In the Plot 1A below, the data are represented in the X-Y coordinate system.
Here, we’ll explain only the basics with simple graphical representation of the data. Understanding the details of PCA requires knowledge of linear algebra. In other words, PCA reduces the dimensionality of a multivariate data to two or three principal components, that can be visualized graphically, with minimal loss of information. The goal of PCA is to identify directions (or principal components) along which the variation in the data is maximal. The information in a given data set corresponds to the total variation it contains. The number of principal components is less than or equal to the number of original variables. These new variables correspond to a linear combination of the originals. Principal component analysis is used to extract the important information from a multivariate data table and to express this information as a set of few new variables called principal components. If you have more than 3 variables in your data sets, it could be very difficult to visualize a multi-dimensional hyperspace. Each variable could be considered as a different dimension. Principal component analysis ( PCA) allows us to summarize and to visualize the information in a data set containing individuals/observations described by multiple inter-correlated quantitative variables.
