\u4e4b\uff0c\u5e0c\u671b\u80fd\u5920\u5728\u76e1\u91cf\u4fdd\u6709\u539f\u59cb\u6578\u64da\u8a0a\u606f\u7684\u60c5\u6cc1\u4e0b\uff0c\u4ee5\u66f4\u7cbe\u7c21\u5316\u7684\u5f62\u5f0f\u4f86\u5448\u73fe\u539f\u59cb\u6578\u64da\u3002<\/p>\n<p><strong>PCA \u539f\u7406<\/strong><\/p>\n<p>\u4e3b\u6210\u5206\u5206\u6790\u7684\u76ee\u7684\u662f\u5c07\u8cc7\u6599\u9032\u884c\u964d\u7dad\uff0c\u4e26\u627e\u51fa\u6700\u80fd\u5920\u89e3\u91cb\u8cc7\u6599\u7684\u65b9\u5411\uff1a\u627e\u5230\u4e00\u500b\u6216\u4e00\u500b\u4ee5\u4e0a\u7684\u6295\u5f71\u8ef8\uff08\u5411\u91cf\uff09\uff0c\u5c07\u8cc7\u6599\u9ede\u7dda\u6027\u6295\u5f71\u5230\u9019\u500b\uff08\u4e9b\uff09\u8ef8\u4e0a\u5f8c\uff0c\u4f7f\u5f97\u8cc7\u6599\u6709\u6700\u5927\u7684\u8b8a\u7570\u91cf\uff0c\u800c\u4e14\u65b0\u7279\u5fb5\u5f7c\u6b64\u4e4b\u9593\u7dda\u6027\u4e0d\u76f8\u95dc\u3002<\/p>\n<p>\u5047\u8a2d\u6709 n \u500b\u6a23\u672c\u9ede\uff0c<img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-1-e1702431327765.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"86\" height=\"36\" class=\"alignnone size-full wp-image-33248\" \/> x<sub>i<\/sub> \u2208 R<sup>p<\/sup>\uff0c\u900f\u904e\u4e3b\u6210\u5206\u5206\u6790\u5c07\u8cc7\u6599\u9ede\u6295\u5f71\u5230\u65b0\u5ea7\u6a19\u8ef8\u7684\u505a\u6cd5\u70ba\uff1a<\/p>\n<p>1. \u5148\u5c07\u8cc7\u6599\u4e2d\u5fc3\u79fb\u81f3\u539f\u9ede\uff08\u4ea6\u5373\u4f7f\u5e73\u5747\u6578\u70ba 0\uff09\uff0c\u5728\u6b64\u4e0d\u59a8\u5047\u8a2d\u5e73\u5747\u6578\u7686\u5df2\u70ba\u96f6\u3002<br \/>\n2. \u627e\u5230\u65b0\u7684\u5ea7\u6a19\u8ef8\uff0c\u4f7f\u5f97\u6295\u5f71\u5f8c\u7684\u8cc7\u6599\u6709\u6700\u5927\u7684\u8b8a\u7570\u91cf\u3002\u9019\u500b\u554f\u984c\u53ef\u4ee5\u900f\u904e\u89e3\u5171\u8b8a\u7570\u6578\u77e9\u9663\uff08covariance matrix\uff09S \u7684\u7279\u5fb5\u503c\u5206\u89e3\uff08eigenvalue decomposition\uff09\u5f97\u5230\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-3-e1702431895898.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"224\" height=\"150\" class=\"aligncenter size-full wp-image-33264\" \/><br \/>\nv<sub>j<\/sub><sup>\u22a4<\/sup>v<sub>j<\/sub> = 1 \u53ca v<sub>l<\/sub><sup>\u22a4<\/sup>v<sub>j<\/sub> = 0\uff0cl \u2260 j\u3002<\/p>\n<p>\u9019\u88e1\u7684 v<sub>j<\/sub> \u2208 R<sup>p<\/sup> \u5c0d\u61c9\u7684\u662f\u5171\u8b8a\u7570\u6578\u77e9\u9663 S \u7684\u7b2c j \u500b\u7279\u5fb5\u5411\u91cf\uff08eigenvector\uff09\uff0c\u03bb<sub>j<\/sub> \u5373\u70ba\u7b2c j \u500b\u6700\u5927\u7684\u7279\u5fb5\u503c\uff08eigenvalue\uff09\u3002\u8209\u4f8b\u4f86\u8aaa\uff0c<img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-4-e1702432058862.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"100\" height=\"40\" class=\"alignnone size-full wp-image-33269\" \/> \u5247\u70ba\u539f\u8cc7\u6599\u9ede\u6295\u5f71\u5230 v<sub>1<\/sub> \u4e0a\u7684\u65b0\u5ea7\u6a19\uff0c\u9019\u4e9b\u6295\u5f71\u5f8c\u7684\u8cc7\u6599\u9ede\u5728 v<sub>1<\/sub> \u9019\u500b\u65b9\u5411\u6709\u6700\u5927\u7684\u8b8a\u7570\u91cf\u3002\u56e0\u6b64\uff0c\u4e3b\u6210\u5206\u5206\u6790\u85c9\u7531\u7279\u5fb5\u503c\u5206\u89e3\u4f86\u627e k \u500b\u65b0\u7684\u5ea7\u6a19\u8ef8\uff0c\u627e\u5230\u7684 k \u500b\u7279\u5fb5\u5411\u91cf\u4e5f\u5c31\u662f\u8cc7\u6599\u7684\u4e3b\u6210\u5206\uff0c\u800c\u4e14 k \u500b\u4e3b\u6210\u5206\u5f7c\u6b64\u4e4b\u9593\u70ba\u6b63\u4ea4\uff08orthogonal\uff09\uff0c\u8cc7\u6599\u6295\u5f71\u5f8c\u7684\u8b8a\u7570\u7a0b\u5ea6\u5247\u662f\u7531\u7279\u5fb5\u503c\u4f86\u63cf\u8ff0\u3002\u4ee5\u4e00\u500b\u4f8b\u5b50\u4f86\u8aaa\u660e\uff0c\u4ee4\u7279\u5fb5\u5411\u91cf\u77e9\u9663\u70baV = [ v<sub>1<\/sub> v<sub>2<\/sub> \u2026 v<sub>k<\/sub> ] \u2208 R<sup>p\u00d7k<\/sup>\uff0c\u5176\u5c0d\u61c9\u7684\u7279\u5fb5\u503c\u70ba \u03bb<sub>1<\/sub> \u2265 \u03bb<sub>2<\/sub> \u2265 \u2026 \u2265 \u03bb<sub>k<\/sub> &gt; 0\uff0c\u5c07\u539f\u8cc7\u6599\u9ede x<sub>1<\/sub> \u6295\u5f71\u5230\u65b0\u7684\u5ea7\u6a19\u7a7a\u9593\u4e0a\u5f97\u5230\u7684\u65b0\u7279\u5fb5\u70ba z<sub>1<\/sub>=[z<sub>11<\/sub> z<sub>12<\/sub> \u22ef z<sub>1k<\/sub> ]<sup>\u22a4<\/sup> \u2208 R<sup>k<\/sup>\uff1a<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-5-e1702432645845.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"761\" height=\"196\" class=\"aligncenter size-full wp-image-33272\" srcset=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-5-e1702432645845.png 761w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-5-e1702432645845-300x77.png 300w\" sizes=\"(max-width: 761px) 100vw, 761px\" \/><\/p>\n<p>\u5176\u4e2d v<sub>j<\/sub><sup>\u22a4<\/sup>v<sub>j<\/sub> = 1 \u53ca v<sub>l<\/sub><sup>\u22a4<\/sup>v<sub>j<\/sub> = 0\uff0cl \u2260 j\u3002\u4ee5\u6b64\u985e\u63a8\uff0c\u6211\u5011\u53ef\u4ee5\u5c07 n \u500b\u6a23\u672c\u9ede\u6295\u5f71\u5f8c\u5f97\u5230<br \/>\n[z<sub>1<\/sub> z<sub>2<\/sub> \u22ef z<sub>n<\/sub>]<sub>k\u00d7n<\/sub>=[v<sub>1<\/sub> v<sub>2<\/sub> \u22ef v<sub>k<\/sub>]<sup>\u22a4<\/sup> [x<sub>1<\/sub> x<sub>2<\/sub> \u22ef x<sub>n<\/sub>]<sub>p\u00d7n<\/sub>\uff0c<br \/>\n\u5176\u4e2d z<sub>i<\/sub>=[z<sub>i1<\/sub> z<sub>i2<\/sub> \u22ef z<sub>ik<\/sub> ]<sup>\u22a4<\/sup>\u3002\u6211\u5011\u7a31 v<sub>j<\/sub> \u70ba\u7b2c j \u500b\u4e3b\u6210\u5206\uff0cz<sub>i<\/sub> \u5247\u88ab\u7a31\u4f5c\u4e3b\u6210\u5206\u5206\u6578\uff08principal component scores\uff09\u3002\u6211\u5011\u6709\u4ee5\u4e0b\u6027\u8cea\uff1a<\/p>\n<p>(i) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-6-e1702433141790.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"150\" height=\"42\" class=\"alignnone size-full wp-image-33274\" \/>\uff0c\u4ea6\u5373\u7b2c j \u500b\u65b0\u7279\u5fb5\u7684\u8b8a\u7570\u6578\u5373\u70ba \u03bb<sub>j<\/sub>\uff1b\u5169\u5169\u7279\u5fb5\u4e4b\u9593\u5f7c\u6b64\u4e0d\u76f8\u95dc\u3002<br \/>\n(ii) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-7-e1702433438914.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"120\" height=\"45\" class=\"alignnone size-full wp-image-33278\" \/>\uff0c\u4ea6\u5373\u539f\u7279\u5fb5\u7684\u8b8a\u7570\u6578\u7e3d\u548c\uff08\u5171\u8b8a\u7570\u6578\u77e9\u9663\u7684 trace\uff09\u5373\u70ba\u7279\u5fb5\u503c\u7684\u7e3d\u548c\u3002<br \/>\n(iii) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-8-e1702433358318.