{"id":18071,"date":"2023-10-24T09:34:38","date_gmt":"2023-10-24T01:34:38","guid":{"rendered":"https:\/\/virtual.math.ntnu.edu.tw\/?p=18071"},"modified":"2023-10-25T13:58:33","modified_gmt":"2023-10-25T05:58:33","slug":"lecture20231025","status":"publish","type":"post","link":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/2023\/10\/24\/lecture20231025\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u301010\u670825\u65e5\u3011\u674e\u80b2\u6770 \/ Federated Learning for Sparse Principal Component Analysis"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"18071\" class=\"elementor elementor-18071\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-19a5332c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"19a5332c\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-68eb95a1\" data-id=\"68eb95a1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4d878518 elementor-widget elementor-widget-heading\" data-id=\"4d878518\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Federated Learning for Sparse Principal Component Analysis<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51461cf0 elementor-widget elementor-widget-spacer\" data-id=\"51461cf0\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ccaf3ea elementor-widget elementor-widget-text-editor\" data-id=\"4ccaf3ea\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\">\u6642\u3000\u9593\uff1a2023-10-25 14:00 (\u661f\u671f\u4e09) \/ \u5730\u3000\u9ede\uff1aS101 \/ \u8336\u3000\u6703\uff1aS205 (13:30)<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4940900d elementor-widget elementor-widget-image\" data-id=\"4940900d\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img width=\"430\" height=\"410\" src=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2023\/10\/1121025\u674e\u80b2\u6770s.jpg\" class=\"attachment-full size-full\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2023\/10\/1121025\u674e\u80b2\u6770s.jpg 430w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2023\/10\/1121025\u674e\u80b2\u6770s-300x286.jpg 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-26032a62 elementor-widget elementor-widget-text-editor\" data-id=\"26032a62\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 22px; line-height: 26px; text-align: center; color: #cc6633; font-weight: bold;\">Yuh-Jye Li<br \/>\u674e\u80b2\u6770<\/div><div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 18px; line-height: 22px; text-align: center; color: #cc9966; font-weight: bold;\">\u4e2d\u592e\u7814\u7a76\u9662 \u8cc7\u8a0a\u79d1\u6280\u5275\u65b0\u7814\u7a76\u4e2d\u5fc3\u7814\u7a76\u54e1<br \/>\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78 \u61c9\u7528\u6578\u5b78\u7cfb\u6559\u6388<\/div>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5c79e75 elementor-widget elementor-widget-spacer\" data-id=\"5c79e75\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5fd7cb59 elementor-widget elementor-widget-text-editor\" data-id=\"5fd7cb59\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"color: #000000;\">In the rapidly evolving realm of machine learning, algorithm effectiveness often faces limitations due to data quality and availability. Traditional approaches grapple with data sharing due to legal and privacy concerns. The federated learning framework addresses this challenge. Federated learning is a decentralized approach where model training occurs on client sides, preserving privacy by keeping data localized. Instead of sending raw data to a central server, only model updates are exchanged, enhancing data security. We apply this framework to Sparse Principal Component Analysis (SPCA) in this work. SPCA aims to attain sparse component loading while maximizing data variance for improved interpretability. We introduce a least squares approximation to original PCA, adding an <em>l<\/em>1 norm regularization term to enhance principal component sparsity, aiding variable identification and interpretability. The problem is formulated as a consensus optimization challenge and solved using the Alternating Direction Method of Multipliers (ADMM). Our extensive experiments involve both IID and non-IID random features across various data owners. Results on synthetic and public datasets affirm the efficacy of our federated SPCA approach.<\/span><\/p><p><span style=\"color: #000000;\"><strong>\u500b\u4eba\u7db2\u9801 <a style=\"color: #000000;\" href=\"https:\/\/www.citi.sinica.edu.tw\/pages\/yuh-jye\/index_zh.html\">https:\/\/www.citi.sinica.edu.tw\/pages\/yuh-jye\/index_zh.html<\/a><\/strong><\/span><\/p><p><span style=\"color: #000000;\"><strong>\u76f8\u95dc\u8cc7\u8a0a <a style=\"color: #000000;\" href=\"https:\/\/aic.cgu.edu.tw\/p\/404-1044-102897.php?Lang=zh-tw\">https:\/\/aic.cgu.edu.tw\/p\/404-1044-102897.php?Lang=zh-tw<\/a><\/strong><\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-76d951d3 elementor-widget elementor-widget-image\" data-id=\"76d951d3\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img width=\"1240\" height=\"758\" src=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg\" class=\"attachment-full size-full\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg 1240w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-300x183.jpg 300w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-768x469.jpg 768w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-1024x626.jpg 1024w\" sizes=\"(max-width: 1240px) 100vw, 1240px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<p class=\"wpf_wrapper\"><a class=\"print_link\" href=\"\" target=\"_blank\">\u53cb\u5584\u5217\u5370<\/a><\/p><!-- .wpf_wrapper -->","protected":false},"excerpt":{"rendered":"<p>Federated Learning for Sparse Principal Component Analy [&hellip;]<\/p>\n","protected":false},"author":23,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1,124],"tags":[],"_links":{"self":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18071"}],"collection":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/23"}],"replies":[{"embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=18071"}],"version-history":[{"count":9,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18071\/revisions"}],"predecessor-version":[{"id":18135,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18071\/revisions\/18135"}],"wp:attachment":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=18071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=18071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=18071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}