{"id":6050,"date":"2026-04-04T13:30:55","date_gmt":"2026-04-04T18:30:55","guid":{"rendered":"https:\/\/ykim.synology.me\/wordpress\/?p=6050"},"modified":"2026-04-17T20:50:18","modified_gmt":"2026-04-18T01:50:18","slug":"time-series-vectorization-and-embedding-in-ai-ml","status":"publish","type":"post","link":"https:\/\/ykim.synology.me\/wordpress\/time-series-vectorization-and-embedding-in-ai-ml-6050\/","title":{"rendered":"Time Series Vectorization and Embedding in AI\/ML"},"content":{"rendered":"<p>\r\n    <style>\r\n    .k-page-nav { margin-bottom:20px; padding:10px 0; }\r\n    .k-page-nav a, .k-page-nav span {\r\n        display:block; padding:6px 10px; margin-bottom:6px;\r\n        background:#eee; border-radius:4px; text-decoration:none;\r\n        color:#333; font-weight:500;\r\n    }\r\n    .k-page-nav span { background:#333; color:#fff; }\r\n    <\/style>\r\n\r\n    <div class=\"k-page-nav\">\r\n                                    <span>Time Series Vectorization vs. Embedding \ud83d\udd0d \u2014 Page 1<\/span>\r\n                                                <a href=\"https:\/\/ykim.synology.me\/wordpress\/time-series-vectorization-and-embedding-in-ai-ml-6050\/2\/\" class=\"post-page-numbers\">                    Taxonomy Hierarchy \ud83c\udf33 \u2014 Page 2                <\/a>\r\n                                                <a href=\"https:\/\/ykim.synology.me\/wordpress\/time-series-vectorization-and-embedding-in-ai-ml-6050\/3\/\" class=\"post-page-numbers\">                    Comprehensive Guide to Time Series Vectorization \u2014 Page 3                <\/a>\r\n                                                <a href=\"https:\/\/ykim.synology.me\/wordpress\/time-series-vectorization-and-embedding-in-ai-ml-6050\/4\/\" class=\"post-page-numbers\">                    Comprehensive Guide to Time Series Embedding in AI\/ML \u2014 Page 4                <\/a>\r\n                                                <a href=\"https:\/\/ykim.synology.me\/wordpress\/time-series-vectorization-and-embedding-in-ai-ml-6050\/5\/\" class=\"post-page-numbers\">                    Modeling Inter-Sensor Interactions in Time Series Vectorization for AI\/ML \u2014 Page 5                <\/a>\r\n                        <\/div>\r\n\r\n    <\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" style=\"margin-top:var(--wp--preset--spacing--60);margin-bottom:var(--wp--preset--spacing--60)\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Time Series Vectorization vs. Embedding \ud83d\udd0d<\/h2>\n\n\n<style>.kb-table-container6050_59d999-c2{padding-right:var(--global-kb-spacing-5xl, 10rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);overflow-x:auto;}.kb-table6050_59d999-c2 td:nth-of-type(1), .kb-table6050_59d999-c2 th:nth-of-type(1){width:10%;}.kb-table6050_59d999-c2{table-layout:fixed;width:100%;}.kb-table-container .kb-table6050_59d999-c2 th{padding-top:var(--global-kb-spacing-xxs, 0.5rem);padding-right:var(--global-kb-spacing-xxs, 0.5rem);padding-bottom:var(--global-kb-spacing-xxs, 0.5rem);padding-left:var(--global-kb-spacing-xxs, 0.5rem);text-align:center;}.kb-table-container .kb-table6050_59d999-c2 caption{text-align:center;}.kb-table-container .kb-table6050_59d999-c2 td{padding-top:var(--global-kb-spacing-xxs, 0.5rem);padding-right:var(--global-kb-spacing-xxs, 0.5rem);padding-bottom:var(--global-kb-spacing-xxs, 0.5rem);padding-left:var(--global-kb-spacing-xxs, 0.5rem);text-align:left;}.kb-table-container .kb-table6050_59d999-c2 tr{border-top:1px solid var(--global-palette5, #4A5568);border-right:1px solid var(--global-palette5, #4A5568);border-bottom:1px solid var(--global-palette5, #4A5568);border-left:1px solid var(--global-palette5, #4A5568);}@media all and (max-width: 1024px){.kb-table-container .kb-table6050_59d999-c2 tr{border-top:1px solid var(--global-palette5, #4A5568);border-right:1px solid var(--global-palette5, #4A5568);border-bottom:1px solid var(--global-palette5, #4A5568);border-left:1px solid var(--global-palette5, #4A5568);}}@media all and (max-width: 767px){.kb-table-container .kb-table6050_59d999-c2 tr{border-top:1px solid var(--global-palette5, #4A5568);border-right:1px solid var(--global-palette5, #4A5568);border-bottom:1px solid var(--global-palette5, #4A5568);border-left:1px solid var(--global-palette5, #4A5568);}}<\/style><div class=\"kb-table-container kb-table-container6050_59d999-c2 wp-block-kadence-table\"><table class=\"kb-table kb-table6050_59d999-c2\">\n<tr class=\"kb-table-row kb-table-row6050_994e09-d8\">\n<th class=\"kb-table-data kb-table-data6050_6fc097-ca\">\n\n<p class=\"wp-block-paragraph\">\uad6c\ubd84<\/p>\n\n<\/th>\n\n<th class=\"kb-table-data kb-table-data6050_6b2e43-06\">\n\n<p class=\"wp-block-paragraph\">Time Series Vectorization (\ubca1\ud130\ud654)<\/p>\n\n<\/th>\n\n<th class=\"kb-table-data kb-table-data6050_1c131d-e1\">\n\n<p class=\"wp-block-paragraph\">Time Series Embedding (\uc784\ubca0\ub529)<\/p>\n\n<\/th>\n<\/tr>\n\n<tr class=\"kb-table-row kb-table-row6050_d5a6c8-f0\">\n<td class=\"kb-table-data kb-table-data6050_507302-ed\">\n\n<p class=\"wp-block-paragraph\"><strong>\uae30\ubcf8 \uac1c\ub150<\/strong><\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_015e5f-78\">\n\n<p class=\"wp-block-paragraph\">\uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \uc218\ud559\uc801 \ubaa8\ub378\uc774 \uc774\ud574\ud560 \uc218 \uc788\ub294 \ud615\ud0dc(\uace0\uc815\ub41c \uae38\uc774\uc758 \ubca1\ud130)\ub85c \ubcc0\ud658\ud558\ub294 \uacfc\uc815<\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_e1c7e9-a6\">\n\n<p class=\"wp-block-paragraph\">\uace0\ucc28\uc6d0 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \uc800\ucc28\uc6d0\uc758 \ubc00\uc9d1\ub41c \uacf5\uac04(Dense Space)\uc73c\ub85c \ud22c\uc601\ud558\uc5ec \uc758\ubbf8\uc801 \uad00\uacc4\ub97c \ud559\uc2b5\ud558\ub294 \uacfc\uc815<\/p>\n\n<\/td>\n<\/tr>\n\n<tr class=\"kb-table-row kb-table-row6050_adbd38-68\">\n<td class=\"kb-table-data kb-table-data6050_675a51-0e\">\n\n<p class=\"wp-block-paragraph\"><strong>\ubcc0\ud658 \ubc29\uc2dd<\/strong><\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_203fbd-99\">\n\n<p class=\"wp-block-paragraph\">\uc8fc\ub85c \uacb0\uc815\ub860\uc801(Deterministic) \ubc29\uc2dd (\ud1b5\uacc4\uac12, \uc8fc\ud30c\uc218 \ubcc0\ud658 \ub4f1)<\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_9fa65b-d8\">\n\n<p class=\"wp-block-paragraph\">\ud559\uc2b5 \uae30\ubc18(Learning-based) \ubc29\uc2dd (\uc2e0\uacbd\ub9dd, \ub525\ub7ec\ub2dd \ubaa8\ub378 \uc0ac\uc6a9)<\/p>\n\n<\/td>\n<\/tr>\n\n<tr class=\"kb-table-row kb-table-row6050_a53305-9f\">\n<td class=\"kb-table-data kb-table-data6050_dca2de-c9\">\n\n<p class=\"wp-block-paragraph\"><strong>\ud2b9\uc9d5 \ucd94\ucd9c<\/strong><\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_d8f1cc-70\">\n\n<p class=\"wp-block-paragraph\">\uc218\uc791\uc5c5 \uae30\ubc18(Hand-crafted) \ud2b9\uc131 (\ud3c9\uade0, \ubd84\uc0b0, \uc65c\ub3c4, FFT \ub4f1)<\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_d587f6-42\">\n\n<p class=\"wp-block-paragraph\">\ubaa8\ub378\uc774 \uc2a4\uc2a4\ub85c \uc720\uc6a9\ud55c \ud328\ud134\uc744 \ud559\uc2b5 (Hidden Representation)<\/p>\n\n<\/td>\n<\/tr>\n\n<tr class=\"kb-table-row kb-table-row6050_1a1750-95\">\n<td class=\"kb-table-data kb-table-data6050_f1f9de-1a\">\n\n<p class=\"wp-block-paragraph\"><strong>\uacf5\uac04\uc758 \ud2b9\uc131<\/strong><\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_8cf849-82\">\n\n<p class=\"wp-block-paragraph\">\ub370\uc774\ud130\uc758 \ud1b5\uacc4\uc801 \uc18d\uc131\uc744 \ub098\uc5f4\ud568 (\ud76c\uc18c\ud560 \uc218 \uc788\uc74c)<\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_9590e5-02\">\n\n<p class=\"wp-block-paragraph\">\uc720\uc0ac\ud55c \ud328\ud134\uc744 \uac00\uc9c4 \uc2dc\uacc4\uc5f4\uc774 \uae30\ud558\ud559\uc801\uc73c\ub85c \uac00\uae5d\uac8c \ubc30\uce58\ub428 (\ubc00\uc9d1 \ubca1\ud130)<\/p>\n\n<\/td>\n<\/tr>\n\n<tr class=\"kb-table-row kb-table-row6050_ced2a2-06\">\n<td class=\"kb-table-data kb-table-data6050_de01f7-e3\">\n\n<p class=\"wp-block-paragraph\"><strong>\uc8fc\uc694 \uc0ac\ub840<\/strong><\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_feca6f-d2\">\n\n<p class=\"wp-block-paragraph\">TSFRESH, \ud1b5\uacc4\uc801 \uc694\uc57d, \uc6d0-\ud56b \uc778\ucf54\ub529<\/p>\n\n<\/td>\n\n<td class=\"kb-table-data kb-table-data6050_de8aa1-6b\">\n\n<p class=\"wp-block-paragraph\">Time2Vec, Word2Vec \uc2a4\ud0c0\uc77c\uc758 \uc2dc\ud000\uc2a4 \ud559\uc2b5, TS2Vec, RNN\/Transformer\uc758 Hidden State<\/p>\n\n<\/td>\n<\/tr>\n<\/table><\/div>\n\n\n<h5 class=\"wp-block-heading\">1. Time Series Vectorization (\ubca1\ud130\ud654)<\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ubaa9\uc801:<\/strong> \uc6d0\uc2dc(Raw) \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \uba38\uc2e0\ub7ec\ub2dd \uc54c\uace0\ub9ac\uc998(SVM, Random Forest \ub4f1)\uc758 \uc785\ub825\uac12\uc73c\ub85c \uc4f0\uae30 \uc704\ud574 \uc77c\uc815\ud55c \uae38\uc774\uc758 \ubc30\uc5f4\ub85c \ub9cc\ub4dc\ub294 \ub370 \uc9d1\uc911\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ud2b9\uc9d5:<\/strong>\n<ul class=\"wp-block-list\">\n<li>\ud1b5\uacc4\uc801 \ud2b9\uc9d5(Statistical features)\uc744 \ucd94\ucd9c\ud558\ub294 \uacbd\uc6b0\uac00 \ub9ce\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc608\uc2dc:<\/strong> [\ucd5c\uc19f\uac12, \ucd5c\ub313\uac12, \ud3c9\uade0, \ud45c\uc900\ud3b8\ucc28, \ud2b8\ub80c\ub4dc \uacc4\uc218]\uc640 \uac19\uc740 \ud615\ud0dc.