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Clustering multicollinearity and singular vectors

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https://econpapers.repec.org/scripts/redir.pf?u=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0167947322001037;h=repec:eee:csdana:v:173:y:2022:i:c:s0167947322001037
Time Added
6/20/2022, 12:19:08 PM
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Machine Learning
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0
Authors
Hamid Usefi
Abstract
Let A be a matrix with its Moore-Penrose pseudo-inverse A†. It is proved that after re-ordering the columns of A the projector P=I−A†A has a block-diagonal form that is there is a permutation matrix Π such that ΠPΠT=diag(S1S2…Sk). It is further proved that each block Si corresponds to a cluster of columns of A that are linearly dependent with each other. A clustering algorithm is provided that allows to partition the columns of A into clusters where columns in a cluster correlate only with columns within the same cluster. Some applications in supervised and unsupervised learning specially feature selection clustering and sensitivity of solutions of least squares solutions are discussed.
Keywords
Collinearity ; Clustering ; Subset selection ; Machine learning (search for similar items in EconPapers)
Year Published
2022
Series
Computational Statistics & Data Analysis 2022 vol. 173 issue C
Rank
0.76
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