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"120\" height=\"50\" class=\"alignnone size-full wp-image-33279\" \/>\uff0c\u4ea6\u5373\u6240\u6709\u7279\u5fb5\u503c\u7684\u4e58\u7a4d\u5373\u70ba\u5171\u8b8a\u7570\u6578\u77e9\u9663\u7684\u884c\u5217\u5f0f\u3002<\/p>\n<p><strong>\uff0ePCA \u7684\u6b78\u7d0d\u7e3d\u7d50<\/strong><br \/>\n1. \u7cbe\u7c21\u5316\uff08parsimony\uff09\uff1a\u7528\u8f03\u5c11\u7684\u4e3b\u6210\u5206\u4f86\u53d6\u4ee3\u539f\u672c\u7684\u9ad8\u7dad\u5ea6\u7279\u5fb5\u3002<br \/>\n2. \u4ee3\u8868\u6027\uff08representation\uff09\uff1a\u4e3b\u6210\u5206\u4fdd\u6709\u539f\u672c\u7279\u5fb5\u7684\u8a0a\u606f\u3002<br \/>\n3. \u53bb\u76f8\u95dc\uff08decorrelation\uff09\uff1a\u4e3b\u6210\u5206\u5206\u6578\uff08\u5373\u65b0\u7279\u5fb5\uff09\u5f7c\u6b64\u4e4b\u9593\u7121\u7dda\u6027\u76f8\u95dc\u3002<\/p>\n<p><strong>\u7a69\u5065\u4e3b\u6210\u5206\u5206\u6790\u65b9\u6cd5<\/strong><\/p>\n<p>\u96d6\u7136\u4e3b\u6210\u5206\u5206\u6790\u76f8\u7576\u666e\u53ca\u4e14\u5df2\u88ab\u5ee3\u6cdb\u5730\u61c9\u7528\u65bc\u6578\u64da\u5206\u6790\u4e0a\uff0c\u4f46\u662f\u7576\u8cc7\u6599\u4e2d\u6709\u96e2\u7fa4\u503c\uff08outliers\uff09\u7684\u5b58\u5728\uff0c\u6216\u6211\u5011\u7a31\u4e4b\u70ba\u8cc7\u6599\u53d7\u5230\u6c59\u67d3\uff08contaminated\uff09\u6642\uff0c\u4e3b\u6210\u5206\u5206\u6790\u7684\u7d50\u679c\u5bb9\u6613\u7522\u751f\u6709\u504f\u4f30\u8a08\uff08biased estimation\uff09\u3002\u56e0\u6b64\uff0c\u8a31\u591a\u5177\u6709\u7a69\u5065\u6027\uff08robustness\uff09\u7684\u4e3b\u6210\u5206\u5206\u6790\u65b9\u6cd5\u5df2\u88ab\u63d0\u51fa\u4f86\u514b\u670d\u8cc7\u6599\u4e2d\u6709\u96e2\u7fa4\u503c\u5b58\u5728\u7684\u60c5\u6cc1\uff0c\u4f7f\u5f97\u4f30\u8a08\u7684\u7d50\u679c\u66f4\u52a0\u7a69\u5065\u3001\u53ef\u4fe1\u3002\u9762\u5c0d\u6975\u7aef\u503c\u5b58\u5728\u7684\u60c5\u6cc1\uff0c\u4e00\u7a2e\u5e38\u898b\u7684\u7b56\u7565\u662f\u6839\u64da\u7a69\u5065\u6563\u9ede\u77e9\u9663\u4f30\u8a08\uff08robust scatter matrix estimator\uff09\u4f86\u57f7\u884c\u7279\u5fb5\u503c\u5206\u89e3\u3002\u9673\u7d20\u96f2\u7814\u7a76\u54e1\u53ca\u5176\u5408\u4f5c\u8005\uff08\u53f0\u5927\u7684\u6d2a\u5f18\u6559\u6388\u53ca\u65e5\u672c\u7d71\u8a08\u6578\u7406\u7814\u7a76\u6240\u7684\u6c5f\u53e3\u771f\u900f\u6559\u6388\uff09\u5728 2022 \u5e74\u63d0\u51fa\u4e86 Robust Semiparametric PCA[2]<sup>2<\/sup>\uff0c\u6b64\u65b9\u6cd5\u662f\u57fa\u65bc\u534a\u53c3\u6578\u7406\u8ad6\uff08Semiparametric Theory\uff09\u8207 robust scatter estimator \u767c\u5c55\u51fa\u4f86\u7684\u4e00\u7a2e\u5177\u6709\u7a69\u5065\u6027\u7684\u4e3b\u6210\u5206\u5206\u6790\u65b9\u6cd5\u3002<\/p>\n<p><strong>\uff0eRobust Semiparametric PCA\uff08SPPCA\uff09<\/strong><\/p>\n<p>\u8003\u616e\u4e00\u500b\u534a\u53c3\u6578\u6a21\u578b\uff08semiparametric model\uff09\uff1a<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-9-e1702433653722.