Principal Component Analysis (PCA)

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• How to Calculate Principal Component Analysis (PCA) from Scratch in Python | Jason Brownlee - Machine Learning Mastery
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  • Feature-to-Feature Regression for a Two-Step Conditional Independence Test | Q. Zhang, S. Filippi, S. Flaxman, and D. Sejdinovic
• A Beginner's Guide to Eigenvectors, Eigenvalues, PCA, Covariance and Entropy Learning | Chris Nicholson - A.I. Wiki pathmind
• Everything you did and didn't know about PCA | Alex Williams - Its Neutonal

Principal Component Analysis (PCA) goal is to reduce the dimensionality of a data set consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. The new dimensions are called principal components, and they are uncorrelated and ordered by the amount of variance they explain. PCA can help you simplify large data tables, visualize multidimensional data, and identify hidden patterns in your data. This data reduction technique allows the simplifying multidimensional data sets to 2 or 3 dimensions for plotting purposes and visual variance analysis.

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1. Center (and standardize) data
2. First principal component axis
   1. Across centroid of data cloud
   2. Distance of each point to that line is minimized, so that it crosses the maximum variation of the data cloud
3. Second principal component axis
   1. Orthogonal to first principal component
   2. Along maximum variation in the data
4. First PCA axis becomes x-axis and second PCA axis y-axis
5. Continue process until the necessary number of principal components is obtained