Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares

Hyunsoo Kim; Haesun Park; Lars Eldén

doi:10.1109/BIBE.2007.4375705

Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares

Hyunsoo Kim, Haesun Park, Lars Eldén

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

28 Scopus citations

Abstract

Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) have attracted much attention and have been successfully applied to numerous data analysis problems where the elements of the data are necessarily non-negative such as chemical concentrations, spectrometry signal intensities, and digital image pixels. Especially, Andersson and Bro's PARAFAC algorithm with non-negativity constraints (AB-PARAFAC-NC) provided the state-of-the-art NTF algorithm, which uses Bro and de Jong's non-negativity-constrained least squares with single right hand side (NLS/S-RHS). However, solving an NLS with multiple right hand sides (NLS/M-RHS) problem by multiple NLS/S-RHS problems is not recommended due to hidden redundant computation. In this paper, we propose an NTF algorithm based on alternating large-scale non-negativity-constrained least squares (NTF/ANLS) using NLS/M-RHS. In addition, we introduce an algorithm for the regularized NTF based on ANLS (RNTF/ANLS). Our experiments illustrate that our NTF algorithms outperform AB-PARAFAC-NC in terms of computing speed on several data sets we tested.

Original language	English (US)
Title of host publication	Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE
Pages	1147-1151
Number of pages	5
DOIs	https://doi.org/10.1109/BIBE.2007.4375705
State	Published - 2007
Externally published	Yes
Event	7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE - Boston, MA, United States Duration: Jan 14 2007 → Jan 17 2007

Publication series

Name	Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE

Conference

Conference	7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE
Country/Territory	United States
City	Boston, MA
Period	1/14/07 → 1/17/07

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10.1109/BIBE.2007.4375705

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Kim, H., Park, H., & Eldén, L. (2007). Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares. In Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE (pp. 1147-1151). Article 4375705 (Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE). https://doi.org/10.1109/BIBE.2007.4375705

Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares. / Kim, Hyunsoo; Park, Haesun; Eldén, Lars.
Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE. 2007. p. 1147-1151 4375705 (Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kim, H, Park, H & Eldén, L 2007, Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares. in Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE., 4375705, Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE, pp. 1147-1151, 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE, Boston, MA, United States, 1/14/07. https://doi.org/10.1109/BIBE.2007.4375705

Kim H, Park H, Eldén L. Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares. In Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE. 2007. p. 1147-1151. 4375705. (Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE). doi: 10.1109/BIBE.2007.4375705

Kim, Hyunsoo ; Park, Haesun ; Eldén, Lars. / Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares. Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE. 2007. pp. 1147-1151 (Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE).

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abstract = "Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) have attracted much attention and have been successfully applied to numerous data analysis problems where the elements of the data are necessarily non-negative such as chemical concentrations, spectrometry signal intensities, and digital image pixels. Especially, Andersson and Bro's PARAFAC algorithm with non-negativity constraints (AB-PARAFAC-NC) provided the state-of-the-art NTF algorithm, which uses Bro and de Jong's non-negativity-constrained least squares with single right hand side (NLS/S-RHS). However, solving an NLS with multiple right hand sides (NLS/M-RHS) problem by multiple NLS/S-RHS problems is not recommended due to hidden redundant computation. In this paper, we propose an NTF algorithm based on alternating large-scale non-negativity-constrained least squares (NTF/ANLS) using NLS/M-RHS. In addition, we introduce an algorithm for the regularized NTF based on ANLS (RNTF/ANLS). Our experiments illustrate that our NTF algorithms outperform AB-PARAFAC-NC in terms of computing speed on several data sets we tested.",

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AB - Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) have attracted much attention and have been successfully applied to numerous data analysis problems where the elements of the data are necessarily non-negative such as chemical concentrations, spectrometry signal intensities, and digital image pixels. Especially, Andersson and Bro's PARAFAC algorithm with non-negativity constraints (AB-PARAFAC-NC) provided the state-of-the-art NTF algorithm, which uses Bro and de Jong's non-negativity-constrained least squares with single right hand side (NLS/S-RHS). However, solving an NLS with multiple right hand sides (NLS/M-RHS) problem by multiple NLS/S-RHS problems is not recommended due to hidden redundant computation. In this paper, we propose an NTF algorithm based on alternating large-scale non-negativity-constrained least squares (NTF/ANLS) using NLS/M-RHS. In addition, we introduce an algorithm for the regularized NTF based on ANLS (RNTF/ANLS). Our experiments illustrate that our NTF algorithms outperform AB-PARAFAC-NC in terms of computing speed on several data sets we tested.

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Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares

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