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"500\" height=\"148\" class=\"aligncenter size-full wp-image-33284\" \/><\/p>\n<p>\u5176\u4e2dd(x,\u03bc<sub>0<\/sub>,V<sub>0<\/sub>) = (x \u2013 \u03bc<sub>0<\/sub>)<sup>\u22a4<\/sup>V<sub>0<\/sub><sup>-1<\/sup>(x-\u03bc<sub>0<\/sub>)\u3002(\u03bc<sub>0<\/sub>,V<sub>0<\/sub>) \u70ba\u611f\u8208\u8da3\u7684\u53c3\u6578\uff08\u6b32\u4f30\u8a08\u7684\u53c3\u6578\uff09\uff0c\u03c8(\uff65) \u70ba\u7121\u7aae\u591a\u7dad\u7684\u5e72\u64fe\u53c3\u6578\uff08infinite-dimensional nuisance parameter\uff09\uff0c\u5e72\u64fe\u53c3\u6578\u70ba\u4e0d\u611f\u8208\u8da3\uff0c\u4f46\u5fc5\u9808\u8003\u616e\u7684\u53c3\u6578\u3002\u534a\u53c3\u6578\u7406\u8ad6\u5728\u4e0d\u9700\u6307\u6d3e \u03c8(\uff65) \u7684\u5f62\u5f0f\u4e0b\uff0c\u78ba\u4fdd\u4e86\u5c0d\u53c3\u6578\uff08\u03bc<sub>0<\/sub>,V<sub>0<\/sub>\uff09\u4f30\u8a08\u5f0f\u7684\u5efa\u69cb\uff0c\u56e0\u6b64\uff0c\u6839\u64da\u534a\u53c3\u6578\u7406\u8ad6\uff0c SPPCA \u63d0\u51fa\u900f\u904e\u4ee5\u4e0b\u4f30\u8a08\u5f0f\u5c0d\u53c3\u6578\uff08\u03bc<sub>0<\/sub>,V<sub>0<\/sub>\uff09\u505a\u4f30\u8a08\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-10-e1702434054476.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"337\" height=\"100\" class=\"aligncenter size-full wp-image-33291\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-11-e1702434121620.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"450\" height=\"100\" class=\"aligncenter size-full wp-image-33293\" \/><\/p>\n<p>\u5176\u4e2d w(\uff65) \u70ba\u6b0a\u91cd\u51fd\u6578\uff08weight function\uff09\uff0cF(x) \u70baf(x) \u7684\u7d2f\u7a4d\u6a5f\u7387\u51fd\u6578\uff08cdf\uff09\u3002\u4e0a\u8ff0 SPPCA \u5c0d V<sub>0<\/sub> \u7684\u4f30\u8a08\u5f0f\u53ef\u4ee5\u91cd\u65b0\u6574\u7406\u6210\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-12-e1702434256432.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"588\" height=\"100\" class=\"aligncenter size-full wp-image-33295\" \/><\/p>\n<p>\u5176\u4e2d h(u)=w(u)u\u3002SPPCA \u900f\u904e\u5927\u62ec\u865f\u4e2d\u7684\u90e8\u5206\u7d66\u4e88\u6bcf\u500b\u8cc7\u6599\u9ede\u4e0d\u540c\u7684\u6b0a\u91cd\uff0c\u7d0d\u5165 d(x,\u03bc,V) \u7684\u8a0a\u606f\u53ca\u9078\u64c7\u9069\u5408\u7684\u6b0a\u91cd\u51fd\u6578 w(\uff65) \u5f8c\uff0c\u7d66\u4e88\u6975\u7aef\u503c\u8f03\u5c0f\u7684\u6b0a\u91cd\uff0c\u964d\u4f4e\u6975\u7aef\u503c\u5c0d\u4f30\u8a08\u7d50\u679c\u7684\u5f71\u97ff\u7a0b\u5ea6\uff0c\u4ee5\u9054\u5230\u7a69\u5065\u7684\u4f30\u8a08\u7d50\u679c\u3002\u70ba\u4e86\u9054\u5230\u9019\u6a23\u7684\u76ee\u7684\uff0cSPPCA \u5c0d\u65bc\u6b0a\u91cd\u51fd\u6578 w(\uff65) \u7684\u9078\u64c7\u9808\u6eff\u8db3\u4ee5\u4e0b\u5169\u500b\u689d\u4ef6\uff1a<\/p>\n<p>(1) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-13-e1702434523142.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"120\" height=\"35\" class=\"alignnone size-full wp-image-33298\" \/><br \/>\n(2) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_M-14-e1702434538130.png\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"120\" height=\"37\" class=\"alignnone size-full wp-image-33299\" \/><\/p>\n<p>\u689d\u4ef6(1) \u78ba\u4fdd SPPCA \u7684\u5f71\u97ff\u51fd\u6578\uff08influence functions\uff09\u7684\u9577\u5ea6\uff08norm\uff09\u662f\u6709\u754c\u7684\uff1b\u689d\u4ef6(2) \u5247\u4fdd\u8b49\u5728\u6709\u96e2\u7fa4\u503c\u7684\u60c5\u6cc1\u4e0b\uff0cSPPCA \u7684\u4f30\u8a08\u7d50\u679c\u5177\u6709\u7a69\u5065\u6027\u3002<\/p>\n<p><strong>PCA \u65bc\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528<\/strong><\/p>\n<p>\u4e3b\u6210\u5206\u5206\u6790\u7684\u61c9\u7528\u76f8\u7576\u591a\u5143\uff0c\u5728\u5f71\u50cf\u5206\u6790\u4e0a\u53ef\u4ee5\u7528\u65bc<br \/>\n1. \u964d\u7dad\uff1a\u964d\u4f4e\u5f71\u50cf\u6578\u64da\u7684\u7dad\u5ea6\uff0c\u9032\u800c\u6e1b\u5c11\u6578\u64da\u7684\u8907\u96dc\u5ea6\uff0c\u4f46\u540c\u6642\u4fdd\u7559\u539f\u672c\u6578\u64da\u4e2d\u4e3b\u8981\u7684\u7279\u5fb5\uff0f\u7279\u6027\u3002<br \/>\n2. \u7279\u5fb5\u63d0\u53d6\uff08feature extraction\uff09\uff1a\u8b58\u5225\u53ca\u63d0\u53d6\u5f71\u50cf\u4e2d\u6700\u5177\u6709\u4ee3\u8868\u6027\u7684\u7279\u5fb5\uff0c\u52a9\u65bc\u5f8c\u7e8c\u5206\u6790\u548c\u8fa8\u8b58\u5f71\u50cf\u7684\u9032\u884c\u3002<br \/>\n3. \u964d\u566a\uff08denoise\uff09\uff1a\u53bb\u9664\u5f71\u50cf\u4e2d\u4e0d\u5fc5\u8981\u7684\u96dc\u8a0a\uff0c\u4fdd\u7559\u5f71\u50cf\u4e2d\u76f8\u5c0d\u91cd\u8981\u7684\u7d30\u7bc0\uff0c\u63d0\u9ad8\u5f71\u50cf\u7684\u8cea\u91cf\uff0c\u8b93\u5f71\u50cf\u66f4\u52a0\u6e05\u6670\u3002<\/p>\n<p>\u63a5\u4e0b\u4f86\u5c07\u4ecb\u7d39\u4e3b\u6210\u5206\u5206\u6790\u65bc\u4eba\u81c9\u8fa8\u8b58\u7684\u61c9\u7528\uff0c\u900f\u904e\u4e3b\u6210\u5206\u5206\u6790\u65b9\u6cd5\u5c07\u5f71\u50cf\u4e2d\u7684\u81c9\u90e8\u7279\u5fb5\u6293\u53d6\u51fa\u4f86\uff0c\u6e1b\u5c11\u8aa4\u5224\u5f71\u50cf\u7684\u6a5f\u6703\uff0c\u63d0\u9ad8\u81c9\u90e8\u8fa8\u8b58\u7684\u6210\u529f\u7387\u3002<\/p>\n<p><strong>\uff0eOlivetti Faces Dataset<\/strong><\/p>\n<p>Olivetti \u8cc7\u6599\u96c6\u662f\u4e00\u7d44\u5f9e 1992 \u5e74 4 \u6708\u81f3 1994 \u5e74 4 \u6708\u65bc AT&#038;T \u528d\u6a4b\u5be6\u9a57\u5ba4\u62cd\u651d\u7684\u81c9\u90e8\u5f71\u50cf\u3002\u8cc7\u6599\u96c6\u5305\u542b 400 \u5f35\u5c0d\u65bc\u4e0d\u540c\u7684 40 \u500b\u4eba\u6240\u62cd\u651d\u7684\u81c9\u90e8\u5f71\u50cf\uff0c\u6bcf\u500b\u4eba\u5404\u62cd\u651d 10 \u5f35\uff0c\u9019\u4e9b\u5f71\u50cf\u662f\u5728\u4e0d\u540c\u6642\u9593\u3001\u5149\u7dda\u3001\u81c9\u90e8\u8868\u60c5\uff08\u5fae\u7b11\uff0f\u4e0d\u5fae\u7b11\u3001\u775c\u773c\uff0f\u9589\u773c\uff09\u53ca\u81c9\u90e8\u7d30\u7bc0\uff08\u6234\u773c\u93e1\uff0f\u4e0d\u6234\u773c\u93e1\uff09\u4e4b\u4e0b\u62cd\u651d\uff0c\u5716\u4e00\u5c55\u793a 16 \u5f35\u96a8\u6a5f\u9078\u53d6\u7684\u5f71\u50cf\u3002\u6bcf\u4e00\u5f35\u5f71\u50cf\u7686\u88ab\u8f49\u6210\u7070\u968e\uff08\u6578\u503c\u754c\u65bc 0 \u81f3 255 \uff09\u3001\u5927\u5c0f\u70ba 64\u00d764 \u7684\u81c9\u90e8\u5f71\u50cf\u77e9\u9663\u3002<\/p>\n<p><div id=\"attachment_21652\" style=\"width: 558px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-21652\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_1.jpg\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"548\" height=\"490\" class=\"aligncenter size-full wp-image-33306\" srcset=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_1.jpg 548w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_1-300x268.jpg 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><p id=\"caption-attachment-21652\" class=\"wp-caption-text\">\u25b2\u5716\u4e00\uff1aOlivetti faces\u3002<\/p><\/div><br \/>\n&nbsp;<\/p>\n<p>\u5716\u4e8c\u70ba\u900f\u904e\u4e3b\u6210\u5206\u5206\u6790\u7684\u7d50\u679c\uff0c\u7b2c\u4e00\u884c\u5230\u7b2c\u56db\u884c\u5448\u73fe\u4f4e\u7dad\u5ea6\u5f71\u50cf\u91cd\u5efa\uff08low-rank