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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