<\/li>\n\n\n\n<li>\ub3c4\uba54\uc778 \uc9c0\uc2dd\uc774 \ub9ce\uc774 \ubc18\uc601\ub418\uba70, \ubcc0\ud658 \uacfc\uc815\uc774 \ud22c\uba85\ud558\uc5ec \ud574\uc11d\uc774 \uc27d\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2. Time Series Embedding (\uc784\ubca0\ub529)<\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ubaa9\uc801:<\/strong> \ub370\uc774\ud130 \uac04\uc758 &#8216;\uad00\uacc4&#8217;\uc640 &#8216;\ub9e5\ub77d&#8217;\uc744 \ubcf4\uc874\ud558\uba74\uc11c \ub370\uc774\ud130\ub97c \uc555\ucd95\ud558\uc5ec \ud45c\ud604\ud558\ub294 \ub370 \uc9d1\uc911\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ud2b9\uc9d5:<\/strong>\n<ul class=\"wp-block-list\">\n<li>\ub274\ub7f4 \ub124\ud2b8\uc6cc\ud06c\ub97c \ud1b5\ud574 \ub370\uc774\ud130\uc758 \uc7a0\uc7ac\uc801\uc778(Latent) \ud2b9\uc9d5\uc744 \ud3ec\ucc29\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc608\uc2dc:<\/strong> CNN\uc774\ub098 RNN\uc758 \ub9c8\uc9c0\ub9c9 \uce35\uc5d0\uc11c \ub098\uc628 \ucd9c\ub825\uac12.<\/li>\n\n\n\n<li>\ub2e8\uc21c\ud55c \uc218\uce58 \ub098\uc5f4\uc744 \ub118\uc5b4, \uc720\uc0ac\ud55c \ubcc0\ub3d9 \ud328\ud134\uc744 \uac00\uc9c4 \uc2dc\uacc4\uc5f4\ub4e4\uc774 \uc784\ubca0\ub529 \uacf5\uac04 \ub0b4\uc5d0\uc11c \uac00\uae5d\uac8c \uc704\uce58\ud558\ub3c4\ub85d \ud559\uc2b5\ub429\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">Taxonomy Hierarchy \ud83c\udf33<\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:1rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#24292e;--cbp-line-number-width:calc(3 * 0.6 * 1rem);line-height:1.625rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span role=\"button\" tabindex=\"0\" style=\"color:#24292e;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n Page 1: Time Series Vectorization vs. Embedding\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n\nTime Series Representation\n\u2502\n\u251c\u2500\u2500 Vectorization\n\u2502   \u251c\u2500\u2500 Deterministic\n\u2502   \u251c\u2500\u2500 Hand-crafted Features\n\u2502   \u2502   \u251c\u2500\u2500 Statistical Summary\n\u2502   \u2502   \u251c\u2500\u2500 FFT\n\u2502   \u2502   \u2514\u2500\u2500 One-hot Encoding\n\u2502   \u251c\u2500\u2500 Interpretable\n\u2502   \u251c\u2500\u2500 Sparse Space\n\u2502   \u2514\u2500\u2500 Examples\n\u2502       \u251c\u2500\u2500 TSFRESH\n\u2502       \u2514\u2500\u2500 Statistical Summary\n\u2502\n\u2514\u2500\u2500 Embedding\n    \u251c\u2500\u2500 Learning-based\n    \u251c\u2500\u2500 Latent Representation\n    \u2502   \u251c\u2500\u2500 Neural Network\n    \u2502   \u2514\u2500\u2500 Deep Learning\n    \u251c\u2500\u2500 Dense Space\n    \u251c\u2500\u2500 Semantic Relationship\n    \u2514\u2500\u2500 Examples\n        \u251c\u2500\u2500 Time2Vec\n        \u251c\u2500\u2500 Word2Vec-style\n        \u251c\u2500\u2500 TS2Vec\n        \u2514\u2500\u2500 RNN\/Transformer Hidden State\n\n\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n Page 2: Comprehensive Guide to Time Series Vectorization\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n\nTime Series Vectorization\n\u2502\n\u251c\u2500\u2500 Feature-based\n\u2502   \u251c\u2500\u2500 Statistical Moments\n\u2502   \u2502   \u251c\u2500\u2500 Mean \/ Median\n\u2502   \u2502   \u251c\u2500\u2500 Std \/ Variance\n\u2502   \u2502   \u251c\u2500\u2500 Skewness \/ Kurtosis\n\u2502   \u2502   \u2514\u2500\u2500 Quantiles \/ IQR\n\u2502   \u2514\u2500\u2500 Temporal &amp; Structural\n\u2502       \u251c\u2500\u2500 Autocorrelation\n\u2502       \u251c\u2500\u2500 Peaks \/ Valleys\n\u2502       \u251c\u2500\u2500 Slope \/ Trend\n\u2502       \u2514\u2500\u2500 Crossing Rates\n\u2502\n\u251c\u2500\u2500 Frequency-Domain\n\u2502   \u251c\u2500\u2500 Fourier Transform (FFT)\n\u2502   \u2514\u2500\u2500 Wavelet Transform\n\u2502\n\u251c\u2500\u2500 Model-based\n\u2502   \u251c\u2500\u2500 ARMA \/ ARIMA Parameters\n\u2502   \u2514\u2500\u2500 SAX (Symbolic Aggregate Approximation)\n\u2502\n\u251c\u2500\u2500 Automated Libraries\n\u2502   \u251c\u2500\u2500 TSFRESH\n\u2502   \u2514\u2500\u2500 Catch22\n\u2502\n\u2514\u2500\u2500 Dimensionality Reduction\n    \u251c\u2500\u2500 PCA\n    \u2514\u2500\u2500 SVD\n\n\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n Page 3: Comprehensive Guide to Time Series Embedding\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n\nTime Series Embedding\n\u2502\n\u251c\u2500\u2500 Methodologies\n\u2502   \u251c\u2500\u2500 Supervised\n\u2502   \u2502   \u251c\u2500\u2500 LSTM\n\u2502   \u2502   \u2514\u2500\u2500 CNN\n\u2502   \u251c\u2500\u2500 Unsupervised \/ Self-Supervised\n\u2502   \u2502   \u251c\u2500\u2500 Autoencoder (AE)\n\u2502   \u2502   \u251c\u2500\u2500 Contrastive Learning\n\u2502   \u2502   \u2502   \u251c\u2500\u2500 TS2Vec\n\u2502   \u2502   \u2502   \u2514\u2500\u2500 TNC\n\u2502   \u2502   \u2514\u2500\u2500 Generative Models\n\u2502   \u2502       \u251c\u2500\u2500 VAE\n\u2502   \u2502       \u2514\u2500\u2500 GAN\n\u2502   \u251c\u2500\u2500 Shapelet-based\n\u2502   \u2502   \u2514\u2500\u2500 Learning Shapelets\n\u2502   \u2514\u2500\u2500 Prototype-based\n\u2502       \u2514\u2500\u2500 TapNet\n\u2502\n\u2514\u2500\u2500 Architectures\n    \u251c\u2500\u2500 Recurrent Neural Networks\n    \u2502   \u251c\u2500\u2500 RNN\n    \u2502   \u251c\u2500\u2500 LSTM\n    \u2502   \u2514\u2500\u2500 GRU\n    \u251c\u2500\u2500 Temporal Convolutional Networks\n    \u2502   \u2514\u2500\u2500 Dilated Causal Convolution\n    \u2514\u2500\u2500 Transformers \/ Attention\n        \u251c\u2500\u2500 Informer\n        \u251c\u2500\u2500 Autoformer\n        \u2514\u2500\u2500 PatchTST\n\n\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n Page 4: Modeling Inter-Sensor Interactions in Vectorization\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n\nInter-Sensor Interaction Vectorization\n\u2502\n\u251c\u2500\u2500 Spatial-Temporal Learning\n\u2502   \u251c\u2500\u2500 Graph Neural Networks (GNN)\n\u2502   \u2502   \u251c\u2500\u2500 Static Graph\n\u2502   \u2502   \u2514\u2500\u2500 Dynamic Graph\n\u2502   \u2502       \u2514\u2500\u2500 Adaptive Adjacency Matrix\n\u2502   \u2514\u2500\u2500 Graph Convolutional Networks (GCN)\n\u2502\n\u251c\u2500\u2500 Attention \/ Transformers\n\u2502   \u251c\u2500\u2500 Multi-Head Self-Attention\n\u2502   \u2502   \u251c\u2500\u2500 Temporal Attention\n\u2502   \u2502   \u2514\u2500\u2500 Spatial (Sensor) Attention\n\u2502   \u2514\u2500\u2500 Cross-Dimension Attention\n\u2502       \u2514\u2500\u2500 Cross-Variable Dependency\n\u2502\n\u251c\u2500\u2500 Convolutional Approaches\n\u2502   \u251c\u2500\u2500 2D CNN (Time \u00d7 Sensor Image)\n\u2502   \u2502   \u2514\u2500\u2500 Intersensor Correlation Heatmap\n\u2502   \u2502       \u251c\u2500\u2500 Pearson Correlation\n\u2502   \u2502       \u2514\u2500\u2500 Mutual Information\n\u2502   \u2514\u2500\u2500 Dilated Convolution\n\u2502\n\u2514\u2500\u2500 Correlation &amp; Decomposition\n    \u251c\u2500\u2500 Multi-view Vectorization\n    \u2502   \u2514\u2500\u2500 Deep CCA (DCCA)\n    \u2514\u2500\u2500 Tensor Decomposition\n        \u251c\u2500\u2500 Tucker Decomposition\n        \u2514\u2500\u2500 CP Decomposition<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki github-light\" style=\"background-color: #fff\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\"> Page 1: