{"id":6103,"date":"2026-04-08T19:26:44","date_gmt":"2026-04-09T00:26:44","guid":{"rendered":"https:\/\/ykim.synology.me\/wordpress\/?p=6103"},"modified":"2026-04-10T03:51:27","modified_gmt":"2026-04-10T08:51:27","slug":"mean-variance-and-agreement-correlation-metrics-for-ai-ml-performance-evaluation","status":"publish","type":"post","link":"https:\/\/ykim.synology.me\/wordpress\/mean-variance-and-agreement-correlation-metrics-for-ai-ml-performance-evaluation-6103\/","title":{"rendered":"Mean, Variance, and Agreement Metrics for Regression in AI\/ML"},"content":{"rendered":"\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(1 * 0.6 * 1rem);line-height:1.5rem;--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>Regression metrics\n\u251c\u2500\u2500 Mean-based\n\u2502   \u251c\u2500\u2500 Scale-dependent   \u2192 MAE, MSE, RMSE, Huber\n\u2502   \u2514\u2500\u2500 Scale-independent \u2192 MPE, MAPE, SMAPE, CV(RMSE)\n\u251c\u2500\u2500 Variance-based\n\u2502   \u2514\u2500\u2500 Scale-independent \u2192 R\u00b2, Adj. R\u00b2\n\u2514\u2500\u2500 Mean+Variance-based (Hybrid)\n    \u2514\u2500\u2500 Scale-independent \u2192 CCC, KGE<\/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\">Regression metrics<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Mean-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u251c\u2500\u2500 Scale-dependent   \u2192 MAE, MSE, RMSE, Huber<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Scale-independent \u2192 MPE, MAPE, SMAPE, CV(RMSE)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u251c\u2500\u2500 Variance-based<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2502   \u2514\u2500\u2500 Scale-independent \u2192 R\u00b2, Adj. R\u00b2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">\u2514\u2500\u2500 Mean+Variance-based (Hybrid)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    \u2514\u2500\u2500 Scale-independent \u2192 CCC, KGE<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">1. Executive Summary<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In advanced engineering domains\u2014such as semiconductor manufacturing, virtual metrology, and multi-sensor time-series analysis\u2014the validation of predictive models requires more than a single performance score. We must distinguish between <strong>how well a model tracks a trend<\/strong> (Precision) versus <strong>how close the prediction is to the physical truth<\/strong> (Accuracy).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This report establishes a rigorous taxonomy for evaluation metrics, categorized into <strong>Variance-based<\/strong>, <strong>Mean-based<\/strong>, and <strong>Agreement-based<\/strong> indices. This hierarchy provides a systematic framework for interpreting model performance relative to the ideal $y=x$ (1:1) line, with a specific focus on the risks associated with the <strong>Low Variance Effect<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. Metric Hierarchy and Detailed Analysis<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">I. Variance Index (Trend &amp; Correlation Focus)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">These metrics assess the <strong>linearity<\/strong> and the strength of the relationship between observed and predicted values. They focus on whether the model captures the &#8220;shape&#8221; of the data, regardless of absolute magnitude.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. Pearson Correlation Coefficient ($r$)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: $$r = \\frac{\\sum (y_i &#8211; \\mu_y)(\\hat{y_i} &#8211; \\mu_{\\hat{y}})}{\\sqrt{\\sum (y_i &#8211; \\mu_y)^2 \\sum (\\hat{y_i} &#8211; \\mu_{\\hat{y}})^2}}$$<br>where $y_i$: Observed ground truth value,<br>\u2003\u2003\u2003$\\hat{y}_i$: Predicted value from the model, <br>\u2003\u2003\u2003$\\mu_y, \\mu_{\\hat{y}}$: Means of observed and predicted values respectively<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> $r$ measures how tightly data clusters around <em>any<\/em> straight line. A perfect $r=1$ does not guarantee the data is on the $1:1$ line; it could be on $y = 2x + 10$.<\/li>\n\n\n\n<li><strong>Limitation (Low Variance Effect):<\/strong> If the data has very low variance (e.g., a sensor outputting a nearly constant value), the denominator approaches zero. This makes $r$ extremely sensitive to tiny amounts of noise, often resulting in a low or undefined correlation despite the prediction being physically close to the truth.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Initial feature selection and identifying sensors with similar behavioral patterns.