reconstructions\uff09\u7684\u7d50\u679c\uff0c\u7b2c\u4e94\u884c\u5230\u7b2c\u516b\u884c\u5448\u73fe PCA \u63d0\u53d6\u7684\u81c9\u90e8\u7279\u5fb5\uff08eigenfaces\uff09\uff0c\u6216\u7a31\u70ba\u57fa\u5e95\u7a7a\u9593\uff08leading basis functions\uff09\u3002\u5728\u9019\u500b\u5206\u6790\u4e2d\uff0c\u4ee5\u7dad\u5ea6 126 \u7684\u81c9\u90e8\u7279\u5fb5\u77e9\u9663\uff08\u5176\u4e2d\u5305\u542b mean face\uff09\u4f86\u5c0d\u539f\u672c\u7dad\u5ea6 4096 \u7684\u81c9\u90e8\u5f71\u50cf\u77e9\u9663\u9032\u884c\u4f4e\u7dad\u5ea6\u5f71\u50cf\u91cd\u5efa\u3002<\/p>\n<p><div id=\"attachment_21652\" style=\"width: 1860px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-21652\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2.jpg\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"1850\" height=\"820\" class=\"aligncenter size-full wp-image-33307\" srcset=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2.jpg 1850w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2-300x133.jpg 300w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2-1024x454.jpg 1024w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2-768x340.jpg 768w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2-1536x681.jpg 1536w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_2-1080x479.jpg 1080w\" sizes=\"(max-width: 1850px) 100vw, 1850px\" \/><p id=\"caption-attachment-21652\" class=\"wp-caption-text\">\u25b2\u5716\u4e8c\uff1aPCA \u7684\u4f4e\u7dad\u5ea6\u5f71\u50cf\u91cd\u5efa\uff08low-rank reconstructions\uff09\u53ca\u57fa\u5e95\u7a7a\u9593\uff08leading basis functions\uff09\u3002<\/p><\/div><br \/>\n&nbsp;<\/p>\n<p>\u63a5\u4e0b\u4f86\u5448\u73fe\u5f71\u50cf\u4e2d\u5b58\u5728\u96e2\u7fa4\u503c\u7684\u5206\u6790\u7d50\u679c\uff0c\u5c07\u6587\u737b\u4e0a\u7684\u5169\u7a2e\u7a69\u5065\u4e3b\u6210\u5206\u5206\u6790\u65b9\u6cd5\u61c9\u7528\u65bc Olivetti \u8cc7\u6599\u96c6\u4e2d\uff1a\uff081\uff092011 \u5e74\u7531 Cand\u00e8s \u7b49\u5b78\u8005\u6240\u63d0\u51fa\u7684 robust PCA3 \u53ca\uff082\uff09\u524d\u8ff0\u4ecb\u7d39\u7684 Robust Semiparametric PCA<sup>3<\/sup>\u3002\u6b64\u5206\u6790\u5c07 20 \u5f35\u96a8\u6a5f\u65cb\u8f49\u7684\u62db\u8ca1\u8c93\u5f71\u50cf\uff08\u5716\u4e09\u5c55\u793a 16 \u5f35\u96a8\u6a5f\u9078\u53d6\u7684\u5f71\u50cf\uff09\u4f5c\u70ba\u96e2\u7fa4\u503c\u52a0\u5165 Olivetti \u8cc7\u6599\u96c6\u4e2d\uff0c\u56e0\u6b64\uff0c\u8cc7\u6599\u4e2d\u542b\u6709 420 \u5f35\u5f71\u50cf\u3002<\/p>\n<p><div id=\"attachment_21652\" style=\"width: 590px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-21652\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_3.jpg\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"580\" height=\"520\" class=\"aligncenter size-full wp-image-33310\" srcset=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_3.jpg 580w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_3-300x269.jpg 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><p id=\"caption-attachment-21652\" class=\"wp-caption-text\">\u25b2\u5716\u4e09\uff1a Outliers\u3002<\/p><\/div><br \/>\n&nbsp;<\/p>\n<p>\u7531\u5716\u56db\u7684\u7d50\u679c\u986f\u793a\uff0cCand\u00e8s \u7b49\u5b78\u8005\u6240\u63d0\u51fa\u7684 robust PCA \u627e\u51fa\u7684\u7279\u5fb5\u53d7\u5230\u4e86\u96e2\u7fa4\u503c\u7684\u6c61\u67d3\uff0c\u57fa\u5e95\u7a7a\u9593\u5716\u50cf\u4e2d\u660e\u986f\u53ef\u4ee5\u770b\u5230\u62db\u8ca1\u8c93\u7684\u5f71\u50cf\uff0c\u5f9e\u5f71\u50cf\u91cd\u5efa\u7684\u7d50\u679c\u53ef\u4ee5\u770b\u51fa\u81c9\u90e8\u8868\u60c5\u6709\u4e00\u9ede\u6a21\u7cca\u3001\u8f2a\u5ed3\u4e0d\u5920\u6e05\u695a\uff0c\u4e26\u4e14\u5931\u53bb\u4e86\u4e00\u4e9b\u7d30\u7bc0\u3002\u6211\u5011\u63d0\u51fa\u7684 Robust Semiparametric PCA \u5728\u6975\u7aef\u503c\u5b58\u5728\u7684\u60c5\u6cc1\u4e0b\uff0c\u80fd\u5920\u8f03\u70ba\u4e0d\u53d7\u5230\u96e2\u7fa4\u503c\u7684\u5f71\u97ff\uff0c\u6210\u529f\u8b58\u5225\u51fa\u4e3b\u8981\u7684\u7279\u5fb5\uff08\u898b\u5716\u4e94\uff09\uff0c\u5f71\u50cf\u91cd\u5efa\u7684\u7d50\u679c\u66f4\u63a5\u8fd1\u771f\u5be6\u60c5\u6cc1\uff08\u5373\u5716\u4e00\uff09\uff0c\u8207 Cand\u00e8s \u7b49\u5b78\u8005\u6240\u63d0\u51fa robust PCA\uff0c\u76f8\u6bd4\u5177\u6709\u66f4\u7cbe\u7d30\u7684\u81c9\u90e8\u7279\u5fb5\u3002<\/p>\n<div id=\"attachment_21652\" style=\"width: 1860px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-21652\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4.jpg\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"1850\" height=\"820\" class=\"aligncenter size-full wp-image-33311\" srcset=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4.jpg 1850w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4-300x133.jpg 300w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4-1024x454.jpg 1024w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4-768x340.jpg 768w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4-1536x681.jpg 1536w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_4-1080x479.jpg 1080w\" sizes=\"(max-width: 1850px) 100vw, 1850px\" \/><p id=\"caption-attachment-21652\" class=\"wp-caption-text\">\u25b2\u5716\u56db\uff1aCand\u00e8s \u7b49\u5b78\u8005\u6240\u63d0\u51fa\u7684robust PCA \u7684\u4f4e\u7dad\u5ea6\u5f71\u50cf\u91cd\u5efa\uff08low-rank reconstructions\uff09\u53ca\u57fa\u5e95\u7a7a\u9593\uff08leading basis functions\uff09\u3002<\/p><\/div>\n<p><div id=\"attachment_21652\" style=\"width: 1860px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-21652\" src=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5.jpg\" alt=\"\u3010\u5c08\u6b04\u3011\u4e3b\u6210\u5206\u5206\u6790\u53ca\u5176\u5728\u5f71\u50cf\u8655\u7406\u4e0a\u7684\u61c9\u7528\" width=\"1850\" height=\"820\" class=\"aligncenter size-full wp-image-33312\" srcset=\"https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5.jpg 1850w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5-300x133.jpg 300w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5-1024x454.jpg 1024w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5-768x340.jpg 768w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5-1536x681.jpg 1536w, https:\/newsletter.sinica.edu.tw\/wp-content\/uploads\/2023\/12\/3-4_5-1080x479.jpg 1080w\" sizes=\"(max-width: 1850px) 100vw, 1850px\" \/><p id=\"caption-attachment-21652\" class=\"wp-caption-text\">\u25b2\u5716\u4e94\uff1a\u6211\u5011\u7684 Robust Semiparametric PCA \u7684\u4f4e\u7dad\u5ea6\u5f71\u50cf\u91cd\u5efa\uff08low-rank reconstructions\uff09\u53ca\u57fa\u5e95\u7a7a\u9593\uff08leading