[jira] [Created] (SYSTEMML-1146) Improve PCA description in documentation

["Deron Eriksson (JIRA)" <ji...@apache.org>]

Deron Eriksson created SYSTEMML-1146:
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             Summary: Improve PCA description in documentation
                 Key: SYSTEMML-1146
                 URL: https://issues.apache.org/jira/browse/SYSTEMML-1146
             Project: SystemML
          Issue Type: Improvement
          Components: Documentation
            Reporter: Deron Eriksson
            Priority: Minor


David P. Nichols reports that the first sentence of the PCA description in the Algorithms Reference is inaccurate (http://apache.github.io/incubator-systemml/algorithms-matrix-factorization.html#principal-component-analysis).

"Principal Component Analysis (PCA) is a simple, non-parametric method to transform the given data set with possibly correlated columns into a set of linearly uncorrelated or orthogonal columns, called principal components." 

The problem with this statement is that principal component scores typically will not be uncorrelated unless the input data have been centered (or began with means of 0). Orthogonal and uncorrelated are not the same thing. Whether or not two vectors are orthogonal is a function of the raw values, while covariance and hence correlation are functions of the centered values. 

It looks like the text was taken from Wikipedia's Principal component analysis entry. Whoever wrote that part of that entry seems to be assuming that principal components analysis always involves working on a matrix of centered (or centered and scaled) data, but that is not always the case. The default in SystemML is not to center input columns, so typically resulting data columns will not be uncorrelated, though they will be orthogonal.




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