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A Method of Initialization for Nonnegative Matrix Factorization

Yong-Deok Kim, Seungjin Choi
2007 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07  
Nonnegative matrix factorization (NMF) is a widely-used method for multivariate nonnegative data analysis, due to its ability to learn a parts-based representation.  ...  The initialization method is based on the hierarchical clustering of attributes through a similarity measure re ecting 'closeness to rank-one'.  ...  INTRODUCTION Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data such as images, documents, and spectrograms [1, 2, 3, 4] .  ... 
doi:10.1109/icassp.2007.366291 dblp:conf/icassp/KimC07 fatcat:em3lau7t25bexog62pe7qmqqsm

Fast rank-2 nonnegative matrix factorization for hierarchical document clustering

Da Kuang, Haesun Park
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
Nonnegative matrix factorization (NMF) has been successfully used as a clustering method especially for flat partitioning of documents.  ...  In this paper, we propose an efficient hierarchical document clustering method based on a new algorithm for rank-2 NMF.  ...  INTRODUCTION Nonnegative matrix factorization (NMF) has received wide recognition in many data mining areas such as text analysis [24] .  ... 
doi:10.1145/2487575.2487606 dblp:conf/kdd/KuangP13 fatcat:42anvzn6rfaj5fk264gdingmpi


Xiaoxu Han
2007 Computational Systems Bioinformatics  
In this work, we describe a subspace consensus kernel clustering algorithm based on the projected gradient nonnegative matrix factorization (PG-NMF).  ...  The algorithm is a consensus kernel hierarchical clustering (CKHC) method in the subspace generated by the PG-NMF.  ...  kernel hierarchical clustering at rank r Output: the consensus tree T at rank r // Run PG-NMF X~WH to do feature selection at rank r N times Input: nonnegative matrix X (n×m), rank r, PG-NMF running  ... 
doi:10.1142/9781860948732_0010 fatcat:drscwtsesfcm7iudjcfnztqiva

Fast Clustering and Topic Modeling Based on Rank-2 Nonnegative Matrix Factorization [article]

Da Kuang, Barry Drake, Haesun Park
2015 arXiv   pre-print
Our method is based on fast Rank-2 nonnegative matrix factorization (NMF) that performs binary clustering and an efficient node splitting rule.  ...  In this paper, we propose a fast method for hierarchical clustering and topic modeling called HierNMF2.  ...  The proposed approaches are based on fast and cache-efficient algorithms for Rank-2 nonnegative matrix factorization that performs binary clustering and topoic modeling, as well as an efficient decision  ... 
arXiv:1509.01208v3 fatcat:nwsg2fnlmjfo7ja3p4nynhm44y

DC-NMF: nonnegative matrix factorization based on divide-and-conquer for fast clustering and topic modeling

Rundong Du, Da Kuang, Barry Drake, Haesun Park
2017 Journal of Global Optimization  
Nonnegative matrix factorization (NMF) has proven to be a successful method for cluster and topic discovery in unlabeled data sets.  ...  Given an input matrix where the columns represent data items, we build a binary tree structure of the data items using a recently-proposed efficient algorithm for computing rank-2 NMF, and then gather  ...  One of the best known examples of constrained matrix low rank approximation is the nonnegative matrix factorization (NMF).  ... 
doi:10.1007/s10898-017-0515-z fatcat:4yiqltdchnckjeixbhrvp7lmda

Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology

Karthik Devarajan, Barbara Bryant
2008 PLoS Computational Biology  
Nonnegative matrix factorization (NMF) was introduced as an unsupervised, partsbased learning paradigm involving the decomposition of a nonnegative matrix V into two nonnegative matrices, W and H, via  ...  In the context of a p6n gene expression matrix V consisting of observations on p genes from n samples, each column of W defines a metagene, and each column of H represents the metagene expression pattern  ...  A non-nested hierarchical clustering scheme showing the over-represented functional groups from the gene list is created from different rank factorizations and demonstrated to better characterize groups  ... 
doi:10.1371/journal.pcbi.1000029 pmid:18654623 pmcid:PMC2447881 fatcat:v6gdrtlfh5afxj2xkoexinlzaq

A flexible R package for nonnegative matrix factorization

Renaud Gaujoux, Cathal Seoighe
2010 BMC Bioinformatics  
Nonnegative Matrix Factorization (NMF) is an unsupervised learning technique that has been applied successfully in several fields, including signal processing, face recognition and text mining.  ...  Conclusions: The NMF package helps realize the potential of Nonnegative Matrix Factorization, especially in bioinformatics, providing easy access to methods that have already yielded new insights in many  ...  Estimating the factorization rank A critical parameter in NMF is the factorization rank r. It defines the number of metagenes used to approximate the target matrix.  ... 
doi:10.1186/1471-2105-11-367 pmid:20598126 pmcid:PMC2912887 fatcat:mqbfiy57m5av3in7tzwoxiwwna

eTREE: Learning Tree-structured Embeddings [article]

Faisal M. Almutairi, Yunlong Wang, Dong Wang, Emily Zhao, Nicholas D. Sidiropoulos
2020 arXiv   pre-print
Matrix factorization (MF) plays an important role in a wide range of machine learning and data mining models.  ...  The proposed model not only exploits the tree structure prior, but also learns the hierarchical clustering in an unsupervised data-driven fashion.  ...  NMF models aim to decompose the data matrix into low-rank latent factor matrices as X = AB T , where A ∈ R N ×R , B M ×R only have nonnegative values, and R ≤ min(N, M ) is the matrix rank.  ... 
arXiv:2012.10853v1 fatcat:ljazf5qvhrcb3baierqzd7gw5y

