Why do we maximize variance during Principal Component Analysis?

machine-learning feature-extraction
karthik A picture karthik A · Sep 12, 2012 · Viewed 11.3k times · Source

I'm trying to read through PCA and saw that the objective was to maximize the variance. I don't quite understand why. Any explanation of other related topics would be helpful

Answer

LSerni picture LSerni · Sep 12, 2012

Variance is a measure of the "variability" of the data you have. Potentially the number of components is infinite (actually, after numerization it is at most equal to the rank of the matrix, as @jazibjamil pointed out), so you want to "squeeze" the most information in each component of the finite set you build.

If, to exaggerate, you were to select a single principal component, you would want it to account for the most variability possible: hence the search for maximum variance, so that the one component collects the most "uniqueness" from the data set.

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