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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.  ...  We propose a Bayesian model based on automatic relevance determination in which the columns of the dictionary matrix and the rows of the activation matrix are tied together through a common scale parameter  ...  INTRODUCTION Given a data matrix V of dimensions F × N with nonnegative entries, nonnegative matrix factorization (NMF) consists in finding a low-rank factorization V ≈V WH (1) where W and H are nonnegative  ... 
arXiv:1111.6085v3 fatcat:fkjooflehfhzldy6qawfpp5n7q

Nonlinear matrix factorization with unified embedding for social tag relevance learning

Zechao Li, Jing Liu, Hanqing Lu
2013 Neurocomputing  
In this paper, we propose a nonlinear matrix factorization method with the priors of inter-and intra-correlations among images and tags to effectively predict the tag relevance to the visual contents.  ...  Similarly, we can obtain the top relevant images corresponding to any tag so as to perform the task of image search by keywords.  ...  Unlike the existing matrix factorization work, this paper proposes a nonlinear matrix factorization approach with unified embedding (MFUE) to learn the tag relevance for social image retrieval.  ... 
doi:10.1016/j.neucom.2012.02.046 fatcat:uzpkbqlubrh6jojqdq3ffy46ma

AUTOMATIC RELEVANCE DETERMINATION IN NONNEGATIVE MATRIX FACTORIZATION BASED ON A ZERO-INFLATED COMPOUND POISSON-GAMMA DISTRIBUTION

Hiroyasu Abe, Hiroshi Yadohisa
2016 Journal of the Japanese Society of Computational Statistics  
In this paper, we consider the determination of the number of factors in nonnegative matrix factorization (NMF) for a zero-inflated data matrix.  ...  This zero-inflated case leads to poor approximation to the nonnegative data matrix.  ...  At the end of the algorithm, the effective factors are determined to be all mth factors such that the estimated relevance weight λ m are larger than the minimum (16).  ... 
doi:10.5183/jjscs.1608001_233 fatcat:pkf5wlrcenegznni56gyrvtnbi

Inferring missing relevance judgments from crowd workers via probabilistic matrix factorization

Hyun Joon Jung, Matthew Lease
2012 Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval - SIGIR '12  
We show how probabilistic matrix factorization, a standard approach in collaborative filtering, can be used to infer missing worker judgments such that all workers influence output labels.  ...  Experiments on crowd judgments from the 2010 TREC Relevance Feedback Track show promise of the PMF approach merits further investigation and analysis.  ...  Probabilistic Matrix Factorization (PMF). Suppose we have M tasks (examples to be labeled), N workers, and a label matrix R in which Rij indicates the label of worker i for task j.  ... 
doi:10.1145/2348283.2348486 dblp:conf/sigir/JungL12 fatcat:wdcqxvgxzvg6xkstcgfg4cvise

Identyfikacja krytycznych czynników sukcesu (CSFS) za pomocą macierzy istotności-sterowalności (Relevance-Manageability Matrix) na przykładzie firm sektora transportu lądowego / Identification of critical success factors by Relevance-Manageability Matrix on the example of land transport sector companies

Andrzej Niemiec
2016 Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu  
Relevance-Manageability Matrix turned out to be a simple and useful tool in the selection of the key success factors.  ...  Keywords: land transport, critical success factors, Relevance-Manageability Matrix. Wstęp Transport jest strategicznym działem gospodarki.  ... 
doi:10.15611/pn.2016.442.29 fatcat:b4oqiq4jknaexbgpwxyc6ba34a

Non-negative matrix factorization for the analysis of complex gene expression data: identification of clinically relevant tumor subtypes

Attila Frigyesi, Mattias Höglund
2008 Cancer Informatics  
Non-negative matrix factorization (NMF) is a relatively new approach to analyze gene expression data that models data by additive combinations of non-negative basis vectors (metagenes).  ...  This analysis also revealed that NMF could not factorize one of the data sets in a meaningful way.  ...  Non-negative matrix factorization (NMF) We assume that our gene expression (microarray) data is in the form of a matrix A with n rows corresponding to genes and m columns corresponding to samples and that  ... 
pmid:19259414 pmcid:PMC2623306 fatcat:kap5chbxqndvhix43jmz4kgmjy

Automatic Relevance Determination in Nonnegative Matrix Factorization with the /spl beta/-Divergence

V. Y. F. Tan, C. Fevotte
2013 IEEE Transactions on Pattern Analysis and Machine Intelligence  
This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the -divergence.  ...  We propose a Bayesian model based on automatic relevance determination (ARD) in which the columns of the dictionary matrix and the rows of the activation matrix are tied together through a common scale  ...  Ç INTRODUCTION G IVEN a data matrix V of dimensions F Â N with nonnegative entries, nonnegative matrix factorization (NMF) consists in finding a low-rank factorization V %V ¼ 4 WH; ð1Þ where W and H  ... 
doi:10.1109/tpami.2012.240 pmid:23681989 fatcat:t6du4bgss5b4jcytksjkrsr52e

Interaction of chondrocytes, extracellular matrix and growth factors: relevance for articular cartilage tissue engineering

