{"id":15791,"date":"2020-04-18T14:53:43","date_gmt":"2020-04-18T13:53:43","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?p=15791"},"modified":"2020-04-18T15:34:03","modified_gmt":"2020-04-18T14:34:03","slug":"how-to-normalize-and-standardize-data-in-r-for-great-heatmap-visualization","status":"publish","type":"post","link":"https:\/\/www.datanovia.com\/en\/blog\/how-to-normalize-and-standardize-data-in-r-for-great-heatmap-visualization\/","title":{"rendered":"How to Normalize and Standardize Data in R for Great Heatmap Visualization"},"content":{"rendered":"<div id=\"rdoc\">\n<p><strong>Data normalization<\/strong> methods are used to make variables, measured in different scales, have comparable values. This preprocessing steps is important for clustering and heatmap visualization, principal component analysis and other machine learning algorithms based on distance measures.<\/p>\n<p>This article describes the following data rescaling approaches:<\/p>\n<ul>\n<li>Standard scaling or standardization<\/li>\n<li>Normalization or Min-Max scaling<\/li>\n<li>Percentile transformation<\/li>\n<\/ul>\n<p>Codes will be provided to demonstrate how to standardize, normalize and percentilize data in R. The R package <code>heatmaply<\/code> contains helper functions for normalizing and visualizing data as interactive heatmap.<\/p>\n<p>Contents:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#prerequisites\">Prerequisites<\/a><\/li>\n<li><a href=\"#heatmap-of-the-raw-data\">Heatmap of the raw data<\/a><\/li>\n<li><a href=\"#standard-scaling\">Standard scaling<\/a><\/li>\n<li><a href=\"#normalization\">Normalization<\/a><\/li>\n<li><a href=\"#percentile-transformation\">Percentile transformation<\/a><\/li>\n<li><a href=\"#references\">References<\/a><\/li>\n<\/ul>\n<\/div>\n<div id=\"prerequisites\" class=\"section level2\">\n<h2>Prerequisites<\/h2>\n<p>The <code>heatmaply<\/code> R package will be used to interactively visualize the data before and after transformation.<\/p>\n<p>Install the packages using <code>install.packages(\"heatmaply\")<\/code>, then load it as follow:<\/p>\n<pre class=\"r\"><code>library(heatmaply)<\/code><\/pre>\n<\/div>\n<div id=\"heatmap-of-the-raw-data\" class=\"section level2\">\n<h2>Heatmap of the raw data<\/h2>\n<pre class=\"r\"><code>heatmaply(\r\n  mtcars, \r\n  xlab = \"Features\",\r\n  ylab = \"Cars\", \r\n  main = \"Raw data\"\r\n)<\/code><\/pre>\n<p><iframe width=\"95%\" height=\"600\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-tutorial\/figures\/data-normalization-in-r-for-heatmap-visualization-interactive-heatmap-raw-data.html\" frameborder=\"2\"><br \/>\n<\/iframe><\/p>\n<\/div>\n<div id=\"standard-scaling\" class=\"section level2\">\n<h2>Standard scaling<\/h2>\n<p><strong>Standard scaling<\/strong>, also known as standardization or Z-score normalization, consists of subtracting the mean and divide by the standard deviation. In such a case, each value would reflect the distance from the mean in units of standard deviation.<\/p>\n<p>If we would assume all variables come from some normal distribution, then scaling would bring them all close to the standard normal distribution. The resulting distribution has a mean of 0 and a standard deviation of 1.<\/p>\n<p><strong>Standard scaling formula<\/strong>:<\/p>\n<p><span class=\"math display\">\\[Transformed.Values = \\frac{Values - Mean}{Standard.Deviation}\\]<\/span><\/p>\n<p>An alternative to standardization is the <strong>mean normalization<\/strong>, which resulting distribution will have between -1 and 1 with mean = 0.<\/p>\n<p><strong>Mean normalization formula<\/strong>:<\/p>\n<p><span class=\"math display\">\\[Transformed.Values = \\frac{Values - Mean}{Maximum - Minimum}\\]<\/span><\/p>\n<div class=\"success\">\n<p>Standardization and Mean Normalization can be used for algorithms that assumes zero centric data like <em>Principal Component Analysis<\/em>(PCA).<\/p>\n<\/div>\n<p>The following R code standardizes the <code>mtcars<\/code> data set and creates a heatmap:<\/p>\n<pre class=\"r\"><code>heatmaply(\r\n  scale(mtcars), \r\n  xlab = \"Features\",\r\n  ylab = \"Cars\", \r\n  main = \"Data Scaling\"\r\n)<\/code><\/pre>\n<p><iframe width=\"95%\" height=\"600\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-tutorial\/figures\/data-normalization-in-r-for-heatmap-visualization-interactive-heatmap-scaling.html\" frameborder=\"2\"><br \/>\n<\/iframe><\/p>\n<\/div>\n<div id=\"normalization\" class=\"section level2\">\n<h2>Normalization<\/h2>\n<p>When variables in the data comes from possibly different (and non-normal) distributions, other transformations may be in order. Another possibility is to normalize the variables to brings data to the 0 to 1 scale by subtracting the minimum and dividing by the maximum of all observations.