TY - GEN
T1 - Non-negative tensor factorization based on alternating large-scale non-negativity-constrained least squares
AU - Kim, Hyunsoo
AU - Park, Haesun
AU - Eldén, Lars
PY - 2007
Y1 - 2007
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=47649132194&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=47649132194&partnerID=8YFLogxK
U2 - 10.1109/BIBE.2007.4375705
DO - 10.1109/BIBE.2007.4375705
M3 - Conference contribution
AN - SCOPUS:47649132194
SN - 1424415098
SN - 9781424415090
T3 - Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE
SP - 1147
EP - 1151
BT - Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE
T2 - 7th IEEE International Conference on Bioinformatics and Bioengineering, BIBE
Y2 - 14 January 2007 through 17 January 2007
ER -