caa a22 4500 605478430 CHVBK 20210128100405.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10994-014-5470-z doi (NATIONALLICENCE)springer-10.1007/s10994-014-5470-z A unified statistical approach to non-negative matrix factorization and probabilistic latent semantic indexing [Elektronische Daten] [Karthik Devarajan, Guoli Wang, Nader Ebrahimi] Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix $$V$$ V into the product of two nonnegative matrices, $$W$$ W and $$H$$ H , such that $$V \sim WH$$ V ∼ W H . It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a variety of areas such as natural language processing, neuroscience, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. There has also been simultaneous development of a related statistical latent class modeling approach, namely, probabilistic latent semantic indexing (PLSI), for analyzing and interpreting co-occurrence count data arising in natural language processing. In this paper, we present a generalized statistical approach to NMF and PLSI based on Renyi's divergence between two non-negative matrices, stemming from the Poisson likelihood. Our approach unifies various competing models and provides a unique theoretical framework for these methods. We propose a unified algorithm for NMF and provide a rigorous proof of monotonicity of multiplicative updates for $$W$$ W and $$H$$ H . In addition, we generalize the relationship between NMF and PLSI within this framework. We demonstrate the applicability and utility of our approach as well as its superior performance relative to existing methods using real-life and simulated document clustering data. The Author(s), 2014 Nonnegative matrix factorization nationallicence Probabilistic latent semantic indexing nationallicence Renyi's divergence nationallicence $$\lambda $$ λ -log-likelihood nationallicence EM algorithm nationallicence Biomedical informatics nationallicence Devarajan Karthik Department of Biostatistics and Bioinformatics, Fox Chase Cancer Center, Temple University Health System, 19111, Philadelphia, PA, USA aut Wang Guoli 3M Health Information Systems, 20814, Bethesda, MD, USA aut Ebrahimi Nader Division of Statistics, Northern Illinois University, 60115, DeKalb, IL, USA aut Machine Learning Springer US; http://www.springer-ny.com 99/1(2015-04-01), 137-163 0885-6125 99:1<137 2015 99 10994 https://doi.org/10.1007/s10994-014-5470-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-014-5470-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Devarajan Karthik Department of Biostatistics and Bioinformatics, Fox Chase Cancer Center, Temple University Health System, 19111, Philadelphia, PA, USA aut NATIONALLICENCE 700 1- Wang Guoli 3M Health Information Systems, 20814, Bethesda, MD, USA aut NATIONALLICENCE 700 1- Ebrahimi Nader Division of Statistics, Northern Illinois University, 60115, DeKalb, IL, USA aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 99/1(2015-04-01), 137-163 0885-6125 99:1<137 2015 99 10994