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. Coefficient of Determination ($R^2$)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$R^2 = 1 &#8211; \\frac{SS_{res}}{SS_{tot}} = 1 &#8211; \\frac{\\sum (y_i &#8211; \\hat{y}_i)^2}{\\sum (y_i &#8211; \\mu_y)^2}$$<br>where $SS_{res}$: Residual sum of squares (unexplained variance),<br>\u2003\u2003\u2003$SS_{tot}$: Total sum of squares (total variance in data)<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> Represents the proportion of variance explained by the model. While it penalizes distance from the 1:1 line more than $r$, it can still be misleading if the model is systematically biased.<\/li>\n\n\n\n<li><strong>Limitation (Low Variance Effect):<\/strong> $R^2$ is notoriously deceptive when target variance is low. Because the denominator ($SS_{tot}$) is small, even a tiny prediction error can result in a negative or near-zero $R^2$, suggesting a &#8220;bad&#8221; model even when the absolute error (RMSE) is within acceptable engineering tolerances.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Standard benchmark for regression model explanatory power in manufacturing yield analysis.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">3. Explained Variance Score<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$ExpVar = 1 &#8211; \\frac{Var(y &#8211; \\hat{y})}{Var(y)}$$<br>where $Var(y &#8211; \\hat{y})$: Variance of the residuals,<br>\u2003\u2003\u2003$Var(y)$: Variance of the ground truth<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> Similar to $R^2$, but it ignores the mean of the residuals. It focuses purely on whether the <em>fluctuations<\/em> in the prediction match the <em>fluctuations<\/em> in the truth.<\/li>\n\n\n\n<li><strong>Limitation (Low Variance Effect):<\/strong> Like $R^2$, this metric collapses when $Var(y)$ is small. It fails to provide a meaningful score for stable processes where the goal is to maintain a constant setpoint.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Signal processing where the relative change is more important than the absolute baseline.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">II. Mean Index (Magnitude &amp; Distance Focus)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">These metrics measure the <strong>physical distance<\/strong> between the predicted vector and the ground truth. They are essential for understanding the actual &#8220;cost&#8221; of an error.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. Mean Absolute Error (MAE)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$MAE = \\frac{1}{n} \\sum_{i=1}^{n} |y_i &#8211; \\hat{y}_i|$$<br>where $n$: Number of samples<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> The average vertical distance to the 1:1 line.<\/li>\n\n\n\n<li><strong>Limitation:<\/strong> Does not highlight large, infrequent errors; it treats all deviations linearly. It is unaffected by the Low Variance Effect, making it more reliable for stable processes.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Situations where the error cost is strictly proportional to error magnitude.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. Mean Squared Error (MSE) \/ RMSE<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$MSE = \\frac{1}{n} \\sum_{i=1}^{n} (y_i &#8211; \\hat{y}_i)^2, \\quad RMSE = \\sqrt{MSE}$$<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> The average of the squared distances to the 1:1 line. RMSE represents the &#8220;typical&#8221; distance in original units.<\/li>\n\n\n\n<li><strong>Limitation:<\/strong> Heavily influenced by outliers. While robust to low variance in the <em>target<\/em>, these metrics do not tell you if the model is capturing the <em>trend<\/em> of the data.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Standard loss function for training; critical for thickness prediction where large deviations lead to wafer scrap.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">3. Mean Percentage Error (MPE) \/ Mean Absolute Percentage Error (MAPE)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$MPE = \\frac{100%}{n} \\sum_{i=1}^{n} \\frac{y_i &#8211; \\hat{y}i}{y_i}, \\quad MAPE = \\frac{100%}{n} \\sum_{i=1}^{n} \\left| \\frac{y_i &#8211; \\hat{y}_i}{y_i} \\right|$$<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> These metrics evaluate the relative deviation from the 1:1 line. MPE measures the average percentage bias (whether the model consistently overestimates or underestimates), while MAPE represents the average magnitude of percentage error relative to the identity line.