Non linear PCA and the benefits over linear PCA

Abstract

The increasingly complex world revolves around data with often high dimensionality. To combat this issue, Principal Component Analysis (PCA) aims to reduce the dimension of the problem to sieve out the most important combinations of random variables which account for the highest variance of the problem. However, traditional PCA is too demanding and restrictive and thus arises the need for a more robust form of PCA, termed Non-Linear PCA (NLPCA). This study will focus on one form of Non-Linear PCA, known as Kernel PCA, and examine how effective it is in analyzing and conducting statistical inference on different sets of data in comparison to solely traditional PCA.