Orthogonal nonnegative matrix factorization with the Kullback–Leibler divergence
Copyright policy )Orthogonal nonnegative matrix factorization with the Kullback–Leibler divergence
Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing.
10 pages, corrected some typos
- Université de Mons (UMONS) Belgium
- University of Mons Belgium
Machine Learning, Signal Processing (eess.SP), FOS: Computer and information sciences, Information Retrieval, Signal Processing, FOS: Electrical engineering, electronic engineering, information engineering, Machine Learning (stat.ML), Information Retrieval (cs.IR), Machine Learning (cs.LG)
Machine Learning, Signal Processing (eess.SP), FOS: Computer and information sciences, Information Retrieval, Signal Processing, FOS: Electrical engineering, electronic engineering, information engineering, Machine Learning (stat.ML), Information Retrieval (cs.IR), Machine Learning (cs.LG)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!