{"id":1456,"date":"2025-09-14T04:47:31","date_gmt":"2025-09-13T21:47:31","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=1456"},"modified":"2025-09-14T17:16:16","modified_gmt":"2025-09-14T10:16:16","slug":"reinventing-k-means-clustering","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/reinventing-k-means-clustering\/","title":{"rendered":"Reinventing K-Means Clustering: An Interactive First Step"},"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\/klasterisasi-k-rerata\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">K-means clustering is a classic algorithm in machine learning, but how does it actually start? In this interactive resource, you will explore its very first iteration. Once you understand this step clearly, you will be able to uncover how the following iterations continue until the algorithm finally stops.<\/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\">Reinventing the K-Means Clustering<\/h3>\n\n\n\n<p class=\"has-text-align-center\">Let&#8217;s discover how the first iteration of the algorithm works!<\/p>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n  <div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 440px; height: 440px;\"><\/div>\n  <figcaption>Iteration 1-1<\/figcaption>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<p>You can use these instructions and questions to explore the first step of Iteration 1.<\/p>\n\n\n\n<ul><li>Start by dragging two points (<em>k<\/em> = 2) to random positions within the data.<\/li><li>Notice how the data points are divided into two clusters, one in blue and the other in red. What do you think determines which cluster each point belongs to?<\/li><li>After placing the two points, observe the new points that appear (marked by arrows). In your opinion, how are these new points calculated?<\/li><\/ul>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-white-background-color has-white-color is-style-dots\"\/>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n  <div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 440px; height: 440px;\"><\/div>\n  <figcaption>Iteration 1-2<\/figcaption>\n<\/figure>\n\n<script>\n  var calculator1 = Desmos.GraphingCalculator(document.getElementById('calculator1'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator2 = Desmos.GraphingCalculator(document.getElementById('calculator2'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n\n  var state1 = {\n    \"version\": 11,\n    \"randomSeed\": \"91146fa45d098bcba5d9c0d7e57e31d0\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -5.25,\n            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\"2.021\",\n                            \"4.741\",\n                            \"1.668\",\n                            \"1.677\",\n                            \"2.735\",\n                            \"-0.215\",\n                            \"0.853\",\n                            \"1.01\",\n                            \"4.571\",\n                            \"-1.526\",\n                            \"-2.444\",\n                            \"-3.354\",\n                            \"-2.528\",\n                            \"-2.53\",\n                            \"-1.648\",\n                            \"-0.394\",\n                            \"-1.314\",\n                            \"-3.62\",\n                            \"-0.52\",\n                            \"-1.801\",\n                            \"-3.845\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"4\",\n                        \"color\": \"#388c46\",\n                        \"latex\": \"x_{1}\"\n                    },\n                    {\n                        \"values\": [\n                            \"2.276\",\n                            \"4.768\",\n                            \"2.132\",\n                            \"3.634\",\n                            \"3.297\",\n                            \"1.784\",\n                            \"-0.387\",\n                            \"1.64\",\n                            \"2.954\",\n                            \"0.365\",\n                            \"2.144\",\n                            \"-3.654\",\n                            \"-1.351\",\n                            \"-0.953\",\n                            \"-1.955\",\n                            \"1.261\",\n                            \"-3.104\",\n                            \"-3.348\",\n                            \"-4.456\",\n                            \"-1.222\",\n                            \"-1.26\",\n                            \"-1.969\",\n 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\"viewport\": {\n            \"xmin\": -5.25,\n            \"ymin\": -5.25,\n            \"xmax\": 5.25,\n            \"ymax\": 5.25\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-5.25\",\n            \"xmax\": \"5.25\",\n            \"ymin\": \"-5.25\",\n            \"ymax\": \"5.25\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Data\",\n                \"collapsed\": true\n            },\n            {\n                \"id\": \"6\",\n                \"type\": \"table\",\n                \"folderId\": \"2\",\n                \"columns\": [\n                    {\n                        \"values\": [\n                            \"3.118\",\n                            \"3.344\",\n                            \"2.021\",\n                            \"4.741\",\n                            \"1.668\",\n                            \"1.677\",\n                            \"2.735\",\n                            \"-0.215\",\n                            \"0.853\",\n                            \"1.01\",\n                            \"4.571\",\n                            \"-1.526\",\n                            \"-2.444\",\n                            \"-3.354\",\n                            \"-2.528\",\n                            \"-2.53\",\n                            \"-1.648\",\n                            \"-0.394\",\n                            \"-1.314\",\n                            \"-3.62\",\n                            \"-0.52\",\n                            \"-1.801\",\n                            \"-3.845\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"4\",\n                        \"color\": \"#388c46\",\n                        \"latex\": \"x_{1}\"\n                    },\n                    {\n                        \"values\": [\n                            \"2.276\",\n                            \"4.768\",\n                            \"2.132\",\n                            \"3.634\",\n                            \"3.297\",\n                            \"1.784\",\n                            \"-0.387\",\n                            \"1.64\",\n                            \"2.954\",\n                            \"0.365\",\n                            \"2.144\",\n                            \"-3.654\",\n                            \"-1.351\",\n                            \"-0.953\",\n                            \"-1.955\",\n                            \"1.261\",\n                            \"-3.104\",\n                            \"-3.348\",\n                            \"-4.456\",\n                            \"-1.222\",\n                            \"-1.26\",\n                            \"-1.969\",\n                            \"-2.597\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"5\",\n                        \"color\": \"#6042a6\",\n                        \"latex\": \"y_{1}\"\n                    }\n                ]\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"42\",\n                \"title\": \"Template panah\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"43\",\n                \"folderId\": \"42\",\n                \"color\": \"#000000\",\n                \"latex\": \"p_{1}\\\\left(x\\\\right)=\\\\left(0\\\\cos\\\\left(x\\\\right)-0\\\\sin\\\\left(x\\\\right),0\\\\sin\\\\left(x\\\\right)+0\\\\cos\\\\left(x\\\\right)\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\",\n                \"pointSize\": \"5\",\n                \"movablePointSize\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"44\",\n                \"folderId\": \"42\",\n                \"color\": \"#000000\",\n                \"latex\": \"p_{2}\\\\left(x\\\\right)=\\\\left(-0.25\\\\cos\\\\left(x\\\\right)-0.15\\\\sin\\\\left(x\\\\right),-0.25\\\\sin\\\\left(x\\\\right)+0.15\\\\cos\\\\left(x\\\\right)\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\",\n                \"pointSize\": \"5\",\n                \"movablePointSize\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"45\",\n                \"folderId\": \"42\",\n                \"color\": \"#000000\",\n                \"latex\": \"p_{3}\\\\left(x\\\\right)=\\\\left(-0.2\\\\cos\\\\left(x\\\\right)-0\\\\sin\\\\left(x\\\\right),-0.2\\\\sin\\\\left(x\\\\right)+0\\\\cos\\\\left(x\\\\right)\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\",\n                \"pointSize\": \"5\",\n                \"movablePointSize\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"47\",\n                \"folderId\": \"42\",\n                \"color\": \"#000000\",\n                \"latex\": \"p_{4}\\\\left(x\\\\right)=\\\\left(-0.25\\\\cos\\\\left(x\\\\right)+0.15\\\\sin\\\\left(x\\\\right),-0.25\\\\sin\\\\left(x\\\\right)-0.15\\\\cos\\\\left(x\\\\right)\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\",\n                \"pointSize\": \"5\",\n                \"movablePointSize\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"49\",\n                \"folderId\": \"42\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(p_{1}\\\\left(0\\\\right),p_{2}\\\\left(0\\\\right),p_{3}\\\\left(0\\\\right),p_{4}\\\\left(0\\\\right)\\\\right)\",\n                \"hidden\": true,\n                \"lines\": false,\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"9\",\n                \"title\": \"Iterasi 1.2\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"52\",\n                \"folderId\": \"9\",\n                \"text\": \"Kondisi pengelompokan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"39\",\n                \"folderId\": \"9\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(b_{1y}-a_{1y}\\\\right)\\\\left(y-C_{1}.y\\\\right)=-\\\\left(b_{1x}-a_{1x}\\\\right)\\\\left(x-C_{1}.x\\\\right)\",\n                \"lines\": true,\n                \"fillOpacity\": \".2\",\n                \"lineWidth\": \"3\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"27\",\n                \"folderId\": \"9\",\n                \"color\": \"#000000\",\n                \"latex\": \"P_{1}=\\\\left\\\\{\\\\left(b_{1y}-a_{1y}\\\\right)\\\\left(a_{1y}-C_{1}.y\\\\right)\\\\le-\\\\left(b_{1x}-a_{1x}\\\\right)\\\\left(a_{1x}-C_{1}.x\\\\right):1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"32\",\n                \"folderId\": \"9\",\n                \"color\": \"#000000\",\n                \"latex\": \"P_{2}\\\\left(x,y\\\\right)=\\\\left\\\\{\\\\left(b_{1y}-a_{1y}\\\\right)\\\\left(y-C_{1}.y\\\\right)\\\\le-\\\\left(b_{1x}-a_{1x}\\\\right)\\\\left(x-C_{1}.x\\\\right):1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"54\",\n                \"folderId\": \"9\",\n                \"text\": \"Menampilkan titik-titik tiap kelompok:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"29\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"K_{1}=\\\\left(x_{1},y_{1}\\\\right)\\\\left\\\\{P_{2}\\\\left(x_{1},y_{1}\\\\right)=1\\\\right\\\\}\",\n                \"pointSize\": \"15\",\n                \"movablePointSize\": \"15\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"35\",\n                \"folderId\": \"9\",\n                \"color\": \"#000000\",\n                \"latex\": \"L_{1}=\\\\left\\\\{P_{2}\\\\left(x_{1},y_{1}\\\\right)=1:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"33\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"K_{2}=\\\\left(x_{1},y_{1}\\\\right)\\\\left\\\\{P_{2}\\\\left(x_{1},y_{1}\\\\right)=0\\\\right\\\\}\",\n                \"pointSize\": \"15\",\n                \"movablePointSize\": \"15\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"56\",\n                \"folderId\": \"9\",\n                \"text\": \"Titik tengah lanjutan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"10\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"A_{1}=\\\\left(a_{1x},a_{1y}\\\\right)\",\n                \"hidden\": true,\n                \"pointStyle\": \"CROSS\",\n                \"dragMode\": \"NONE\",\n                \"pointSize\": \"15\",\n                \"movablePointSize\": \"15\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"58\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(a_{1x}+t,a_{1y}+t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \"8\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"59\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(a_{1x}+t,a_{1y}-t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \"8\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"60\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(a_{1x}+t,a_{1y}+t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"lineWidth\": \"4\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"61\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(a_{1x}+t,a_{1y}-t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"lineWidth\": \"4\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"9\",\n                \"color\": \"#388c46\",\n                \"latex\": \"a_{1x}=-3\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"-5\",\n                    \"max\": \"0\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"12\",\n                \"folderId\": \"9\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"a_{1y}=3\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"-5\",\n                    \"max\": \"5\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"13\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"B_{1}=\\\\left(b_{1x},b_{1y}\\\\right)\",\n                \"hidden\": true,\n                \"pointStyle\": \"CROSS\",\n                \"dragMode\": \"NONE\",\n                \"pointSize\": \"15\",\n                \"movablePointSize\": \"15\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(b_{1x}+t,b_{1y}+t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \"8\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(b_{1x}+t,b_{1y}-t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"colorLatex\": \"w_{putih}\",\n                \"lineWidth\": \"8\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"67\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(b_{1x}+t,b_{1y}+t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"lineWidth\": \"4\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"68\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(b_{1x}+t,b_{1y}-t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                },\n                \"lineWidth\": \"4\",\n                \"domain\": {\n                    \"min\": \"-0.2\",\n                    \"max\": \"0.2\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"9\",\n                \"color\": \"#c74440\",\n                \"latex\": \"b_{1x}=3\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0.1\",\n                    \"max\": \"5\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"15\",\n                \"folderId\": \"9\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"b_{1y}=-3\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"-5\",\n                    \"max\": \"5\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"19\",\n                \"folderId\": \"9\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{1}=\\\\left(\\\\frac{a_{1x}+b_{1x}}{2},\\\\frac{a_{1y}+b_{1y}}{2}\\\\right)\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"63\",\n                \"title\": \"Warna\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"64\",\n                \"folderId\": \"63\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"w_{putih}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n\n  \/\/ Source\n  var C1xHelper = calculator1.HelperExpression({ latex: 'C_{K1x}' });\n  var C1yHelper = calculator1.HelperExpression({ latex: 'C_{K1y}' });\n  var C2xHelper = calculator1.HelperExpression({ latex: 'C_{K2x}' });\n  var C2yHelper = calculator1.HelperExpression({ latex: 'C_{K2y}' });\n\n  \/\/ Sink\n  C1xHelper.observe('numericValue', function() {\n    var value = C1xHelper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '11', latex: `a_{1x}=${value}` });\n    }\n  });\n  C1yHelper.observe('numericValue', function() {\n    var value = C1yHelper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '12', latex: `a_{1y}=${value}` });\n    }\n  });\n  C2xHelper.observe('numericValue', function() {\n    var value = C2xHelper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '14', latex: `b_{1x}=${value}` });\n    }\n  });\n  C2yHelper.observe('numericValue', function() {\n    var value = C2yHelper.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '15', latex: `b_{1y}=${value}` });\n    }\n  });\n\n<\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<p>Use these prompts to compare the clusters and resulted points after the first update in Iteration 1.<\/p>\n\n\n\n<ul><li>The two cross-shaped points you see here are the updated positions from the previous step.<\/li><li>Compare the clusters in Iteration 1-2 with those in Iteration 1-1. Are they the same, or have they changed? If they changed, how?<\/li><li>What do you think will happen in Iteration 2? When do you think the iterations will stop?<\/li><\/ul>\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=Clustering\">Clustering<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Cluster+Analysis\">Cluster Analysis<\/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 k-means clustering, one of the most widely used machine learning algorithms, works from the ground up. This interactive tool lets you choose initial points, watch how clusters form, and see how centroids shift. A hands-on way to explore the basics of machine learning and data science as well as promote computational thinking.<\/p>\n","protected":false},"author":1,"featured_media":1471,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"advanced_seo_description":"","spay_email":""},"jetpack_shortlink":"https:\/\/wp.me\/P93lma-nu","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1456"}],"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=1456"}],"version-history":[{"count":27,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1456\/revisions"}],"predecessor-version":[{"id":1508,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1456\/revisions\/1508"}],"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\/1471"}],"wp:attachment":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media?parent=1456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}