Time Series Vectorization vs. Embedding<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">Time Series Representation<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Vectorization<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Deterministic<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Hand-crafted Features<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Statistical Summary<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 FFT<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 One-hot Encoding<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Interpretable<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Sparse Space<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Examples<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u251c\u2500\u2500 TSFRESH<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u2514\u2500\u2500 Statistical Summary<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2514\u2500\u2500 Embedding<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Learning-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Latent Representation<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u251c\u2500\u2500 Neural Network<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u2514\u2500\u2500 Deep Learning<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Dense Space<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Semantic Relationship<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2514\u2500\u2500 Examples<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u251c\u2500\u2500 Time2Vec<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u251c\u2500\u2500 Word2Vec-style<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u251c\u2500\u2500 TS2Vec<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u2514\u2500\u2500 RNN\/Transformer Hidden State<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\"> Page 2: Comprehensive Guide to Time Series Vectorization<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">Time Series Vectorization<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Feature-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Statistical Moments<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Mean \/ Median<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Std \/ Variance<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Skewness \/ Kurtosis<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 Quantiles \/ IQR<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Temporal &amp; Structural<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u251c\u2500\u2500 Autocorrelation<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u251c\u2500\u2500 Peaks \/ Valleys<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u251c\u2500\u2500 Slope \/ Trend<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u2514\u2500\u2500 Crossing Rates<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Frequency-Domain<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Fourier Transform (FFT)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Wavelet Transform<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Model-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 ARMA \/ ARIMA Parameters<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 SAX (Symbolic Aggregate Approximation)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Automated Libraries<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 TSFRESH<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Catch22<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2514\u2500\u2500 Dimensionality Reduction<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 PCA<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2514\u2500\u2500 SVD<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\"> Page 3: Comprehensive Guide to Time Series Embedding<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">Time Series Embedding<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Methodologies<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Supervised<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 LSTM<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 CNN<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Unsupervised \/ Self-Supervised<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Autoencoder (AE)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Contrastive Learning<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2502   \u251c\u2500\u2500 TS2Vec<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2502   \u2514\u2500\u2500 TNC<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 Generative Models<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502       \u251c\u2500\u2500 VAE<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502       \u2514\u2500\u2500 GAN<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Shapelet-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 Learning Shapelets<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Prototype-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u2514\u2500\u2500 TapNet<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2514\u2500\u2500 Architectures<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Recurrent Neural Networks<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u251c\u2500\u2500 RNN<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u251c\u2500\u2500 LSTM<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u2514\u2500\u2500 GRU<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Temporal Convolutional Networks<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u2514\u2500\u2500 Dilated Causal Convolution<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2514\u2500\u2500 Transformers \/ Attention<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u251c\u2500\u2500 Informer<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u251c\u2500\u2500 Autoformer<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u2514\u2500\u2500 PatchTST<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\"> Page 4: Modeling Inter-Sensor Interactions in Vectorization<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">Inter-Sensor Interaction Vectorization<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Spatial-Temporal Learning<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Graph Neural Networks (GNN)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Static Graph<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 Dynamic Graph<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502       \u2514\u2500\u2500 Adaptive Adjacency Matrix<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Graph Convolutional Networks (GCN)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Attention \/ Transformers<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Multi-Head Self-Attention<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u251c\u2500\u2500 Temporal Attention<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 Spatial (Sensor) Attention<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Cross-Dimension Attention<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502       \u2514\u2500\u2500 Cross-Variable Dependency<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Convolutional Approaches<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 2D CNN (Time \u00d7 Sensor Image)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502   \u2514\u2500\u2500 Intersensor Correlation Heatmap<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502       \u251c\u2500\u2500 Pearson Correlation<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2502       \u2514\u2500\u2500 Mutual Information<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Dilated Convolution<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2514\u2500\u2500 Correlation &amp; Decomposition<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u251c\u2500\u2500 Multi-view Vectorization<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2502   \u2514\u2500\u2500 Deep CCA (DCCA)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2514\u2500\u2500 Tensor Decomposition<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u251c\u2500\u2500 Tucker Decomposition<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">        \u2514\u2500\u2500 CP Decomposition<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">Comprehensive Guide to Time Series Vectorization<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. Introduction to Time Series Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Time Series Vectorization is the foundational process of transforming raw, sequential data points into a structured, numerical format that machine learning models can process. Unlike static data, time series data is characterized by its temporal ordering, where the relative position of each data point conveys critical information about trends, seasonality, and cycles. Vectorization serves as the bridge between raw observations and the mathematical input required by algorithms like Support Vector Machines (SVM), Random Forests, and Gradient Boosting Trees [1].