A Tutorial On Principal Component Analysis
Derivation, Discussion and Singular Value Decomposition.
Jon Shlens | jonshlens@ucsd.edu 25 March 2003 | Version 1

Principal component analysis (PCA) is a mainstay of modern data analysis – a black box that is widely used but poorly understood. The goal of this paper is to dispel the magic behind this black box.
This tutorial focuses on building a solid intuition for how and why principal component analysis works; furthermore, it crystallizes this knowledge by deriving from first principals, the mathematics behind PCA.
This tutorial does not shy away from explaining the ideas informally, nor does it shy away from the mathematics.
The hope is that by addressing both aspects, readers of all levels will be able to gain a better understanding of the power of PCA as well as the when, the how and the why of applying this technique.
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Update: Access version 2 of the tutorial here

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