<\/p>\n<p>This preserves the shape of each variable\u2019s distribution while making them easily comparable on the same \u201cscale\u201d.<\/p>\n<p><strong>Formula to normalize data between 0 and 1<\/strong> :<\/p>\n<p><span class=\"math display\">\\[Transformed.Values = \\frac{Values - Minimum}{Maximum - Minimum}\\]<\/span><\/p>\n<p><strong>Formula to rescale the data between an arbitrary set of values [a, b]<\/strong>:<\/p>\n<p><span class=\"math display\">\\[<br \/>\nTransformed.Values = a + \\frac{(Values - Minimum)(b-a)}{Maximum - Minimum}<br \/>\n\\]<\/span><\/p>\n<p>where <code>a,b<\/code> are the min-max values.<\/p>\n<p><strong>Normalize data in R<\/strong>. Using the Min-Max normalization function on <code>mtcars<\/code> data easily reveals columns with only two (<code>am<\/code>, <code>vs<\/code>) or three (<code>gear<\/code>, <code>cyl<\/code>) variables compared with variables that have a higher resolution of possible values:<\/p>\n<pre class=\"r\"><code>heatmaply(\r\n  normalize(mtcars),\r\n  xlab = \"Features\",\r\n  ylab = \"Cars\", \r\n  main = \"Data Normalization\"\r\n)<\/code><\/pre>\n<p><iframe width=\"95%\" height=\"600\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-tutorial\/figures\/data-normalization-in-r-for-heatmap-visualization-interactive-heatmap-normalization.html\" frameborder=\"2\"><br \/>\n<\/iframe><\/p>\n<\/div>\n<div id=\"percentile-transformation\" class=\"section level2\">\n<h2>Percentile transformation<\/h2>\n<p>An alternative to <code>normalize<\/code> is the <code>percentize<\/code> function. This is similar to ranking the variables, but instead of keeping the rank values, divide them by the maximal rank. This is done by using the <code>ecdf<\/code> of the variables on their own values, bringing each value to its empirical percentile. The benefit of the percentize function is that each value has a relatively clear interpretation, it is the percent of observations with that value or below it.<\/p>\n<pre class=\"r\"><code>heatmaply(\r\n  percentize(mtcars),\r\n  xlab = \"Features\",\r\n  ylab = \"Cars\", \r\n  main = \"Percentile Transformation\"\r\n)<\/code><\/pre>\n<p><iframe width=\"95%\" height=\"600\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-tutorial\/figures\/data-normalization-in-r-for-heatmap-visualization-interactive-heatmap-percentile-transformation.html\" frameborder=\"2\"><br \/>\n<\/iframe><\/p>\n<div class=\"warning\">\n<p>Notice that for binary variables (0 and 1), the percentile transformation will turn all 0 values to their proportion and all 1 values will remain 1. This means the transformation is not symmetric for 0 and 1. Hence, if scaling for clustering, it might be better to use rank for dealing with tie values (if no ties are present, then percentize will perform similarly to rank).<\/p>\n<\/div>\n<\/div>\n<div id=\"references\" class=\"section level2\">\n<h2>References<\/h2>\n<ul>\n<li><a href=\"https:\/\/cran.r-project.org\/web\/packages\/heatmaply\/vignettes\/heatmaply.html\">Introduction to heatmaply<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p><!--end rdoc--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Data normalization methods are used to make variables, measured in different scales, have comparable values. This preprocessing steps is important for clustering and heatmap visualization, principal component analysis and other [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":15715,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rating_form_position":"","rating_results_position":"","mr_structured_data_type":"","footnotes":""},"categories":[123,134],"tags":[363,135],"class_list":["post-15791","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cluster-analysis","category-data-visualization","tag-heatmap","tag-interactive-visualization"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to Normalize and Standardize Data in R for Great Heatmap Visualization - Datanovia<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.datanovia.com\/en\/blog\/how-to-normalize-and-standardize-data-in-r-for-great-heatmap-visualization\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Normalize and Standardize Data in R for Great Heatmap Visualization - Datanovia\" \/>\n<meta property=\"og:description\" content=\"Data normalization methods are used to make variables, measured in different scales, have comparable values. 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