basis functions\uff09\u3002<\/p><\/div><br \/>\n&nbsp;<\/p>\n<p><strong>\u7e3d\u7d50<\/strong><\/p>\n<p>\u672c\u6587\u4ecb\u7d39\u4e86\u4e3b\u6210\u5206\u5206\u6790\u7684\u539f\u7406\uff0c\u5305\u62ec\u5982\u4f55\u627e\u5230\u6700\u80fd\u5920\u89e3\u91cb\u6578\u64da\u8b8a\u7570\u7684\u4e3b\u6210\u5206\uff0c\u4ee5\u53ca\u5982\u4f55\u964d\u4f4e\u6578\u64da\u7dad\u5ea6\u3002\u6b64\u5916\uff0c\u9084\u8a0e\u8ad6\u4e86\u7a69\u5065\u6027\u4e3b\u6210\u5206\u5206\u6790\u65b9\u6cd5\u53ca\u5176\u5728\u5f71\u50cf\u964d\u7dad\u65b9\u9762\u7684\u61c9\u7528\uff0c\u7279\u5225\u662f\u4ecb\u7d39\u4e86\u4e00\u7a2e\u7a31\u70ba Robust Semiparametric PCA \u7684\u65b9\u6cd5\uff0c\u4ee5\u61c9\u5c0d\u6578\u64da\u4e2d\u7684\u96e2\u7fa4\u503c\u3002\u5728\u9019\u4e4b\u4e2d\uff0c\u534a\u53c3\u6578\u7406\u8ad6\uff08Semiparametric Theory\uff09\u662f\u7d71\u8a08\u5b78\u4e2d\u4e00\u500b\u91cd\u8981\u7684\u7406\u8ad6\u6846\u67b6\uff0c\u5b83\u6574\u5408\u4e86\u53c3\u6578\u65b9\u6cd5\u548c\u975e\u53c3\u6578\u65b9\u6cd5\u7684\u512a\u9ede\uff0c\u4f7f\u5176\u61c9\u7528\u65bc\u4e00\u4e9b\u8907\u96dc\u6a21\u578b\u7684\u63a8\u8ad6\u6642\uff0c\u64c1\u6709\u66f4\u5927\u7684\u9748\u6d3b\u6027\u3002\u9019\u7a2e\u534a\u53c3\u6578\u65b9\u6cd5\u4f7f\u7d71\u8a08\u5b78\u5bb6\u80fd\u5920\u66f4\u9748\u6d3b\u5730\u61c9\u5c0d\u8907\u96dc\u7684\u6578\u64da\u60c5\u5883\uff0c\u9032\u800c\u505a\u51fa\u66f4\u70ba\u53ef\u9760\u7684\u63a8\u65b7\u548c\u9810\u6e2c\u3002<\/p>\n<hr>\n<p><sup>1<\/sup> Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.<br \/>\n<sup>2<\/sup> Hung, H., Huang, S. Y., and Eguchi, S. (2022). Robust self-tuning semiparametric PCA for contaminated elliptical distribution. IEEE Transactions on Signal Processing, 70, 5885-5897.<br \/>\n<sup>3<\/sup> Cand\u00e8s, E. J., Li, X., Ma, Y., and Wright, J. (2011). Robust principal component analysis? Journal of the ACM, 58(3), 1-37.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; \u96a8\u8457\u5927\u6578\u64da\u6642\u4ee3\u7684\u5230\u4f86\uff0c\u5728\u8a31\u591a\u7814\u7a76\u9818\u57df\u8207\u61c9\u7528\u4e0a\u5f80\u5f80\u9762\u81e8\u5927\u91cf\u9ad8\u7dad\u5ea6\u6578\u64da\u7684\u5206\u6790\u3002\u5927\u91cf\u6578\u64da\u63d0\u4f9b\u66f4\u591a\u7684\u8a0a\u606f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":33324,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[990,983],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/posts\/33242"}],"collection":[{"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/comments?post=33242"}],"version-history":[{"count":49,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/posts\/33242\/revisions"}],"predecessor-version":[{"id":33314,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/posts\/33242\/revisions\/33314"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/media\/33324"}],"wp:attachment":[{"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/media?parent=33242"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/categories?post=33242"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/newsletter.sinica.edu.tw\/wp-json\/wp\/v2\/tags?post=33242"}],"curies":[{"name":"wp","href":"https:\/api.w.org\/{rel}","templated":true}]}}