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Selecting β-Divergence for Nonnegative Matrix Factorization by Score Matching [chapter]

Zhiyun Lu, Zhirong Yang, Erkki Oja
2012 Lecture Notes in Computer Science  
Nonnegative Matrix Factorization (NMF) based on the family of β-divergences has shown to be advantageous in several signal processing and data analysis tasks.  ...  Next, we adopt a recent estimation method called Score Matching for β selection in order to overcome the difficulty of calculating the normalizing constant in Tweedie distribution.  ...  Conclusions and Future Work We have proposed an efficiently computable criterion for selecting β-divergence for nonnegative matrix factorization.  ... 
doi:10.1007/978-3-642-33266-1_52 fatcat:2qsh4faitrespodm357dhdkpci

Learning the Information Divergence [article]

Onur Dikmen and Zhirong Yang and Erkki Oja
2014 arXiv   pre-print
Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor Embedding, topic models, and Bayesian network optimization.  ...  Next, we reformulate alpha-divergence in terms of beta-divergence, which enables automatic selection of alpha by maximum likelihood with reuse of the learning principle for beta-divergence.  ...  Divergence selection in NMF The objective in nonnegative matrix factorization (NMF) is to find a low-rank approximation to the observed data by expressing it as a product of two nonnegative matrices, i.e  ... 
arXiv:1406.1385v1 fatcat:gjccxa5co5dnhgmgxse7roq2e4

Nonnegative matrix factorization for spectral data analysis

V. Paul Pauca, J. Piper, Robert J. Plemmons
2006 Linear Algebra and its Applications  
In this paper, we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification  ...  Very often the data to be analyzed is nonnegative, and it is often preferable to take this constraint into account in the analysis process.  ...  General nonnegative matrix factorization One nonnegative matrix factorization algorithm developed by Lee and Seung [14] is based on multiplicative update rules of W and H .  ... 
doi:10.1016/j.laa.2005.06.025 fatcat:46wxaj7b4zhy3fgo5oyhubivsq

Soft nonnegative matrix co-factorizationwith application to multimodal speaker diarization

N. Seichepine, S. Essid, C. Fevotte, O. Cappe
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
This paper presents a new method for bimodal nonnegative matrix factorization (NMF).  ...  It allows for a soft co-factorization, which takes into account the relationship that exists between the modalities being processed, but returns different factors for distinct modalities.  ...  concatenation of β 1 V video and β 2 V audio , using either K = Q or K = Q + 1, and 3) our soft nonnegative matrix co-factorization (sNMcF) method.  ... 
doi:10.1109/icassp.2013.6638316 dblp:conf/icassp/SeichepineEFC13 fatcat:z26kou6fz5e7fj76gqatlejsvy

Nonnegative matrix factorization for real time musical analysis and sight-reading evaluation

Chih-Chieh Cheng, Diane J. Hu, Lawrence K. Saul
2008 Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing  
The pattern-matching in the backend is achieved by nonnegative matrix factorization, an algorithm that represents notes as combinations of learned templates and chords as combinations of single notes.  ...  In this paper, we describe a real-time system for sightreading evaluation of solo instrumental music.  ...  Given a large nonnegative matrix Y, the goal of NMF is to derive a low-rank approximation Y ≈Ŷ whereŶ = WX factorizes as the product of two smaller nonnegative matrices W and X.  ... 
doi:10.1109/icassp.2008.4518035 dblp:conf/icassp/ChengHS08 fatcat:7rxt5trnfjfjxiuj7tkiezvsrm

Single-Channel Audio Source Separation with NMF: Divergences, Constraints and Algorithms [chapter]

Cédric Févotte, Emmanuel Vincent, Alexey Ozerov
2018 Signals and Communication Technology  
Spectral decomposition by nonnegative matrix factorisation (NMF) has become state-of-the-art practice in many audio signal processing tasks, such as source separation, enhancement or transcription.  ...  We present the standard majorisation-minimisation strategy to address optimisation for NMF with common β -divergence, a family of measures of fit that takes the quadratic cost, the generalised Kullback-Leibler  ...  nonnegativity of the factors W and H.  ... 
doi:10.1007/978-3-319-73031-8_1 fatcat:nqf4mgbt6jh5pa2jej4jzk2pli

Automatic Relevance Determination in Nonnegative Matrix Factorization with the β-Divergence [article]

Vincent Y. F. Tan, Cédric Févotte
2012 arXiv   pre-print
This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the \beta-divergence.  ...  A family of majorization-minimization algorithms is proposed for maximum a posteriori (MAP) estimation.  ...  Taylan Cemgil for discussions on Tweedie distributions, as well as Morten Mørup and Matt Hoffman for sharing their code.  ... 
arXiv:1111.6085v3 fatcat:fkjooflehfhzldy6qawfpp5n7q

