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Directional clustering through matrix factorization

Directional clustering through matrix factorization
Directional clustering through matrix factorization
This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions.
2162-237X
2095-2107
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead

Blumensath, Thomas (2016) Directional clustering through matrix factorization. IEEE Transactions on Neural Networks and Learning Systems, 27 (10), 2095-2107. (doi:10.1109/TNNLS.2015.2505060).

Record type: Article

Abstract

This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions.

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B16_NNLS_final.pdf - Accepted Manuscript
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More information

Submitted date: 19 May 2014
Accepted/In Press date: 20 November 2015
Published date: 7 January 2016
Organisations: Signal Processing & Control Grp

Identifiers

Local EPrints ID: 369214
URI: http://eprints.soton.ac.uk/id/eprint/369214
ISSN: 2162-237X
PURE UUID: a56cfabc-b97d-412f-ba15-efdfdcdf84e0

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Date deposited: 30 Sep 2014 11:01
Last modified: 25 Nov 2019 20:40

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