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arXiv · 1907.12159

Approximating the Span of Principal Components via Iterative Least-Squares

Yariv Aizenbud·Barak Sober
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Abstract

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the variance is maximized, its first introduction by Pearson at 1901 was done through defining a non-linear least-squares minimization problem of fitting a plane to scattered data points. Thus, it seems natural that PCA and linear least-squares regression are somewhat related, as they both aim at fitting planes to data points. In this paper, we present a connection between the two approaches. Specifically, we present an iterated linear least-squares approach, yielding a sequence of subspaces, which converges to the space spanned by the leading principal components (i.e., principal space).

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Yariv Aizenbud, Barak Sober. 2019-07-28. Approximating the Span of Principal Components via Iterative Least-Squares. https://arxiv.org/abs/1907.12159

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