A Tutorial on Principal Component Analysis

Principal component analysis (PCA) is a standard tool in modern data analysis - in diverse fields from neuroscience to computer graphics - because it is a simple, nonparametric method for extracting relevant information from confusing data sets. With minimal effort PCA provides a roadmap for how to reduce a complex data set to a lower dimension to reveal the sometimes hidden, simplified structures that often underlie it. The goal of this tutorial is to provide both an intuitive feel for PCA, and a thorough discussion of this topic. We will begin with a simple example and provide an intuitive explanation of the goal of PCA. We will continue by adding mathematical rigor to place it within the framework of linear algebra to provide an explicit solution.