P.M. van der Kraan, P. Buma, T. van Kuppevelt, W.B. van Den Berg
2002 Osteoarthritis and Cartilage  
Results: Structural matrix macromolecules (e.g. collagen, hyaluronate), but also growth factors (e.g.  ...  Objective: In this review we discuss the role of the extracellular matrix in the regulation of chondrocyte function and the relevance for cartilage tissue engineering.  ...  Therefore the focus of this paper will be on the interaction between chondrocytes, extracellular matrix and growth factors and the relevance of these interactions for cartilage tissue engineering.  ... 
doi:10.1053/joca.2002.0806 pmid:12479385 fatcat:cxom577lhjg35gyls3hdyly4hq

Direct identification of bacteria in urine samples by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and relevance of defensins as interfering factors

H. L. Kohling, A. Bittner, K.-D. Muller, J. Buer, M. Becker, H. Rubben, A. W. Rettenmeier, F. Mosel
2012 Journal of Medical Microbiology  
In recent studies, matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) has proven to be able to rapidly identify bacteria obtained from cultures.  ...  Abbreviations: CoU, Clinic of Urology; DHB, dihydroxybenzoic acid; IMMi, Institute of Medical Microbiology; MALDI-TOF MS, matrix-assisted laser desorption/ionization time-of-flight mass spectrometry; SARAMIS  ...  Subsequently, 0.3 ml 2.5-dihydroxybenzoic acid matrix solution (DHB Matrix Solution; AnagnosTec) was added.  ... 
doi:10.1099/jmm.0.032284-0 pmid:22275503 fatcat:vas7ddejpjbt3nlhntvtlep2hi

Toward a Factor Analytic Definition of Academic Relevance

Steven E. Permut
1974 Educational and Psychological Measurement  
However, it was felt that both the correlation matrix as well as the cross-products matrix should be examined as input to the factor analytic solution.  ...  TOWARD A FACTOR ANALYTIC DEFINITION OF ACADEMIC RELEVANCE STEVEN E. PERMUT!  ... 
doi:10.1177/001316447403400412 fatcat:s3nbgj3scrdxbfewmm7xcrqlye

Nucleon decay matrix elements with the Wilson quark action: an update

S. Aoki, M. Fukugita, S. Hashimoto, K-I. Ishikawa, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneda, S. Kaya, Y. Kuramashi, M. Okawa, T. Onogi (+5 others)
2000 Nuclear Physics B - Proceedings Supplements  
The contribution of irrelevant form factor which has caused an underestimate of the matrix elements in previous studies is subtracted in this calculation.  ...  We present preliminary results of a new lattice computation of hadronic matrix elements of baryon number violating operators which appear in the low-energy effective Lagrangian of (SUSY-)Grand Unified  ...  In Fig. 2 , we plot our results for the relevant form factors at q 2 =0.  ... 
doi:10.1016/s0920-5632(00)91640-2 fatcat:nw3eejrtizduvpipa33hmzijy4

Nucleon decay matrix elements with the Wilson quark action: an update

S Aoki
2000 Nuclear Physics B - Proceedings Supplements  
The contribution of irrelevant form factor which has caused an underestimate of the matrix elements in previous studies is subtracted in this calculation.  ...  We present preliminary results of a new lattice computation of hadronic matrix elements of baryon number violating operators which appear in the low-energy effective Lagrangian of (SUSY-)Grand Unified  ...  In Fig. 2 , we plot our results for the relevant form factors at q 2 =0.  ... 
doi:10.1016/s0920-5632(00)00245-0 fatcat:nodqz7z3qngtbmkf65tskr7zky

Design and Application of Evaluation Indicators for Accounting Information Disclosure of Chemical Companies

Rong Fu, Jianmei Liu, Weiwei Zhao
2018 Chemical Engineering Transactions  
of chemical companies was established, through analysis, it's found that the degree of importance was: relevance, reliability, saliency.  ...  The 10 items of environment accounting information disclosure were divided into three dimensions: relevance, saliency, and reliability, and a quality evaluation system for the accounting information disclosure  ...  and Reliability Relevance important 2 Relevance and Saliency Relevance Very important 4 Reliability and Saliency Reliability important 3 Table 5 : 5 Project layer judgment matrix C C1  ... 
doi:10.3303/cet1866231 doaj:cb5e390b0e1a4bc28880e124d88855bc fatcat:fod6kom3gjfu3bhxqyrzx53thm

Personalization Recommendation Algorithm Based on Trust Correlation Degree and Matrix Factorization

Weimin Li, Xiaokang Zhou, Shohei Shimizu, Mingjun Xin, Jiulei Jiang, Honghao Gao, Qun Jin
2019 IEEE Access  
The recommendation algorithm using matrix factorization and trusted relevance degree has higher prediction accuracy than the basic matrix decomposition and social matrix factorization in terms of accuracy  ...  In this paper, a recommendation algorithm with trusted relevance combined with matrix factorization is proposed.  ...  The results show that the algorithm based on matrix factorization combining trust relevancy outperforms the basic matrix factorization (BaseMF) and SocialMF in terms of recommendation accuracy and stability  ... 
doi:10.1109/access.2018.2885084 fatcat:lwpdshiayfgh3ek6ucxcevt3ri

Page 304 of Educational and Psychological Measurement Vol. 55, Issue 2 [page]

1995 Educational and Psychological Measurement  
The extracted factor matrix was submitted to oblique rotation using a quartimin method, and the final pattern factor matrix is shown in Table 1.  ...  Table 2 shows the correlation matrix among these factors. Bartlett’s test of sphericity easily rejected the hypothesis that this was an identity matrix,  ... 
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