{"id":168210,"date":"2026-02-18T06:38:06","date_gmt":"2026-02-18T05:38:06","guid":{"rendered":"https:\/\/liora.io\/en\/?p=168210"},"modified":"2026-08-08T12:29:19","modified_gmt":"2026-08-08T11:29:19","slug":"pca-principal-component-analysis-what-is-it","status":"publish","type":"post","link":"https:\/\/liora.io\/en\/pca-principal-component-analysis-what-is-it","title":{"rendered":"PCA (Principal Component Analysis): What is it?"},"content":{"rendered":"\n

Do you know the PCA? A very useful method used in dimension reduction, discover how it works in this article.<\/strong><\/p>\n\n\n

What is the Principal Component Analysis?<\/h2>\n\n\n

Who has never had in his hands a dataset containing a very large number of variables without knowing which are the most important?\u00a0 How to reduce this dataset to represent it simply on 2 or 3 axes? Here is the PCA!<\/p>\n\n\n

Principal Component Analysis answers these questions. PCA is a well-known method of dimension reduction<\/strong> that will allow the transformation of highly correlated variables<\/strong> into new variables that are decorrelated from each other.<\/p>\n\n\n

The principle is simple: It is a matter of summarizing the information <\/strong>contained in a large database<\/a> into a certain number of synthetic variables called: Principal Components.<\/p>\n\n\n

The idea is then to be able to project these data on the nearest hyperplane<\/strong> to have a simple representation of our data.<\/p>\n\n\n

Of course, dimension reduction means a loss of information<\/strong>. This is the challenge of a Principal Component Analysis. We must be able to reduce the dimension of our data while keeping a maximum of information.<\/p>\n\n\n

How does a Principal Component Analysis work?<\/h3>\n\n\n

To illustrate the principle of PCA, we will take for example a dataset <\/strong><\/p>\n\n\n

\"ACP_1\"<\/figure>\n\n\n

Thereafter it is important to center and reduce our variables<\/strong> to mitigate the scale effect because they are not calculated on the same basis.<\/p>\n\n\n

Once this step has been completed, we must see our data as a matrix<\/strong> from which we will calculate from which we will calculate eigenvalues<\/strong> and eigenvectors<\/strong>.<\/p>\n\n\n

In linear algebra, the notion of eigenvector corresponds to the study of privileged axes<\/strong>, according to which an application of a space in itself behaves like a dilation, multiplying the vectors by a constant called an eigenvalue. The vectors to which it applies are called eigenvectors, combined in an eigenspace.<\/strong><\/p>\n\n\n

After importing the PCA module from sklearn.decomposition, the eigenvalues returned are<\/p>\n\n\n

The eigenvalues are: [3.48753851 1.47902877 1.15061758 0.93557048 0.65529084 0.15140052]<\/p>\n\n\n

These eigenvalues will allow us to determine the optimal number of factors\/principal components<\/strong> for our PCA. For example, if the optimal number of components is 2, then our data will be represented on two axes<\/strong>, and so on.<\/p>\n\n\n

\"Illustration<\/figure>\n\n\n

On this graph which represents the number of factors to choose from according to the eigenvalues, we indicate that the optimal choice of factor <\/strong>is 2 (thanks to the elbow method). Thus, we will go from dimension 9 to dimension 2 which considerably reduces the basic dimension<\/strong>. As said before, there will necessarily be a loss of information<\/strong> following this reduction. However, we still keep a rate of information of almost 70% which will allow us to have a representation close to my representation in 9 dimensions.<\/p>\n\n\n

Once the PCA module has calculated the coordinates of our data<\/strong>, all that remains to be done is to represent them, but before doing so, we are going to take an interest in a tool<\/strong> that is very often used when performing a Principal Component Analysis, namely the correlation circle<\/strong>.<\/p>\n\n\n

\"ACP_4\"<\/figure>\n\n\n

As our representation is done on 2 axes, the correlation circle is a practical tool <\/strong>that allows us to visualize the importance of each explanatory<\/strong> variable for each representation axis. The direction of each arrow indicates the axis explained by the variable and the direction indicates whether the correlation is positive or negative.<\/p>\n\n\n

We notice that variables<\/strong> such as ‘income’, ‘gdpp’, and ‘health’ are positively correlated to the first axis, while ‘child_mort’ or ‘total_fer’ are also positively correlated<\/strong> but negatively. We can then look at the representation of countries in the two axes chosen by the PCA and see the influence of the variable ‘life_expec’ on their representations.<\/p>\n\n\n

\"ACP_5\"<\/figure>\n\n\n

Here is a representation of each country<\/strong> (167) on 2 axes. To judge the quality of our representation, we decided to color each country according to the life expectancy of each one in 3 groups, we can observe a certain trend. We can then notice that the countries with a high life expectancy are concentrated in the lower right part<\/strong> of the graph. According to the correlation circle<\/strong>, the individuals in this part are partly explained by the variables ‘health’, ‘income’, or ‘gdb’. It can be concluded that countries spending more on health have a higher life expectancy<\/strong>. The same is true for the countries in the upper left part of the graph. According to the correlation circle, this part is mostly explained by the variables ‘child_death’ or ‘total_iron’.<\/p>\n\n\n

If you want to learn more about Principal Component Analysis<\/strong> or other dimension reduction methods<\/strong>, there are several modules dedicated to it in our Data Analyst training<\/a>.<\/p>\n\n\n

Discover our Data Science courses<\/a><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"

Do you know the PCA? A very useful method used in dimension reduction, discover how it works in this article. What is the Principal Component Analysis? Who has never had in his hands a dataset containing a very large number of variables without knowing which are the most important?\u00a0 How to reduce this dataset to […]<\/p>\n","protected":false},"author":74,"featured_media":207098,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[2433],"class_list":["post-168210","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-ai"],"acf":[],"_links":{"self":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/168210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/users\/74"}],"replies":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/comments?post=168210"}],"version-history":[{"count":4,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/168210\/revisions"}],"predecessor-version":[{"id":209832,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/168210\/revisions\/209832"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/media\/207098"}],"wp:attachment":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/media?parent=168210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/categories?post=168210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}