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. The Core Challenge of Time Series Data<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The primary difficulty in time series analysis is that raw data often varies in length, contains noise, or has non-stationary properties. Traditional machine learning models require a fixed-length input vector (a &#8220;feature vector&#8221;). Vectorization solves this by summarizing a sequence of arbitrary length into a fixed set of informative dimensions. This process is distinct from embedding, as vectorization often relies on explicit, human-interpretable statistical properties or mathematical transformations rather than learned latent representations [2].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Techniques for Feature-Based Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Feature-based vectorization is the most common approach in industrial applications. It involves extracting specific descriptive statistics from a time window.<\/p>\n\n\n<style>.kadence-column6050_50e5e1-af > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_50e5e1-af > .kt-inside-inner-col,.kadence-column6050_50e5e1-af > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_50e5e1-af > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_50e5e1-af > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_50e5e1-af > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_50e5e1-af > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_50e5e1-af{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_50e5e1-af > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_50e5e1-af > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_50e5e1-af\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">3.1. Statistical Moments and Distributional Features<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Basic vectorization begins with calculating the moments of the data distribution within a specific timeframe. These include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mean and Median:<\/strong> Representing the central tendency of the series.<\/li>\n\n\n\n<li><strong>Standard Deviation and Variance:<\/strong> Capturing the volatility or spread.<\/li>\n\n\n\n<li><strong>Skewness and Kurtosis:<\/strong> Identifying the asymmetry and &#8220;tailedness&#8221; of the data distribution.<\/li>\n\n\n\n<li><strong>Quantiles and Interquartile Range (IQR):<\/strong> Providing a robust measure of data dispersion against outliers [3].<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">3.2. Temporal and Structural Features<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Beyond simple statistics, vectorization captures the &#8220;shape&#8221; of the data.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Autocorrelation:<\/strong> Measuring how a signal correlates with a delayed version of itself.<\/li>\n\n\n\n<li><strong>Number of Peaks and Valleys:<\/strong> Identifying the frequency of local extrema.<\/li>\n\n\n\n<li><strong>Slope\/Trend:<\/strong> Determining the linear or non-linear rate of change over time.<\/li>\n\n\n\n<li><strong>Crossing Rates:<\/strong> Calculating how often the series crosses its mean or zero, which indicates oscillation frequency [1].<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">4. Frequency-Domain Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sometimes, the most important information is not when something happened, but how often. Signal processing techniques allow for vectorization in the frequency domain.<\/p>\n\n\n<style>.kadence-column6050_22c7f5-cb > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_22c7f5-cb > .kt-inside-inner-col,.kadence-column6050_22c7f5-cb > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_22c7f5-cb > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_22c7f5-cb > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_22c7f5-cb > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_22c7f5-cb > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_22c7f5-cb{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_22c7f5-cb > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_22c7f5-cb > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_22c7f5-cb\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">4.1. Fourier Transforms (FFT)<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">The Fast Fourier Transform (FFT) decomposes a time-based signal into its constituent frequencies. The resulting coefficients (amplitudes and phases of sine waves) form a vector that describes the periodic nature of the series. This is particularly useful for identifying seasonality in data like electricity consumption or heartbeat rhythms [4].<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4.2. Wavelet Transforms<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">While FFT loses temporal resolution, Wavelet Transforms provide a way to vectorize data by capturing both frequency and time information simultaneously. This is achieved by using &#8220;wavelets&#8221; that scale and shift, making it ideal for non-stationary signals where the frequency changes over time [4].<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">5. Model-Based Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In this approach, a time series is represented by the parameters of a model fitted to it.<\/p>\n\n\n<style>.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col,.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_dc5b1b-5d{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_dc5b1b-5d > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_dc5b1b-5d\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">5.1. ARMA\/ARIMA Parameters<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">One can fit an Autoregressive Integrated Moving Average (ARIMA) model to a specific time series and use the resulting coefficients ($\\phi$, $\\theta$) as the feature vector. This effectively reduces a long sequence into a few parameters that describe its underlying stochastic process [5].<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">5.2. Symbolic Aggregate Approximation (SAX)<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">SAX is a unique vectorization method that transforms a continuous time series into a string of symbols (discretization). By dividing the time axis into frames and the value axis into regions (quantiles), the series becomes a &#8220;word.&#8221; This word can then be converted into a bag-of-words vector, similar to natural language processing [2].<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">6. Advanced Libraries for Automated Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Manually selecting features can be labor-intensive. Several libraries have been developed to automate the generation of thousands of potential features.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>TSFRESH (Time Series Feature Extraction based on Scalable Hypothesis testing):<\/strong> This Python library extracts hundreds of features and uses hypothesis testing to identify which ones are statistically significant for the given target variable, preventing over-fitting.<\/li>\n\n\n\n<li><strong>Catch22:<\/strong> A high-performance library that selects 22 &#8220;canonical&#8221; features that have been shown to perform well across diverse time series datasets, offering a balance between speed and accuracy [3].<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">7. Dimensionality Reduction in Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Generating a large number of features often leads to the &#8220;curse of dimensionality.