%0 Generic %1 fedorov2016unified %A Fedorov, Igor %A Nalci, Alican %A Giri, Ritwik %A Rao, Bhaskar D. %A Nguyen, Truong Q. %A Garudadri, H. %D 2016 %K NNMF acreuser bayesian %T A Unified Bayesian Framework for Sparse Non-negative Matrix Factorization %U http://arxiv.org/abs/1604.02181 %X In this work, we study the sparse non-negative matrix factorization (Sparse NMF or S-NMF) problem. NMF and S-NMF are popular machine learning tools which decompose a given non-negative dataset into a dictionary and an activation matrix, where both are constrained to be non-negative. We review how common concave sparsity measures from the compressed sensing literature can be extended to the S-NMF problem. Furthermore, we show that these sparsity measures have a Bayesian interpretation and each one corresponds to a specific prior on the activations. We present a comprehensive Sparse Bayesian Learning (SBL) framework for modeling non-negative data and provide details for Type I and Type II inference procedures. We show that efficient multiplicative update rules can be employed to solve the S-NMF problem for the penalty functions discussed and present experimental results validating our assertions.

@misc{fedorov2016unified, abstract = {In this work, we study the sparse non-negative matrix factorization (Sparse NMF or S-NMF) problem. NMF and S-NMF are popular machine learning tools which decompose a given non-negative dataset into a dictionary and an activation matrix, where both are constrained to be non-negative. We review how common concave sparsity measures from the compressed sensing literature can be extended to the S-NMF problem. Furthermore, we show that these sparsity measures have a Bayesian interpretation and each one corresponds to a specific prior on the activations. We present a comprehensive Sparse Bayesian Learning (SBL) framework for modeling non-negative data and provide details for Type I and Type II inference procedures. We show that efficient multiplicative update rules can be employed to solve the S-NMF problem for the penalty functions discussed and present experimental results validating our assertions.}, added-at = {2016-04-11T06:33:50.000+0200}, author = {Fedorov, Igor and Nalci, Alican and Giri, Ritwik and Rao, Bhaskar D. and Nguyen, Truong Q. and Garudadri, H.}, biburl = {https://www.bibsonomy.org/bibtex/2a301fa1cfd9c2f0d8c2b757f2dc48bf8/pixor}, description = {1604.02181v1.pdf}, interhash = {8e0c112c7d1fb420c7f9975463da3381}, intrahash = {a301fa1cfd9c2f0d8c2b757f2dc48bf8}, keywords = {NNMF acreuser bayesian}, note = {cite arxiv:1604.02181v1.pdfComment: Submitted to IEEE Transactions on Signal Processing}, timestamp = {2016-04-11T06:33:50.000+0200}, title = {A Unified Bayesian Framework for Sparse Non-negative Matrix Factorization}, url = {http://arxiv.org/abs/1604.02181}, year = 2016 }