Orthogonal nonnegative matrix t-factorizations for clustering

Ding, Chris; Li, Tao; Peng, Wei; Park, Haesun

doi:10.1145/1150402.1150420

Cited by 977 publications

(950 citation statements)

References 27 publications

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“…Our framework uses the non-negative matrix factorization technique given in [9], [5]. Let A ∈ R n×n + and B ∈ R m×m + be the adjacency matrices of the graphs G 1 and G 2 , respectively, whereas C ∈ R n×m + be the adjacency matrix for the links between nodes in G 1 and G 2 .…”

Section: Proposed Frameworkmentioning

confidence: 99%

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Identifying Cohesive Subgroups and Their Correspondences in Multiple Related Networks

Mandayam-Comar

Tan

Jain

2010

2010 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology

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Abstract-Identifying cohesive subgroups in networks, also known as clustering is an active area of research in link mining with many practical applications. However, most of the early work in this area has focused on partitioning a single network or a bipartite graph into clusters/communities. This paper presents a framework that simultaneously clusters nodes from multiple related networks and learns the correspondences between subgroups in different networks. The framework also allows the incorporation of prior information about potential relationships between the subgroups. We have performed extensive experiments on both synthetic and real-life data sets to evaluate the effectiveness of our framework. Our results show superior performance of simultaneous clustering over independent clustering of individual networks.

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Section: Proposed Frameworkmentioning

confidence: 99%

“…The decomposition of A into a 3-factor XU X t instead of a 2-factor XX t enables the framework to deal with directed links [23], [5]. The matrix V reflects the correspondence between the subgroups derived from the two networks.…”

Section: A Joint Clustering Of Multiple Networkmentioning

confidence: 99%

Identifying Cohesive Subgroups and Their Correspondences in Multiple Related Networks

Mandayam-Comar

Tan

Jain

2010

2010 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology

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“…For this data set there are also negative values in the matrix X. In this case, the Gibbs sampler is still valid to seek the nonnegative matrices U and V. It has been indicated by [6] that the NMF model has the character of clustering. In the NMR data, four spectroscopy samples were acquired for the neurons and the rest four samples were for neural stem cells.…”

Section: Nuclear Magnetic Resonance Spectroscopy Datamentioning

confidence: 98%

Pseudo-marginal Markov Chain Monte Carlo for Nonnegative Matrix Factorization

Zhong

2016

Neural Process Lett

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A pseudo-marginal Markov chain Monte Carlo (PMCMC) method is proposed for nonnegative matrix factorization (NMF). The sampler jointly simulates the joint posterior distribution for the nonnegative matrices and the matrix dimensions which indicate the number of the nonnegative components in the NMF model. We show that the PMCMC sampler is a generalization of a version of the reversible jump Markov chain Monte Carlo (RJMCMC). An illustrative synthetic data was used to demonstrate the ability of the proposed PMCMC sampler in inferring the nonnegative matrices and as well as the matrix dimensions. The proposed sampler was also applied to a nuclear magnetic resonance (NMR) spectroscopy data to infer the number of nonnegative components.

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“…As concerning the possibility of making the bases or the encoding matrices closer to the Stiefel manifold (the Stiefel manifold is the set of all real l × k matrices with orthogonal columns {Q ∈ R l×k | Q Q = I k }, being I k the k × k identity matrix) (which means that vectors in W or H should be orthonormal to each other), two different update rules have been proposed in [37] to add orthogonality on W or H, respectively. Particularly, when one desires that matrix W is as close as possible to the identity matrix of conformal dimension (i.e., W W ≈ I r ), the multiplicative update rule (1) can be modified as described in Algorithm 2 (see [38] for details).…”

Section: Nmf Algorithms With Orthogonal Constraintsmentioning

confidence: 99%

Nonnegative Matrix Factorizations Performing Object Detection and Localization

Casalino

Buono

Minervini

2012

Applied Computational Intelligence and Soft Computing

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We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by nonnegative matrix factorizations. Nonnegative matrix factorization represents an emerging example of subspace methods, which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing individual objects. In this paper, we present a prototype system based on some nonnegative factorization algorithms, which differ in the additional properties added to the nonnegative representation of data, in order to investigate if any additional constraint produces better results in general object detection via nonnegative matrix factorizations.

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Orthogonal nonnegative matrix t-factorizations for clustering

Cited by 977 publications

References 27 publications

Identifying Cohesive Subgroups and Their Correspondences in Multiple Related Networks

Identifying Cohesive Subgroups and Their Correspondences in Multiple Related Networks

Pseudo-marginal Markov Chain Monte Carlo for Nonnegative Matrix Factorization

Nonnegative Matrix Factorizations Performing Object Detection and Localization

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