<\/li>\n\n\n\n<li><strong>Limitation:<\/strong> <mark style=\"background-color:rgba(0, 0, 0, 0);color:#ff0000\" class=\"has-inline-color\">The most significant weakness is the &#8220;division by zero&#8221; or &#8220;near-zero&#8221; problem<\/mark>; if the target value is zero or very small, the metrics explode to infinity. Additionally, <mark style=\"background-color:rgba(0, 0, 0, 0);color:#ff0000\" class=\"has-inline-color\">MAPE is asymmetric, as it penalizes overestimations more heavily than underestimations in certain contexts<\/mark>. <mark style=\"background-color:rgba(0, 0, 0, 0);color:#ff0000\" class=\"has-inline-color\">MAPE is highly sensitive to the magnitude of the actual values, where errors are heavily penalized (or amplified) as the denominator approaches zero.<\/mark> The primary weakness of MAPE is its dependence on a variable denominator ($y_i$). However, <mark style=\"background-color:rgba(0, 0, 0, 0);color:#0026ff\" class=\"has-inline-color\">if the data scale remains consistent across all points, the denominator functions effectively as a constant. In such cases, MAPE becomes a stable metric, behaving similarly to MSE or RMSE by scaling linearly with absolute error<\/mark>. Unlike CCC, they do not distinguish between scale shifts and location shifts.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Essential for communicating model performance to non-technical stakeholders in business terms; widely used in financial forecasting and yield management to understand the &#8220;percentage of accuracy&#8221; relative to the target thickness or price.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">4. CV(RMSE) (Coefficient of Variation of RMSE)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$CV(RMSE) = \\frac{RMSE}{\\mu_y}$$<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> Normalizes the error by the mean.<\/li>\n\n\n\n<li><strong>Limitation (Low Variance Effect):<\/strong> If the mean ($\\mu_y$) is near zero, this metric explodes. However, it is generally more stable than $R^2$ for low-variance, non-zero datasets.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Comparing model performance across different sensor types with varying scales.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">III. Agreement Index (Fidelity &amp; Calibration Focus)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">These evaluate <strong>Fidelity<\/strong>: the requirement that the model must follow the trend <em>and<\/em> match the absolute values simultaneously.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. Lin\u2019s Concordance Correlation Coefficient (CCC)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$\\rho_c = \\frac{2 \\rho \\sigma_y \\sigma_{\\hat{y}}}{\\sigma_y^2 + \\sigma_{\\hat{y}}^2 + (\\mu_y &#8211; \\mu_{\\hat{y}})^2}$$<br>where $\\rho$: Pearson correlation coefficient,<br>\u2003\u2003\u2003$\\sigma_y, \\sigma_{\\hat{y}}$: Standard deviations of observed and predicted values<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> Directly measures how far the data deviates from the 45-degree line. It combines $r$ (precision) with a bias penalty (accuracy).<\/li>\n\n\n\n<li><strong>Limitation (Low Variance Effect):<\/strong> Since $\\rho$ (Pearson) is a component, CCC will also decrease if the variance of the data is extremely low, potentially masking a model that is actually performing well in terms of absolute distance.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Validating new metrology sensors against gold-standard lab measurements.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. Kling-Gupta Efficiency (KGE)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong> $$KGE = 1 &#8211; \\sqrt{(r-1)^2 + (\\alpha-1)^2 + (\\beta-1)^2}$$<br>where $r$: Pearson correlation,<br>\u2003\u2003\u2003$\\alpha = \\sigma_{\\hat{y}}\/\\sigma_y$ (Variability ratio),<br>\u2003\u2003\u2003$\\beta = \\mu_{\\hat{y}}\/\\mu_y$ (Bias ratio)<\/li>\n\n\n\n<li><strong>Relation to 1:1 Line:<\/strong> A holistic &#8220;Agreement&#8221; metric. Reaches 1.0 only if $r, \\alpha, \\beta$ are all 1.<\/li>\n\n\n\n<li><strong>Limitation (Low Variance Effect):<\/strong> Extremely sensitive to the variability ratio ($\\alpha$). If the ground truth has nearly zero variance ($\\sigma_y \\approx 0$), $\\alpha$ becomes undefined or unstable, causing the KGE to fail.<\/li>\n\n\n\n<li><strong>Application:<\/strong> Complex industrial process control and high-fidelity \uc2dc\uacc4\uc5f4 (time-series) simulation.