Clustering, multicollinearity, and singular vectors

• URL: http://arxiv.org/abs/2008.03368v1
• Date: Fri, 7 Aug 2020 20:32:34 GMT
• Title: Clustering, multicollinearity, and singular vectors
• Authors: Hamid Usefi
• Abstract summary: Let $A$ be a matrix with its pseudo-matrix $Adagger$ and set $S=I-AdaggerA$. 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.
• Score: 2.055949720959582
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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