Corpus ID: 221090137

# Clustering, multicollinearity, and singular vectors.

@article{Usefi2020ClusteringMA,
title={Clustering, multicollinearity, and singular vectors.},
author={H. Usefi},
journal={arXiv: Learning},
year={2020}
}
• H. Usefi
• Published 2020
• Computer Science, Mathematics
• arXiv: Learning
• 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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