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Computer Science > Numerical Analysis

arXiv:1301.3389 (cs)
[Submitted on 15 Jan 2013 (v1), last revised 18 Mar 2013 (this version, v2)]

Title:The Diagonalized Newton Algorithm for Nonnegative Matrix Factorization

Authors:Hugo Van hamme
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Abstract:Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated by the low-rank product of two matrices with non-negative entries. In this paper, the approximation quality is measured by the Kullback-Leibler divergence between the data and its low-rank reconstruction. The existence of the simple multiplicative update (MU) algorithm for computing the matrix factors has contributed to the success of NMF. Despite the availability of algorithms showing faster convergence, MU remains popular due to its simplicity. In this paper, a diagonalized Newton algorithm (DNA) is proposed showing faster convergence while the implementation remains simple and suitable for high-rank problems. The DNA algorithm is applied to various publicly available data sets, showing a substantial speed-up on modern hardware.
Comments: 8 pages + references; International Conference on Learning Representations, 2013
Subjects: Numerical Analysis (math.NA); Machine Learning (cs.LG)
Cite as: arXiv:1301.3389 [cs.NA]
  (or arXiv:1301.3389v2 [cs.NA] for this version)
  https://doi.org/10.48550/arXiv.1301.3389

Submission history

From: Hugo Van hamme [view email]
[v1] Tue, 15 Jan 2013 15:59:46 UTC (249 KB)
[v2] Mon, 18 Mar 2013 09:15:29 UTC (251 KB)
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