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On Rank Selection in Non-Negative Matrix Factorization Using Concordance.
- Source :
-
Mathematics (2227-7390) . Nov2023, Vol. 11 Issue 22, p4611. 18p. - Publication Year :
- 2023
-
Abstract
- The choice of the factorization rank of a matrix is critical, e.g., in dimensionality reduction, filtering, clustering, deconvolution, etc., because selecting a rank that is too high amounts to adjusting the noise, while selecting a rank that is too low results in the oversimplification of the signal. Numerous methods for selecting the factorization rank of a non-negative matrix have been proposed. One of them is the cophenetic correlation coefficient ( c c c ), widely used in data science to evaluate the number of clusters in a hierarchical clustering. In previous work, it was shown that c c c performs better than other methods for rank selection in non-negative matrix factorization (NMF) when the underlying structure of the matrix consists of orthogonal clusters. In this article, we show that using the ratio of c c c to the approximation error significantly improves the accuracy of the rank selection. We also propose a new criterion, c o n c o r d a n c e , which, like c c c , benefits from the stochastic nature of NMF; its accuracy is also improved by using its ratio-to-error form. Using real and simulated data, we show that c o n c o r d a n c e , with a CUSUM-based automatic detection algorithm for its original or ratio-to-error forms, significantly outperforms c c c . It is important to note that the new criterion works for a broader class of matrices, where the underlying clusters are not assumed to be orthogonal. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 22
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 173862806
- Full Text :
- https://doi.org/10.3390/math11224611