Principal Component Analysis (PCA) is a statistical technique that is used to simplify the complexity in high-dimensional data while retaining trends and patterns. It does this by transforming the data into fewer dimensions, which are called principal components. These principal components are new variables that are constructed as linear combinations or mixtures of the initial variables. The idea is to reduce the dimensionality of a data set, while preserving as much as possible of the variation present in the data set. The PCA works in columns, meaning it operates on the variables of the data set, not on the individual observations. The goal is to find a smaller set of variables that are uncorrelated (orthogonal) and that capture most of the information of the original data set. This is achieved by converting the original variables into a new set of variables, the principal components, which are uncorrelated with each other and ordered so that the first few retain most of the variation present in all of the original variables.

Choice A is incorrect. Principal Component Analysis (PCA) does not work in columns to group borrowers based on their variables' profile. PCA is a dimensionality reduction technique that identifies the directions (principal components) in which the data varies the most and projects it onto these directions to reduce its dimensions.

Choice C is incorrect. While PCA can be used for segmentation, it does not operate by grouping borrowers based on their variables' profile in rows. Instead, it transforms a large set of possibly correlated variables into a smaller set of uncorrelated variables or principal components.

Choice D is incorrect. PCA does not work in rows to convert a set of variables into a smaller, more statistically significant one. It operates by transforming the original data space into an equivalent space where each axis corresponds to a principal component that captures as much of the variance in the data as possible.

Things to Remember

• Principal Component Analysis (PCA) is primarily a technique used to reduce the dimensions of a dataset consisting of many interrelated variables, while preserving as much of the variability as possible.
• PCA works by identifying the principal components (PCs) that capture the most variance in the data. These components are linear combinations of the original variables.