[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-160259-en":3,"doc-seo-160259-105":29,"detail-sidebar-cat-0-en-105":89},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},160259,687207412472,"Angel","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",4,"Exam","Principal Component Analysis questions - Principal component analysis and clustering in R","Practical class material focused on performing and interpreting principal component analysis (PCA) and applying clustering to quantitative data. The tutorial uses the FactoMineR package, emphasizing interpretation as the core task. It starts with an illustrative simulation including an outlier challenge, then introduces PCA context, typical questions, and variable/individual roles. A detailed workflow is provided on the decathlon dataset, followed by hierarchical clustering and HCPC, with guided questions and tips for normalization, variable choice, and eigenvector visualization.","Data challenge & SHS: Principal component analysis and clustering  \nin R  \nJulie Josse, Gaël Varoquaux, and Bénédicte Colnet  \nFebruary 2022  \nAbstract  \nThis is the practical class associated with the class 2 on principal component analysis and clustering.  \nIn this tutorial, you will learn how to perform a principal component analysis and how to interpret it. You will also learn how to perform a clustering on quantitative data. This notebook makes an intensive use of the package FactoMineR. Interpretation of the results remains the most important part of this tutorial.  \nContents  \nPrincipal component analysis 2  \nIllustrative example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2  \nGeneral introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2  \nAn example: the decathlon data set   2  \nQuestion 1   3  \nQuestion 2   3  \nQuestion 3   3  \nQuestion 4   3  \nQuestion 5   3  \nFactoShiny ................................................. 3  \nClustering 4  \nHierarchical Cluster Analysis (HCA) ................................... 4  \nQuestion 1   4  \nQuestion 2   4  \nQuestion 3   4  \nHierarchical Clustering on Principal Components (HCPC) ....................... 4  \nOpen question (on your own) .................................... 4  \nAknowledgments: François Husson class on youtube, the book “R pour la statistique et la science des données”.  \nknitr ::opts_chunk$set(echo = TRUE )  \n\\# Load all packages needed to execute the job  \n\\# If the packages are not installed, write  \n\\# install.packages(\"\u003Cname of package>\")  \n\\# Clear any existing variables  \nrm (list = ls ())  \n\\# Set seed for reproducibility  \nset .seed ( 123 )  \nPrincipal component analysis  \nIllustrative example  \nBefore going into details, let us look at a funny example. Imagine that I generate two variables X1 and X2 from normal distributions. We want these variables to be linked (correlated) and such that Xj ∼ N (0, 1) . The following chunk performs the simulation. You can take the output data frame and explore the data first with univariate analysis. And then with a bivariate plot.  \nRemark: An outlier is in the dataset. Can you recover it?  \nlibrary(MASS) \\# for simulations  \nSigma \u003C -matrix (c(1 ,0.8 , 1 ,0.8 ),2 ,2 )  \nsimulated_data \u003C -mvrnorm (n = 500 , mu = c(0 ,0), Sigma) output \u003C -data.frame (simulated_data)  \nnames (output) \u003C - c(\"X1\" , \"X2\" )  \noutput[501 ,] \u003C - c(\"X1\" = 2 , \"X2\" = -2) \\# outlier step  \nGeneral introduction  \nContext  \nPrincipal Component Analysis (usually the shortname is PCA but you can also find ACP in French) focuses on typical data you can find in several domains: observations (or individus) in rows, and variables in column. Note that the PCA focuses on quantitative variables (for example age, or price, but not color or sex) . For example we can study the average temperature depending on cities. In that case cities are rows, and in column the average temperature per month.  \nTypical question an ACP answers  \nA typical question you may ask on your data is: how much the different observations are close to one another considering the variables? (remember that everything you will conclude depends on these variables that you added in your initial model) You can also see PCA as a way to find a low-dimensional representation that  \ncaptures the “essence” of high-dimensional data What can you interpret from data?  \nThe PCA will group similar individuals together. Information are also learned on variables, with the correlated variables (meaning that you have a linear link between two variables), and also which variables synthetize the most the observations, or which variables bring different informations.  \nPackage  \nIn this notebook we propose to use the package FactoMineR and the function PCA.  \nAn example: the decathlon data set  \nThe data set is based on the decathlon results during the Athene’s olympic games and the Décastar (another competition) . For e","cbCaiuwAFKl4oSqG","https://ap.wps.com/l/cbCaiuwAFKl4oSqG","pdf",371289,1,"English","en",105,"# Principal component analysis\n## Illustrative example\n## General introduction\n## An example: the decathlon data set\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n## FactoShiny\n# Clustering\n## Hierarchical Cluster Analysis (HCA)\n## Question 1\n## Question 2\n## Question 3\n## Hierarchical Clustering on Principal Components (HCPC)\n## Open question (on your own)","[{\"question\":\"What is the main purpose of PCA in this tutorial?\",\"answer\":\"PCA aims to find a low-dimensional representation that captures the essence of high-dimensional data, helping group similar individuals and understand how variables synthesize observations.\"},{\"question\":\"Which R package and PCA function are used?\",\"answer\":\"The tutorial proposes the FactoMineR package and the PCA function from it, including guidance to check the normalization step in the documentation (?PCA).\"},{\"question\":\"How does the clustering section build on PCA?\",\"answer\":\"It first covers Hierarchical Cluster Analysis (HCA), then introduces Hierarchical Clustering on Principal Components (HCPC) to perform clustering using the PCA results.\"}]","Principal Component Analysis questions - Principal component analysis and clustering in R | PDF",1788052944,10,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":84,"head_meta":86,"extra_data":88,"updated_unix":27},"principal-component-analysis-questions-principal-component-analysis-and-clustering-in-r","",{"@graph":35,"@context":83},[36,52,66],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/exam/",3,{"item":51,"name":13,"@type":42,"position":11},"https://docshare.wps.com/document/principal-component-analysis-questions-principal-component-analysis-and-clustering-in-r/160259/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":60,"encodingFormat":59,"isAccessibleForFree":61,"interactionStatistic":62},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-08-30",true,{"@type":63,"interactionType":64,"userInteractionCount":4},"InteractionCounter",{"@type":65},"ViewAction",{"@type":67,"mainEntity":68},"FAQPage",[69,75,79],{"name":70,"@type":71,"acceptedAnswer":72},"What is the main purpose of PCA in this tutorial?","Question",{"text":73,"@type":74},"PCA aims to find a low-dimensional representation that captures the essence of high-dimensional data, helping group similar individuals and understand how variables synthesize observations.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"Which R package and PCA function are used?",{"text":78,"@type":74},"The tutorial proposes the FactoMineR package and the PCA function from it, including guidance to check the normalization step in the documentation (?PCA).",{"name":80,"@type":71,"acceptedAnswer":81},"How does the clustering section build on PCA?",{"text":82,"@type":74},"It first covers Hierarchical Cluster Analysis (HCA), then introduces Hierarchical Clustering on Principal Components (HCPC) to perform clustering using the PCA results.","https://schema.org",{"og:url":51,"og:type":85,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":87,"canonical":51},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":90},[91,95,99,102,107,112,117,122,127,130,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":92,"show_sort_weight":93,"slug":94},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":96,"show_sort_weight":97,"slug":98},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":100,"slug":101},70,"exam",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},5,"Comic",60,"comic",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},6,"Technology",50,"technology",{"id":113,"doc_module":4,"doc_module_name":45,"category_name":114,"show_sort_weight":115,"slug":116},7,"Healthcare",40,"healthcare",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":119,"show_sort_weight":120,"slug":121},8,"Research & Report",30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":28,"slug":132},"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":103,"slug":136},19,"General","general"]