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arXiv · 2008.03368

Clustering, multicollinearity, and singular vectors

Hamid Usefi
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Abstract

Let $A$ be a matrix with its pseudo-matrix $A^{\dagger}$ and set $S=I-A^{\dagger}A$. We prove that, after re-ordering the columns of $A$, the matrix $S$ has a block-diagonal form where each block corresponds to a set of linearly dependent columns. This allows us to identify redundant columns in $A$. We explore some applications in supervised and unsupervised learning, specially feature selection, clustering, and sensitivity of solutions of least squares solutions.

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Hamid Usefi. 2020-08-07. Clustering, multicollinearity, and singular vectors. https://arxiv.org/abs/2008.03368

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