Determining Principal Component Cardinality through the Principle of Minimum Description Length

Ami Tavory

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arXiv · 1901.00059

Determining Principal Component Cardinality through the Principle of Minimum Description Length

Ami Tavory

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Abstract

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.

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Ami Tavory. 2018-12-31. Determining Principal Component Cardinality through the Principle of Minimum Description Length. https://arxiv.org/abs/1901.00059

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