&#8221; To ensure the vector is efficient, techniques like Principal Component Analysis (PCA) or Singular Value Decomposition (SVD) are applied. These methods project the high-dimensional feature vector into a lower-dimensional space while preserving as much variance as possible, making the downstream models faster and more robust [5].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">8. Summary of Applications<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Time Series Vectorization is used across various domains:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Finance:<\/strong> Vectorizing stock price movements to classify market regimes (bullish vs. bearish).<\/li>\n\n\n\n<li><strong>Healthcare:<\/strong> Converting ECG or EEG signals into feature vectors for disease diagnosis.<\/li>\n\n\n\n<li><strong>Manufacturing:<\/strong> Transforming sensor data from machinery into vectors to predict equipment failure (Predictive Maintenance).<\/li>\n\n\n\n<li><strong>IoT:<\/strong> Summarizing smart meter data for energy load forecasting [1].<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">9. Conclusion<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">While modern deep learning often favors end-to-end embeddings, traditional vectorization remains vital. It provides interpretability, requires less data to train effectively, and allows for the integration of domain-specific expert knowledge into the modeling process. Understanding the various methods of vectorization\u2014from simple statistics to frequency analysis\u2014is essential for any data scientist working with temporal data [2].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">References<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Medium &#8211; Time Series Feature Extraction: <a href=\"https:\/\/medium.com\/@puneet_61448\/time-series-feature-extraction-856643644f1c\" target=\"_blank\" rel=\"noopener\">https:\/\/medium.com\/@puneet_61448\/time-series-feature-extraction-856643644f1c<\/a><\/li>\n\n\n\n<li>Towards Data Science &#8211; A Review of Time Series Representations: <a href=\"https:\/\/towardsdatascience.com\/a-review-of-time-series-representations-d8689551c6b1\" target=\"_blank\" rel=\"noopener\">https:\/\/towardsdatascience.com\/a-review-of-time-series-representations-d8689551c6b1<\/a><\/li>\n\n\n\n<li>TSFRESH Documentation &#8211; List of Features: <a href=\"https:\/\/tsfresh.readthedocs.io\/en\/latest\/text\/list_of_features.html\" target=\"_blank\" rel=\"noopener\">https:\/\/tsfresh.readthedocs.io\/en\/latest\/text\/list_of_features.html<\/a><\/li>\n\n\n\n<li>Analytics Vidhya &#8211; Introduction to Signal Processing for Time Series: <a href=\"https:\/\/www.analyticsvidhya.com\/blog\/2021\/05\/introduction-to-signal-processing-for-time-series\/\" target=\"_blank\" rel=\"noopener\">https:\/\/www.analyticsvidhya.com\/blog\/2021\/05\/introduction-to-signal-processing-for-time-series\/<\/a><\/li>\n\n\n\n<li>Machine Learning Mastery &#8211; How to Prepare Time Series Data for Machine Learning: <a href=\"https:\/\/machinelearningmastery.com\/how-to-prepare-time-series-data-for-machine-learning\/\" target=\"_blank\" rel=\"noopener\">https:\/\/machinelearningmastery.com\/how-to-prepare-time-series-data-for-machine-learning\/<\/a><\/li>\n<\/ol>\n\n\n\n<!--nextpage-->\n\n\n\n<h1 class=\"wp-block-heading\">Comprehensive Guide to Time Series Embedding in AI\/ML<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. Introduction to Time Series Embedding<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Time series data is a sequence of data points indexed in time order, commonly found in finance, weather forecasting, and sensor monitoring. Unlike static data, time series possess temporal dependencies and high dimensionality, making raw data processing computationally expensive and noisy. <strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#005ff8\" class=\"has-inline-color\">Time series embedding is the process of transforming high-dimensional, raw temporal sequences into a lower-dimensional, continuous vector space<\/mark><\/strong> while preserving the essential structural and temporal characteristics of the original data. This technique is crucial because it allows machine learning models to perform downstream tasks like classification, clustering, and anomaly detection more efficiently by operating on meaningful latent representations [1].<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. Core Concepts and Motivation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The primary goal of embedding is to map a time series <math data-latex=\"T = {t_1, t_2, \\dots, t_n}\"><semantics><mrow><mi>T<\/mi><mo>=<\/mo><mrow><msub><mi>t<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>t<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>t<\/mi><mi>n<\/mi><\/msub><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">T = {t_1, t_2, \\dots, t_n}<\/annotation><\/semantics><\/math> to a vector <math data-latex=\"v \\in \\mathbb{R}^d\"><semantics><mrow><mi>v<\/mi><mo>\u2208<\/mo><msup><mi>\u211d<\/mi><mi>d<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">v \\in \\mathbb{R}^d<\/annotation><\/semantics><\/math>, where <math data-latex=\"d\"><semantics><mi>d<\/mi><annotation encoding=\"application\/x-tex\">d<\/annotation><\/semantics><\/math> is much smaller than <math data-latex=\"n\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math>.<br>Traditional methods like Fourier Transforms or Wavelet Transforms focused on frequency domains, but modern AI\/ML embeddings focus on learning feature representations through deep neural networks.<br>The motivation behind this shift includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Dimensionality Reduction:<\/strong> Reducing the &#8220;curse of dimensionality&#8221; inherent in long sequences.<\/li>\n\n\n\n<li><strong>Noise Robustness:<\/strong> Filtering out local fluctuations to capture the underlying trend or seasonal patterns.<\/li>\n\n\n\n<li><strong>Similarity Search:<\/strong> Enabling the use of Euclidean distance or Cosine similarity to compare sequences that might have different lengths or sampling rates [2].<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">3. Methodologies of Time Series Embedding<\/h2>\n\n\n<style>.kadence-column6050_1b3891-7e > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_1b3891-7e > .kt-inside-inner-col,.kadence-column6050_1b3891-7e > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_1b3891-7e > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_1b3891-7e > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_1b3891-7e > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_1b3891-7e > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_1b3891-7e{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_1b3891-7e > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_1b3891-7e > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_1b3891-7e\"><div class=\"kt-inside-inner-col\">\n<h3 class=\"wp-block-heading\">3.1. Supervised Embedding<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In supervised settings, embeddings are learned as a byproduct of a specific task, such as classification or regression. For instance, a Long Short-Term Memory (LSTM) network or a Convolutional Neural Network (CNN) is trained to predict a label. The output of the penultimate layer (the global pooling layer or the last hidden state) serves as the embedding. While effective for the specific task, these embeddings often lack generalizability to other domains [3].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2. Unsupervised and Self-Supervised Embedding<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This is currently the most active area of research. Methods here aim to learn representations without explicit labels by leveraging the structure of the data itself.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Autoencoders (AE):<\/strong> These models consist of an encoder that compresses the input into a bottleneck (embedding) and a decoder that reconstructs the original signal. By minimizing reconstruction error, the encoder learns to retain the most significant features of the time series.<\/li>\n\n\n\n<li><strong>Contrastive Learning:<\/strong> This approach, exemplified by TS2Vec or TNC (Temporal Neighborhood Coding), treats time series as &#8220;views.