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">3. Comparative Summary Table<\/h2>\n\n\n\n<figure style=\"padding-right:var(--wp--preset--spacing--40);padding-left:var(--wp--preset--spacing--40)\" class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Category<\/th><th class=\"has-text-align-left\" data-align=\"left\">Primary Focus<\/th><th class=\"has-text-align-left\" data-align=\"left\">Best Use Case<\/th><th class=\"has-text-align-left\" data-align=\"left\">Relation to $y=x$<\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Low Variance Effect<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Variance-based<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Trend\/Pattern<\/td><td class=\"has-text-align-left\" data-align=\"left\">Feature selection<\/td><td class=\"has-text-align-left\" data-align=\"left\">High score if linear,<br>even if biased.<\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>High Risk:<\/strong> Scores collapse or become noisy<br>even if the error is small.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Mean-based<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Absolute Error<\/td><td class=\"has-text-align-left\" data-align=\"left\">Model Training<br>(Loss)<\/td><td class=\"has-text-align-left\" data-align=\"left\">0 only if exactly on the line.<\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>Robust:<\/strong> Remains stable and interpretable <br>regardless of variance.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Agreement-based<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fidelity\/Calibration<\/td><td class=\"has-text-align-left\" data-align=\"left\">System Validation<\/td><td class=\"has-text-align-left\" data-align=\"left\">1 only if exactly on the line.<\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>Moderate Risk:<\/strong> Sensitivity inherited <br>from the correlation component.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">4. Professional Recommendation for Engineering Teams<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When deploying AI for semiconductor or sensor infrastructures,<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-theme-palette-14-color\"> <strong>never rely on Variance Indices alone.<\/strong><\/mark> In high-precision manufacturing, sensors often operate within a very tight, stable range (Low Variance). In these cases, Pearson and $R^2$ will suggest the model is failing, when in fact it may be predicting within sub-micron accuracy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Standard Protocol:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Use <strong>RMSE\/MAE<\/strong> as the primary source of truth in low-variance environments.<\/li>\n\n\n\n<li>Use <strong>Agreement Indices (CCC\/KGE)<\/strong> for system-wide validation only when the data range is sufficient.<\/li>\n\n\n\n<li>Always check the <strong>Low Variance Effect<\/strong> before interpreting a drop in $R^2$\u2014it is often a mathematical artifact rather than a loss of predictive power.<\/li>\n<\/ol>\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>1. Executive Summary In advanced engineering domains\u2014such as semiconductor manufacturing, virtual metrology, and multi-sensor time-series analysis\u2014the validation of predictive models requires more than a single performance score. We must distinguish between how well a model tracks a trend (Precision) versus how close the prediction is to the physical truth (Accuracy). This report establishes a rigorous&#8230;<\/p>\n","protected":false},"author":4,"featured_media":6177,"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":2,"footnotes":""},"categories":[56,369],"tags":[],"class_list":["post-6103","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-science-slug","category-evalutaion-metric-slug"],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":1,"sum_votes":3},"jetpack_featured_media_url":"https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/regression-metrics-taxonomy-hierarchy-600x400px.png","_links":{"self":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6103","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=6103"}],"version-history":[{"count":37,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6103\/revisions"}],"predecessor-version":[{"id":6234,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6103\/revisions\/6234"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media\/6177"}],"wp:attachment":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media?parent=6103"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/categories?post=6103"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/tags?post=6103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}