{"id":1827,"date":"2026-02-22T22:41:36","date_gmt":"2026-02-22T22:41:36","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=1827"},"modified":"2026-02-22T22:44:27","modified_gmt":"2026-02-22T22:44:27","slug":"vol23-no2-art3","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/","title":{"rendered":"Statistical Approaches to Calculate Weighted Principal Components with Applications in Human Face Image Analysis"},"content":{"rendered":"<p>Laura Costa Pereira Miranda <a href=\"https:\/\/orcid.org\/0000-0002-2673-0189\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>, Carlos Eduardo Thomaz <a href=\"https:\/\/orcid.org\/0000-0001-5566-1963\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>, Diego Barreto Haddad <a href=\"https:\/\/orcid.org\/0000-0002-7634-5481\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>, Ana Cl\u00e1udia Souza Vidal de Negreiros <a href=\"https:\/\/orcid.org\/0000-0002-6003-5876\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a><br \/>\n&amp; Gilson Antonio Giraldi <a href=\"https:\/\/orcid.org\/0000-0003-0623-9461\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a><\/p>\n<p><strong>Abstract:<\/strong> The main objective of this work is to investigate the efficiency of data weighting techniques for calculating weighted principal components in gender and facial expression experiments, considering classification and reconstruction problems. Specifically, the methodology consists of generating spatial weights (statistical maps) to weight the pixels of the input images. Then, the weighted data are used as input for the principal component analysis (P CA) algorithm. We will consider the following techniques for calculating spatial weights: (a) Student\u2019s t-test; (b) Hyperplanes computed using SVM (Support Vector Machine); (c) Shannon entropy calculated pixel-by-pixel; (d) Inverse Shannon entropy calculated pixel-by-pixel; (e) Jensen-Shannon divergence. The application of techniques (a), (c), (d), (e) for calculating spatial weights in face recognition is the main contribution of this work. The evaluation of the efficiency of the different principal components obtained with each technique is done by analyzing the results of image reconstruction and classification over FEI and FERET databases. For classification, the following<br \/>\nclassifiers were used: K-Nearest Neighbors and Mahalanobis Distance. A quadtree-based methodology was also used to reduce small local variations in the statistical maps, to test its effect on reconstruction and classification.<\/p>\n<p><strong>Keywords:<\/strong> Face Recognition, PCA, Weighting Methods, Classification. Reconstruction.<\/p>\n<p><strong>DOI code:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/lnlm-vol23-no2-art3\">10.21528\/lnlm-vol23-no2-art3<\/a><\/p>\n<p><strong>PDF file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2025\/12\/vol23-no2-art3.pdf\">vol23-no2-art3.pdf<\/a><\/p>\n<p><strong>BibTex file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2025\/12\/vol23-no2-art3.bib\">vol23-no2-art3.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Laura Costa Pereira Miranda , Carlos Eduardo Thomaz , Diego Barreto Haddad , Ana Cl\u00e1udia Souza Vidal de Negreiros &amp; Gilson Antonio Giraldi Abstract: The main objective of this work is to investigate the efficiency of data weighting techniques for <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1811,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1827","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Statistical Approaches to Calculate Weighted Principal Components with Applications in Human Face Image Analysis - Learning and NonLinear Models<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Statistical Approaches to Calculate Weighted Principal Components with Applications in Human Face Image Analysis - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"Laura Costa Pereira Miranda , Carlos Eduardo Thomaz , Diego Barreto Haddad , Ana Cl\u00e1udia Souza Vidal de Negreiros &amp; 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Gilson Antonio Giraldi Abstract: The main objective of this work is to investigate the efficiency of data weighting techniques for Read More ...","og_url":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/","og_site_name":"Learning and NonLinear Models","article_modified_time":"2026-02-22T22:44:27+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. tempo de leitura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/","url":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/","name":"Statistical Approaches to Calculate Weighted Principal Components with Applications in Human Face Image Analysis - Learning and NonLinear Models","isPartOf":{"@id":"https:\/\/sbia.org.br\/lnlm\/#website"},"primaryImageOfPage":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/#primaryimage"},"image":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/#primaryimage"},"thumbnailUrl":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg","datePublished":"2026-02-22T22:41:36+00:00","dateModified":"2026-02-22T22:44:27+00:00","breadcrumb":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/"]}]},{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/#primaryimage","url":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg","contentUrl":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol23-no2\/vol23-no2-art3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Browse issues","item":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/"},{"@type":"ListItem","position":2,"name":"Learning &#038; 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