&#8221; The model learns to bring embeddings of similar segments (e.g., segments from the same sequence or augmented versions) closer together while pushing dissimilar segments apart in the vector space [4].<\/li>\n\n\n\n<li><strong>Generative Models:<\/strong> Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) can also generate embeddings. VAEs, in particular, provide a probabilistic latent space that is useful for uncertainty estimation and anomaly detection.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3.3. Shapelet-Based Embedding<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Shapelets are maximally representative sub-sequences of a time series. Modern &#8220;Learning Shapelets&#8221; methods treat these sub-sequences as trainable parameters. The embedding is formed by calculating the distance between the input time series and a set of learned shapelets. This method is highly interpretable because we can visualize which specific &#8220;shape&#8221; the model is looking for [5].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.4. Prototype-based Embedding<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Prototype-based methods represent each class as a learnable <em>prototype vector<\/em> in the embedding space, and classify a time series by its distance to these prototypes. <strong>TapNet<\/strong> (Zhang et al., 2020) exemplifies this approach for multivariate time series: it uses random group permutation with multi-layer convolutions to learn low-dimensional features, then trains an attentional prototype network that aligns embeddings with class prototypes, performing well even under limited labels [6].<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">4. Architectural Evolutions<\/h2>\n\n\n<style>.kadence-column6050_a4de07-65 > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_a4de07-65 > .kt-inside-inner-col,.kadence-column6050_a4de07-65 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_a4de07-65 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_a4de07-65 > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_a4de07-65 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_a4de07-65 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_a4de07-65{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_a4de07-65 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_a4de07-65 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_a4de07-65\"><div class=\"kt-inside-inner-col\">\n<h3 class=\"wp-block-heading\">4.1. Recurrent Neural Networks (RNNs)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">RNNs and their variants (LSTM, GRU) were the standard for years due to their ability to handle sequential dependencies. The final hidden state $h_t$ is often used as the embedding for the entire sequence. However, they suffer from vanishing gradients and difficulty in capturing very long-term dependencies.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2. Temporal Convolutional Networks (TCNs)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">TCNs use dilated causal convolutions to process sequences. Unlike RNNs, they can be trained in parallel and have a stable gradient flow. TCNs are excellent at capturing multi-scale temporal patterns, making them robust for embedding tasks where local and global trends coexist [7].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.3. Transformers and Attention Mechanisms<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The success of BERT and GPT in NLP has transitioned to time series via models like Informer, Autoformer, and PatchTST. Transformers use self-attention to weight the importance of different time steps regardless of their distance. In embedding, &#8220;Time-Series Transformers&#8221; often treat time steps or &#8220;patches&#8221; of time steps as tokens, producing rich, context-aware embeddings [8].<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">5. Key Challenges in Time Series Embedding<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Challenge<\/th><th class=\"has-text-align-left\" data-align=\"left\">Description<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Variable Length<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Real-world data often comes in varying lengths, requiring global pooling or padding to create fixed-size embeddings.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Shift Invariance<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Patterns may occur at different starting points. Effective embeddings must recognize the same pattern regardless of when it happens.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Multivariate Correlations<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Modern time series (like IoT sensors) involve multiple variables. Embedding must capture both temporal and inter-variable dependencies.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Stationarity<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Non-stationary data (where statistical properties change over time) can lead to unstable embeddings [9].<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">6. Applications<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Clustering:<\/strong> Grouping similar financial assets or consumer behaviors without labels.<\/li>\n\n\n\n<li><strong>Anomaly Detection:<\/strong> Representing &#8220;normal&#8221; behavior as a cluster in the embedding space; points far from the cluster are flagged as anomalies.<\/li>\n\n\n\n<li><strong>Transfer Learning:<\/strong> Pre-training an embedding model on a large dataset (e.g., general electricity usage) and fine-tuning it on a smaller, specific dataset.<\/li>\n\n\n\n<li><strong>Forecast-by-Retrieval:<\/strong> Instead of predicting values directly, a model finds the most similar historical embedding and uses its future trajectory as the prediction [10].<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">7. Future Trends<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The field is moving towards &#8220;Foundation Models&#8221; for time series, similar to Large Language Models. These models are pre-trained on massive amounts of diverse temporal data (weather, traffic, finance) using self-supervised tasks like masked time-series modeling. The resulting embeddings are incredibly versatile and can be applied to zero-shot or few-shot learning tasks across entirely different domains [11].<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">References<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Towards Data Science &#8211; Time Series Representations: <a href=\"https:\/\/towardsdatascience.com\/time-series-representation-learning-a-comprehensive-guide-4f0f6c2c3b2e\" target=\"_blank\" rel=\"noopener\">https:\/\/towardsdatascience.com\/time-series-representation-learning-a-comprehensive-guide-4f0f6c2c3b2e<\/a><\/li>\n\n\n\n<li>Machine Learning Mastery &#8211; Introduction to Time Series Embeddings: <a href=\"https:\/\/machinelearningmastery.com\/embeddings-for-time-series-forecasting\/\" target=\"_blank\" rel=\"noopener\">https:\/\/machinelearningmastery.com\/embeddings-for-time-series-forecasting\/<\/a><\/li>\n\n\n\n<li>arXiv &#8211; Deep Learning for Time Series Classification: A Review: <a href=\"https:\/\/arxiv.org\/abs\/1809.04356\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1809.04356<\/a><\/li>\n\n\n\n<li>Papers with Code &#8211; TS2Vec: Towards Universal Representation of Time Series: <a href=\"https:\/\/paperswithcode.com\/paper\/ts2vec-towards-universal-representation-of\" target=\"_blank\" rel=\"noopener\">https:\/\/paperswithcode.com\/paper\/ts2vec-towards-universal-representation-of<\/a><\/li>\n\n\n\n<li>KDD &#8211; Learning Shapelets: <a href=\"https:\/\/www.kdd.org\/kdd2016\/papers\/files\/rfp0457-grabockaA.