Behavioral clusters in dynamic graphs

James P. Fairbanks, Ramakrishnan Kannan, Haesun Park, David A. Bader
2015 Parallel Computing  
In order to successfully implement this method, we develop a feature based pipeline for dynamic graphs and apply Nonnegative Matrix Factorization (NMF) to these features.  ...  Our method is the first to cluster vertices in a dynamic graph based on arbitrary temporal behaviors.  ...  which uses Nonnegative Matrix Factorization (NMF) on locally extracted features.  ... 
doi:10.1016/j.parco.2015.03.002 fatcat:6jh5pyamxjerdnr4dsfkxded4m

Group Sparsity in Nonnegative Matrix Factorization [chapter]

Jingu Kim, Renato D. C. Monteiro, Haesun Park
2012 Proceedings of the 2012 SIAM International Conference on Data Mining  
In this paper, we develop group sparsity regularization methods for nonnegative matrix factorization (NMF).  ...  Application examples of the proposed method in factor recovery, semi-supervised clustering, and multilingual text analysis are demonstrated. * The work J.  ...  Constrained low-rank factorizations have also been widely used; among them, nonnegative matrix factorization (NMF) imposes nonnegativity constraints on the low-rank factor matrices, and the nonnegativity  ... 
doi:10.1137/1.9781611972825.73 dblp:conf/sdm/KimMP12 fatcat:i445z6hbhrdwjin7nv2zjcxiay

Collaborative Filtering Recommendation Using Nonnegative Matrix Factorization in GPU-Accelerated Spark Platform

Bing Tang, Linyao Kang, Li Zhang, Feiyan Guo, Haiwu He, Shah Nazir
2021 Scientific Programming  
However, as the size of the matrix increases, the processing speed of nonnegative matrix factorization is very slow.  ...  Nonnegative matrix factorization (NMF) has been introduced as an efficient way to reduce the complexity of data compression and its capability of extracting highly interpretable parts from data sets, and  ...  Parallel Nonnegative Matrix Factorization Nonnegative Matrix Factorization.  ... 
doi:10.1155/2021/8841133 fatcat:6tf7qm7zwzce3ebcas7r6dvum4

Rank-Two NMF Clustering for Glioblastoma Characterization

Aymen Bougacha, Ines Njeh, Jihene Boughariou, Omar Kammoun, Kheireddine Ben Mahfoudh, Mariem Dammak, Chokri Mhiri, Ahmed Ben Hamida
2018 Journal of Healthcare Engineering  
In the segmentation process, we apply a rank-two NMF clustering. We have executed our tumor characterization method on BraTS 2015 challenge dataset.  ...  Thus, we provide a nonnegative matrix M from every MRI slice in every segmentation process' step.  ...  Having a nonnegative matrix M ∈ R m * n + and a factorization rank r, discover two nonnegative matrices W ∈ R m * r + and H ∈ R r * n + such that M ≈ WH.  ... 
doi:10.1155/2018/1048164 pmid:30425818 pmcid:PMC6218733 fatcat:crcxqxcuvzfsnjmfathyapb3ty

Hierarchical community detection via rank-2 symmetric nonnegative matrix factorization

Rundong Du, Da Kuang, Barry Drake, Haesun Park
2017 Computational Social Networks  
Our algorithm is based on the highly efficient rank-2 symmetric nonnegative matrix factorization.  ...  Methods: We propose a divide-and-conquer strategy to discover hierarchical community structure, nonoverlapping within each level.  ...  This paper introduces a scalable algorithm based on rank-2 symmetric nonnegative matrix factorization (rank-2 SymNMF) for large-scale hierarchical community detection.  ... 
doi:10.1186/s40649-017-0043-5 pmid:29266136 pmcid:PMC5732610 fatcat:6r5kni7vlncx5bwlymgyc2u7be

Decomposition of Big Tensors With Low Multilinear Rank [article]

Guoxu Zhou and Andrzej Cichocki and Shengli Xie
2014 arXiv   pre-print
; A distributed randomized Tucker decomposition approach for arbitrarily big tensors but with relatively low multilinear rank.  ...  Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations  ...  The K-means algorithm was used to cluster the objects and the accuracy of clustering was defined in [37] .To justify the proposed distributed RandTucker algorithm, we used the MATLAB parallel computing  ... 
arXiv:1412.1885v2 fatcat:ksdgbndpmfc7pmlgxn53u2nup4

The User Behavior Analysis Based on Text Messages Using Parafac and Block Term Decomposition

Bilius Laura Bianca
2018 International Journal of Advanced Computer Science and Applications  
Tensor decompositions represent a start for big data analysis and a start in reduction of dimensionality, object detection, clustering and so on.  ...  The linkage MATLAB function returns a matrix that encodes a tree containing hierarchical clusters of the rows of the input data matrix.  ...  The cluster MATLAB function has two ways of clusterization.  ... 
doi:10.14569/ijacsa.2018.091007 fatcat:afgece5h6ral3b7izf6i7lrbtq
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