Learning mixed divergences in coupled matrix and tensor factorization models

Umut Simsekli, Ali Taylan Cemgil, Beyza Ermis
2015 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Such cost functions are useful for Nonnegative Matrix and Tensor Factorization models with a compound Poisson observation model.  ...  There are several well known matrix and tensor factorization algorithms that minimize the β-divergence; these estimate the mean parameter.  ...  Acknowledgments Funded by TÜBİTAK grant number 110E292, project Bayesian matrix and tensor factorizations (BAYTEN). U. Ş. is also supported by a Ph.D. scholarship from TÜBİTAK.  ... 
doi:10.1109/icassp.2015.7178345 dblp:conf/icassp/SimsekliCE15 fatcat:5wa3i2y4ajb53kifw2icsv4fqy

Weighted Feature Subset Non-negative Matrix Factorization and Its Applications to Document Understanding

Dingding Wang, Tao Li, Chris Ding
2010 2010 IEEE International Conference on Data Mining  
The proposed approach extends non-negative matrix factorization (NMF) by incorporating a weight matrix to indicate the importance of the keywords.  ...  Keywords-Non-negative matrix factorization; feature selection; weighted feature subset non-negative matrix factorization.  ...  In general, NMF factorizes the input nonnegative data matrix X into two nonnegative matrices, X ≈ F G T , where G ∈ R n×k + is the cluster indicator matrix for clustering columns of X and F = (f 1 , ·  ... 
doi:10.1109/icdm.2010.47 dblp:conf/icdm/WangLD10 fatcat:q4hoqyt4onak7ezaqhomuxl22m

Bregman divergence as general framework to estimate unnormalized statistical models [article]

Michael Gutmann, Jun-ichiro Hirayama
2012 arXiv   pre-print
We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and score matching belong to the proposed framework, and explain their interconnection based on supervised  ...  We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one  ...  Acknowledgements J.H. was partially supported by JSPS Research Fellowships for Young Scientists.  ... 
arXiv:1202.3727v1 fatcat:x4ezhyawlbf37luyc6b7ohmrx4

Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF [article]

Valentin Leplat, Nicolas Gillis, Man Shun Ang
2020 arXiv   pre-print
To perform this task, nonnegative matrix factorization (NMF) based on the Kullback-Leibler and Itakura-Saito β-divergences is a standard and state-of-the-art technique that uses the time-frequency representation  ...  It is based on the minimization of β-divergences along with a penalty term that promotes the columns of the dictionary matrix to have a small volume.  ...  We also thank the reviewers for their insightful comments that helped us improve the paper.  ... 
arXiv:1907.02404v2 fatcat:r5ppadc32nezfj67p5ak4m7dky

Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization [article]

Nicolas Gillis, Le Thi Khanh Hien, Valentin Leplat, Vincent Y. F. Tan
2021 arXiv   pre-print
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data.  ...  We propose to use Lagrange duality to judiciously optimize for a set of weights to be used within the framework of the weighted-sum approach, that is, we minimize a single objective function which is a  ...  ACKNOWLEDGMENTS We thank the reviewers and the handling editor for their insightful comments that helped us improve the paper.  ... 
arXiv:1901.10757v3 fatcat:ilttanzoqrcynm77xhblrtbgpm

Evolutionary nonnegative matrix factorization with adaptive control of cluster quality

Liyun Gong, Tingting Mu, Meng Wang, Hengchang Liu, John Y. Goulermas
2018 Neurocomputing  
Nonnegative matrix factorization (NMF) approximates a given data matrix using linear combinations of a small number of nonnegative basis vectors, weighted by nonnegative encoding coefficients.  ...  This enables the exploration of the cluster structure of the data through the examination of the values of the encoding coefficients and therefore, NMF is often used as a popular tool for clustering analysis  ...  Φ F Score-based ! selection! Score-based ! selection! Φ M Φ M Φ M 2 nd Iteration!  ... 
doi:10.1016/j.neucom.2017.06.067 fatcat:zczh3rx3vndzdkd6rx6gb4ly4m

Incorporating Implicit Link Preference Into Overlapping Community Detection

Hongyi Zhang, Irwin King, Michael Lyu
2015 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Unlike conventional matrix factorization approaches, which simply approximate the original adjacency matrix in value, our model maximizes the likelihood of the preference order for each node by following  ...  In this paper, we propose a preference-based nonnegative matrix factorization (PNMF) model to incorporate implicit link preference information.  ...  We define F 1 score to be the average of the F 1 score of the best-matching ground-truth community to each detected community, i.e, F 1 = 1 | Ĉ| Ĉi∈ Ĉ F 1 (C b(i) , Ĉi ), where the best matching function  ... 
doi:10.1609/aaai.v29i1.9155 fatcat:6huo2kwb4vbbrfjba3gmgunt4e

Integrating Document Clustering and Multidocument Summarization

Dingding Wang, Shenghuo Zhu, Tao Li, Yun Chi, Yihong Gong
2011 ACM Transactions on Knowledge Discovery from Data  
Although many of these clustering methods can group the documents effectively, it is still hard for people to capture the meaning of the documents since there is no satisfactory interpretation for each  ...  Current document clustering methods usually represent the given collection of documents as a document-term matrix and then conduct the clustering process.  ...  -SemanSNMF. constructs sentence similarity matrix by using semantic role analysis, and then conducts symmetric nonnegative matrix factorization on the similarity 14:18 D.  ... 
doi:10.1145/1993077.1993078 fatcat:oe3h2c7x6jcp3alaftmq22lwli
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