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/www.kdd.org\/kdd2016\/papers\/files\/rfp0457-grabockaA.pdf<\/a><\/li>\n\n\n\n<li>Zhang et al. \u2013 TapNet: Multivariate Time Series Classification with Attentional Prototypical Network (AAAI 2020): <a href=\"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/6165\" target=\"_blank\" rel=\"noopener\">https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/6165<\/a><\/li>\n\n\n\n<li>Medium &#8211; Temporal Convolutional Networks (TCN) for Time Series: <a href=\"https:\/\/medium.com\/metadata\/temporal-convolutional-networks-for-time-series-forecasting-d32845c43232\" target=\"_blank\" rel=\"noopener\">https:\/\/medium.com\/metadata\/temporal-convolutional-networks-for-time-series-forecasting-d32845c43232<\/a><\/li>\n\n\n\n<li>Hugging Face &#8211; Time Series Transformers: <a href=\"https:\/\/huggingface.co\/blog\/time-series-transformers\" target=\"_blank\" rel=\"noopener\">https:\/\/huggingface.co\/blog\/time-series-transformers<\/a>, <a href=\"https:\/\/huggingface.co\/blog\/patchtst\" target=\"_blank\" rel=\"noopener\">https:\/\/huggingface.co\/blog\/patchtst<\/a><\/li>\n\n\n\n<li>ResearchGate &#8211; Challenges in Multivariate Time Series Analysis: <a href=\"https:\/\/www.researchgate.net\/publication\/344215286_A_Survey_on_Multivariate_Time_Series_Forecasting\" target=\"_blank\" rel=\"noopener\">https:\/\/www.researchgate.net\/publication\/344215286_A_Survey_on_Multivariate_Time_Series_Forecasting<\/a><\/li>\n\n\n\n<li>Analytics Vidhya &#8211; Applications of Time Series Embedding: <a href=\"https:\/\/www.analyticsvidhya.com\/blog\/2021\/06\/time-series-analysis-embedding-techniques\/\" target=\"_blank\" rel=\"noopener\">https:\/\/www.analyticsvidhya.com\/blog\/2021\/06\/time-series-analysis-embedding-techniques\/<\/a><\/li>\n\n\n\n<li>Google Research &#8211; TimesFM: A Foundation Model for Time Series Forecasting: <a href=\"https:\/\/blog.research.google\/2024\/02\/harnessing-power-of-foundation-models-for-time-series.html\" target=\"_blank\" rel=\"noopener\">https:\/\/blog.research.google\/2024\/02\/harnessing-power-of-foundation-models-for-time-series.html<\/a><\/li>\n<\/ol>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">Modeling Inter-Sensor Interactions in Time Series Vectorization for AI\/ML<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In the contemporary landscape of the Internet of Things (IoT) and industrial automation, time series data rarely exists in isolation. Modern systems, ranging from autonomous vehicles to smart power grids, utilize a multitude of sensors to monitor complex environments. To build effective Machine Learning (ML) models, one must move beyond univariate analysis and consider how different sensors interact over time. Vectorization\u2014the process of converting raw, multi-dimensional time series data into a numerical format suitable for deep learning\u2014must explicitly capture these inter-dependencies to be effective [1].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. The Challenge of Multivariate Time Series Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Multi-sensor data is inherently multivariate. Each sensor provides a unique stream of data, often sampled at different frequencies or containing different noise profiles. The primary challenge in vectorization is that the &#8220;state&#8221; of a system is defined not just by the values of individual sensors, but by the correlation and causation existing between them. For instance, in an aircraft engine, a spike in temperature might be normal if accompanied by an increase in fuel flow, but catastrophic if the fuel flow remains constant. Traditional vectorization methods that flatten data into a simple feature vector often lose this structural context [2].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Spatial-Temporal Representation Learning<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To address these interactions, researchers have turned to spatial-temporal modeling. In this context, &#8220;<strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-theme-palette-12-color\">spatial<\/mark><\/strong>&#8221; refers to the relationship between sensors (the sensor topology), while &#8220;<strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-theme-palette-12-color\">temporal<\/mark><\/strong>&#8221; refers to the evolution of data over time.<\/p>\n\n\n<style>.kadence-column6050_e82425-24 > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_e82425-24 > .kt-inside-inner-col,.kadence-column6050_e82425-24 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_e82425-24 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_e82425-24 > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_e82425-24 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_e82425-24 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_e82425-24{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_e82425-24 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_e82425-24 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_e82425-24\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">Graph Neural Networks (GNNs) for Sensor Topology<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">One of the most robust ways to consider sensor interactions is by treating the sensor network as a graph. Each sensor is represented as a node, and the interaction between them is represented as an edge.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Static Graphs:<\/strong> If the physical relationship between sensors is fixed (e.g., sensors on a rigid bridge), a predefined adjacency matrix can guide the vectorization process.<\/li>\n\n\n\n<li><strong>Dynamic Graphs:<\/strong> In many cases, the interaction between sensors changes based on the system&#8217;s state. Modern vectorization techniques use &#8220;Adaptive Adjacency Matrices&#8221; where the model learns which sensors influence each other during the training phase [3].<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Graph Convolutional Networks (GCN)<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">By applying graph convolutions, the vectorization process aggregates features from neighboring sensors. This ensures that the resulting vector for &#8220;Sensor A&#8221; actually contains compressed information about &#8220;Sensors B and C,&#8221; effectively embedding the interaction directly into the latent space [1].<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">3. Attention Mechanisms and Transformers<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The rise of the Transformer architecture has revolutionized how we handle multivariate interactions. Unlike GNNs, which require a graph structure, Attention mechanisms can &#8220;discover&#8221; interactions automatically.<\/p>\n\n\n<style>.kadence-column6050_276662-ea > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_276662-ea > .kt-inside-inner-col,.kadence-column6050_276662-ea > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_276662-ea > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_276662-ea > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_276662-ea > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_276662-ea > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_276662-ea{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_276662-ea > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_276662-ea > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_276662-ea\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">Multi-Head Self-Attention<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">In the vectorization layer, self-attention calculates a weight for every pair of sensors. If Sensor 1 and Sensor 5 are highly correlated during a specific event, the attention score between them increases. This allows the model to focus on the most relevant inter-sensor relationships at any given timestamp.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Temporal Attention:<\/strong> Focuses on which past time steps are important for the current prediction.<\/li>\n\n\n\n<li><strong>Spatial (Sensor) Attention:<\/strong> Focuses on which other sensors provide the most context for the current sensor&#8217;s value [4].<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Cross-Dimension Attention<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Recent advancements have introduced Cross-Dimension Transformers. These models perform attention across the &#8220;Time&#8221; dimension and the &#8220;Sensor&#8221; dimension separately or simultaneously. By doing so, the vectorized output captures &#8220;Cross-Variable Dependencies,&#8221; which are essential for understanding long-term systemic shifts [5].<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">4. Cross-Correlation and Convolutional Approaches<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Before the dominance of Transformers, 2D Convolutional Neural Networks (CNNs) were the standard for capturing sensor interactions.