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Principal Components Analysis (PCA) (Lecture: Sep. 10, 2014)

Introduction

Principal Component Analysis (PCA), first invented by <ref> Karl Pearson </ref> in 1901, is a statistical technique to analyze date and its main purpose is to reduce the dimensionality. Suppose there is a set of data points in a P-dimensional space, PCA’s goal is to find a linear supspace with lower dimensionality q (q \leq p, such that it contains as many as possible of data points. In another word, PCA aims to reduce the dimensionality of the data, while preserving its information (or minimizing the loss of information). Information comes from variation. If all points have the same value in one dimension, that di