Principal Component Analysis: A Natural Approach to Data Exploration

TL;DR

This paper provides an accessible overview of PCA, exploring its theoretical foundations, applications across diverse fields, and experimental validation of its effectiveness in variance explanation and dimensionality reduction.

Contribution

It offers a systematic survey of PCA applications and investigates the impact of data standardization on PCA results, aiding researchers in better understanding and applying PCA.

Findings

PCA effectively explains variance and reduces dimensions.

Standardizing data influences PCA outcomes.

PCA's versatility benefits diverse research areas.

Abstract

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and accessible manner, the basic principles underlying PCA and its applications. Next, we present a systematic, though no exclusive, survey of some representative works illustrating the potential of PCA applications to a wide range of areas. An experimental investigation of the ability of PCA for variance explanation and dimensionality reduction is also developed, which confirms the efficacy of PCA and also shows that standardizing or not the original data can have important effects on the obtained results. Overall, we believe the several covered issues can assist researchers from the most diverse areas in using and interpreting PCA.