<\/p>\n\n\n<style>.kadence-column6050_a61bc0-15 > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_a61bc0-15 > .kt-inside-inner-col,.kadence-column6050_a61bc0-15 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_a61bc0-15 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_a61bc0-15 > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_a61bc0-15 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_a61bc0-15 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_a61bc0-15{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_a61bc0-15 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_a61bc0-15 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_a61bc0-15\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">Time-Series as Images<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">By stacking multiple sensor streams vertically, one can treat a window of time series data as a 2-dimensional image (Time $\\times$ Sensor). A 2D kernel sliding over this &#8220;image&#8221; naturally captures interactions between adjacent rows (sensors).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Intersensor Correlation Heatmaps:<\/strong> Some vectorization pipelines first calculate a Pearson correlation or Mutual Information matrix between all sensor pairs. This matrix is then used as a feature map, ensuring the model explicitly &#8220;sees&#8221; how sensors move together or apart [2].<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Dilated Convolutions<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">To capture interactions across different time scales, dilated convolutions are used. This allows the vectorization process to account for a sensor that reacts to another sensor with a significant time lag, which is common in chemical processes or thermal systems [6].<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">5. Canonical Correlation Analysis (CCA) and Decomposition<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In some specialized AI\/ML workflows, interaction is handled through dimensionality reduction techniques that prioritize shared variance.<\/p>\n\n\n<style>.kadence-column6050_0f23ef-9f > .kt-inside-inner-col{padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6050_0f23ef-9f > .kt-inside-inner-col,.kadence-column6050_0f23ef-9f > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6050_0f23ef-9f > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6050_0f23ef-9f > .kt-inside-inner-col{flex-direction:column;}.kadence-column6050_0f23ef-9f > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6050_0f23ef-9f > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6050_0f23ef-9f{position:relative;}@media all and (max-width: 1024px){.kadence-column6050_0f23ef-9f > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6050_0f23ef-9f > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6050_0f23ef-9f\"><div class=\"kt-inside-inner-col\">\n<h4 class=\"wp-block-heading\">Multi-view Vectorization<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Each sensor can be seen as a different &#8220;view&#8221; of the same underlying physical process. Deep Canonical Correlation Analysis (DCCA) learns non-linear mapping functions for multiple sensors such that the resulting vectors are highly correlated in the latent space. This forces the vectorization to ignore independent noise and focus strictly on the shared interaction signals [3].<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Tensor Decomposition<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">When dealing with extremely high-dimensional sensor data (e.g., thousands of sensors in a smart city), data is often represented as a high-order tensor. Techniques like Tucker Decomposition or CP Decomposition factorize the tensor into core components that represent the interaction between temporal patterns and sensor groupings [7].<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">6. Practical Considerations in Vectorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">When implementing these techniques, several practical factors must be considered:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Heterogeneity:<\/strong> Sensors may measure different units (Pressure vs. Voltage). Normalization is required before interaction modeling to prevent one sensor from dominating the vector space.<\/li>\n\n\n\n<li><strong>Sampling Rates:<\/strong> If Sensor A samples at 100Hz and Sensor B at 10Hz, interpolation or alignment is necessary before cross-sensor vectorization.<\/li>\n\n\n\n<li><strong>Explainability:<\/strong> Using Attention-based vectorization provides &#8220;Attention Maps,&#8221; which allow engineers to see which sensor interactions the AI deemed most important for a specific prediction [4].<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">7. Conclusion<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vectorizing multi-sensor time series is no longer just about flattening arrays. It is about preserving the complex web of relationships that define a system&#8217;s behavior. Whether through the explicit topology of Graph Neural Networks, the dynamic weighting of Transformers, or the spatial-temporal kernels of CNNs, modern AI\/ML models now treat inter-sensor interaction as a first-class citizen in the feature engineering process. By capturing these dependencies, models achieve higher accuracy and greater robustness against sensor-specific noise [5].<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>References<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.mdpi.com\/2072-4292\/13\/18\/3734\" target=\"_blank\" rel=\"noopener\">https:\/\/www.mdpi.com\/2072-4292\/13\/18\/3734<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/abs\/2101.00897\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2101.00897<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2021.654814\/full\" target=\"_blank\" rel=\"noopener\">https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2021.654814\/full<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/proceedings.neurips.cc\/paper\/2017\/file\/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/proceedings.neurips.cc\/paper\/2017\/file\/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/openreview.net\/forum?id=09V_v1_8_1D\" target=\"_blank\" rel=\"noopener\">https:\/\/openreview.net\/forum?id=09V_v1_8_1D<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/abs\/1803.01271\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1803.01271<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10115-020-01460-w\" target=\"_blank\" rel=\"noopener\">https:\/\/link.springer.com\/article\/10.1007\/s10115-020-01460-w<\/a><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<div style='text-align:center' class='yasr-auto-insert-overall'><\/div><div style='text-align:center' class='yasr-auto-insert-visitor'><\/div>","protected":false},"excerpt":{"rendered":"<p>Time Series Vectorization vs. Embedding \ud83d\udd0d 1. Time Series Vectorization (\ubca1\ud130\ud654) 2. Time Series Embedding (\uc784\ubca0\ub529)<\/p>\n","protected":false},"author":4,"featured_media":6055,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_kadence_starter_templates_imported_post":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","yasr_overall_rating":0,"yasr_post_is_review":"","yasr_auto_insert_disabled":"","yasr_review_type":"","fifu_image_url":"","fifu_image_alt":"","iawp_total_views":7,"footnotes":""},"categories":[56,370],"tags":[],"class_list":["post-6050","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-science-slug","category-time-series-slug"],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":1,"sum_votes":5},"jetpack_featured_media_url":"https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/time-series-classification-900x600-1.png","_links":{"self":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/comments?post=6050"}],"version-history":[{"count":15,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6050\/revisions"}],"predecessor-version":[{"id":6317,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6050\/revisions\/6317"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media\/6055"}],"wp:attachment":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media?parent=6050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/categories?post=6050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/tags?post=6050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}