{"id":1514,"date":"2025-10-01T02:24:47","date_gmt":"2025-09-30T19:24:47","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=1514"},"modified":"2025-10-02T14:45:32","modified_gmt":"2025-10-02T07:45:32","slug":"explore-pca","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/explore-pca\/","title":{"rendered":"Exploring Principal Component Analysis (PCA)"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/eksplorasi-aku\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">Principal Component Analysis (PCA) is one of the most powerful techniques for simplifying data while preserving as much information as possible. But what does that actually mean? Basically, PCA looks for new axes (principal components) that capture the most variation in a dataset.<\/p>\n\n\n\n<p>This interactive media lets you explore PCA step by step. On the left, you can manipulate original data points and see how they project onto the original <em>x<\/em> and <em>y<\/em> axes. On the right, you can observe how the same data is represented in the PCA space (PC1 and PC2). By dragging the points and comparing both views, you will develop an intuition for how PCA transforms data and why it is such a useful tool in data science.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull has-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<h3 class=\"has-text-align-center\">PCA Explorer<\/h3>\n\n\n\n<p class=\"has-text-align-center\">Let&#8217;s explore how data transforms from original axes to principal components!<\/p>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 480px; height: 480px;\"><\/div>\n\n\n\n<p>Move the points to see how data projects onto the original <em>x<\/em> and <em>y<\/em> axes.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 480px; height: 480px;\"><\/div>\n\n<script>\n  var calculator1 = 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 \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"x_{2}=x_{1}-x_{rerata}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"18\",\n                \"folderId\": \"2\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"y_{2}=y_{1}-y_{rerata}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"136\",\n                \"folderId\": \"2\",\n                \"text\": \"Banyak titik-titik data:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"n=\\\\operatorname{count}\\\\left(x_{1}\\\\right)\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"16\",\n                \"title\": \"Matriks kovarian\",\n                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\"expression\",\n                \"id\": \"180\",\n                \"folderId\": \"149\",\n                \"color\": \"#388c46\",\n                \"latex\": \"p_{c23}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"181\",\n                \"folderId\": \"149\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"p_{c24}=1\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"158\",\n                \"folderId\": \"149\",\n                \"color\": \"#000000\",\n                \"latex\": \"x_{2}=\\\\frac{15}{24}\\\\left(x_{1}+12\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"159\",\n                \"folderId\": \"149\",\n                \"color\": \"#c74440\",\n                \"latex\": \"y_{2}=\\\\frac{15}{24}\\\\left(y_{1}+12\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"152\",\n                \"folderId\": \"149\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(x_{2},y_{2}\\\\right)\",\n                \"pointOutline\": true,\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"164\",\n                \"folderId\": \"149\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x_{rerata}=\\\\operatorname{mean}\\\\left(x_{2}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"165\",\n                \"folderId\": \"149\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"y_{rerata}=\\\\operatorname{mean}\\\\left(y_{2}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"167\",\n                \"folderId\": \"149\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{rerata},y_{rerata}\\\\right),\\\\left(x_{rerata},y_{rerata}+\\\\frac{15}{24}\\\\right)\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"166\",\n                \"folderId\": \"149\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{rerata},y_{rerata}\\\\right),\\\\left(x_{rerata}+\\\\frac{15}{24},y_{rerata}\\\\right)\\\\right)\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"64\",\n                \"title\": \"Visualisasi proyeksi data\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"143\",\n                \"folderId\": \"64\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{15}{24}\\\\left(t_{eksX}+12\\\\right),t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-3.25\",\n                    \"max\": \"-3\"\n                },\n                \"lineWidth\": \"1.5\",\n                \"domain\": {\n                    \"min\": \"-3.25\",\n                    \"max\": \"-3\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"144\",\n                \"folderId\": \"64\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{15}{24}\\\\left(t_{eksY}+12\\\\right),t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-5.25\",\n                    \"max\": \"-5\"\n                },\n                \"lineWidth\": \"1.5\",\n                \"domain\": {\n                    \"min\": \"-5.25\",\n                    \"max\": \"-5\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"64\",\n                \"color\": \"#c74440\",\n                \"latex\": \"y=-3\\\\left\\\\{0\\\\le x\\\\le15\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"64\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"y=-5\\\\left\\\\{0\\\\le x\\\\le15\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"78\",\n                \"folderId\": \"64\",\n                \"text\": \"Data:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"79\",\n                \"folderId\": \"64\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(x_{2},-3\\\\right)\",\n                \"pointOutline\": true,\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"80\",\n                \"folderId\": \"64\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(y_{2},-5\\\\right)\",\n                \"pointOutline\": true,\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"68\",\n                \"folderId\": \"64\",\n                \"text\": \"Teks:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"145\",\n                \"folderId\": \"64\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{15}{24}\\\\left(t_{eksX}+12\\\\right),-3.25\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${t_{eksX}}\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"146\",\n                \"folderId\": \"64\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{15}{24}\\\\left(t_{eksY}+12\\\\right),-5.25\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${t_{eksY}}\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"69\",\n                \"folderId\": \"64\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(-0.1,-3\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"pc1\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".9\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"70\",\n                \"folderId\": \"64\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(-0.1,-5\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"pc2\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".9\",\n                \"pointOpacity\": \".8\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n\n  \/\/ Source\n  var pc11Helper = calculator1.HelperExpression({ latex: 'p_{c11}' });\n  var pc12Helper = calculator1.HelperExpression({ latex: 'p_{c12}' });\n  var pc13Helper = calculator1.HelperExpression({ latex: 'p_{c13}' });\n  var pc14Helper = calculator1.HelperExpression({ latex: 'p_{c14}' });\n  var pc15Helper = calculator1.HelperExpression({ latex: 'p_{c15}' });\n  var pc16Helper = calculator1.HelperExpression({ latex: 'p_{c16}' });\n  var pc17Helper = calculator1.HelperExpression({ latex: 'p_{c17}' });\n  var pc18Helper = calculator1.HelperExpression({ latex: 'p_{c18}' });\n  var pc19Helper = calculator1.HelperExpression({ latex: 'p_{c19}' });\n  var pc110Helper = calculator1.HelperExpression({ latex: 'p_{c110}' });\n  var pc21Helper = calculator1.HelperExpression({ latex: 'p_{c21}' });\n  var pc22Helper = calculator1.HelperExpression({ latex: 'p_{c22}' });\n  var pc23Helper = calculator1.HelperExpression({ latex: 'p_{c23}' });\n  var pc24Helper = calculator1.HelperExpression({ latex: 'p_{c24}' });\n  var pc25Helper = calculator1.HelperExpression({ latex: 'p_{c25}' });\n  var pc26Helper = calculator1.HelperExpression({ latex: 'p_{c26}' });\n  var pc27Helper = calculator1.HelperExpression({ latex: 'p_{c27}' });\n  var pc28Helper = calculator1.HelperExpression({ latex: 'p_{c28}' });\n  var pc29Helper = calculator1.HelperExpression({ latex: 'p_{c29}' });\n  var pc210Helper = calculator1.HelperExpression({ latex: 'p_{c210}' });\n\n  \/\/ Sink\n  pc11Helper.observe('numericValue', function() {\n    var value = pc11Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '168', latex: `p_{c11}=${value}` });\n    }\n  });\n  pc12Helper.observe('numericValue', function() {\n    var value = pc12Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '169', latex: `p_{c12}=${value}` });\n    }\n  });\n  pc13Helper.observe('numericValue', function() {\n    var value = pc13Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '170', latex: `p_{c13}=${value}` });\n    }\n  });\n  pc14Helper.observe('numericValue', function() {\n    var value = pc14Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '171', latex: `p_{c14}=${value}` });\n    }\n  });\n  pc15Helper.observe('numericValue', function() {\n    var value = pc15Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '172', latex: `p_{c15}=${value}` });\n    }\n  });\n  pc16Helper.observe('numericValue', function() {\n    var value = pc16Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '173', latex: `p_{c16}=${value}` });\n    }\n  });\n  pc17Helper.observe('numericValue', function() {\n    var value = pc17Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '174', latex: `p_{c17}=${value}` });\n    }\n  });\n  pc18Helper.observe('numericValue', function() {\n    var value = pc18Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '175', latex: `p_{c18}=${value}` });\n    }\n  });\n  pc19Helper.observe('numericValue', function() {\n    var value = pc19Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '176', latex: `p_{c19}=${value}` });\n    }\n  });\n  pc110Helper.observe('numericValue', function() {\n    var value = pc110Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '177', latex: `p_{c110}=${value}` });\n    }\n  });\n  \n  pc21Helper.observe('numericValue', function() {\n    var value = pc21Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '178', latex: `p_{c21}=${value}` });\n    }\n  });\n  pc22Helper.observe('numericValue', function() {\n    var value = pc22Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '179', latex: `p_{c22}=${value}` });\n    }\n  });\n  pc23Helper.observe('numericValue', function() {\n    var value = pc23Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '180', latex: `p_{c23}=${value}` });\n    }\n  });\n  pc24Helper.observe('numericValue', function() {\n    var value = pc24Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '181', latex: `p_{c24}=${value}` });\n    }\n  });\n  pc25Helper.observe('numericValue', function() {\n    var value = pc25Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '182', latex: `p_{c25}=${value}` });\n    }\n  });\n  pc26Helper.observe('numericValue', function() {\n    var value = pc26Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '183', latex: `p_{c26}=${value}` });\n    }\n  });\n  pc27Helper.observe('numericValue', function() {\n    var value = pc27Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '184', latex: `p_{c27}=${value}` });\n    }\n  });\n  pc28Helper.observe('numericValue', function() {\n    var value = pc28Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '185', latex: `p_{c28}=${value}` });\n    }\n  });\n  pc29Helper.observe('numericValue', function() {\n    var value = pc29Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '186', latex: `p_{c29}=${value}` });\n    }\n  });\n  pc210Helper.observe('numericValue', function() {\n    var value = pc210Helper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '187', latex: `p_{c210}=${value}` });\n    }\n  });\n\n<\/script>\n\n\n\n<p>See how the same data is projected onto pc1 and pc2. Compare with the original space.<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more contents with related topics in this website.<\/p>\n  <ul class=\"topics-list\">\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mathematics\">Mathematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Statistics\">Statistics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Data+Science\">Data Science<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Statistical+Learning\">Statistical Learning<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Machine+Learning\">Machine Learning<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Dimensionality+Reduction\">Dimensionality Reduction<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Exploratory+Data+Analysis\">Exploratory Data Analysis<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Data+Visualization\">Data Visualization<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Computational+Thinking\">Computational Thinking<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Discover how PCA transforms data, reduces dimensions, and highlights patterns through projections.<\/p>\n","protected":false},"author":1,"featured_media":1533,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"advanced_seo_description":"","spay_email":""},"jetpack_shortlink":"https:\/\/wp.me\/P93lma-oq","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1514"}],"collection":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/comments?post=1514"}],"version-history":[{"count":20,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1514\/revisions"}],"predecessor-version":[{"id":1546,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1514\/revisions\/1546"}],"up":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1140"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media\/1533"}],"wp:attachment":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media?parent=1514"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}