Probabilistic latent semantic indexing
Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval
Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
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Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
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Bayesian Non-negative Matrix Factorization
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Bayesian inference for nonnegative matrix factorisation models
Computational Intelligence and Neuroscience
Detect and track latent factors with online nonnegative matrix factorization
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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Proceedings of the 19th international conference on World wide web
Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
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Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
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Proceedings of the 21st international conference on World Wide Web
A-Optimal Non-negative Projection for image representation
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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ICDM '12 Proceedings of the 2012 IEEE 12th International Conference on Data Mining
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Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information included in the data is insufficient to decompose. Our key idea is that we can ease this problem if complementary data are available that we could integrate into the estimation of the bases and coefficients. In this paper, we propose a novel matrix factorization method called Non-negative Multiple Matrix Factorization (NMMF), which utilizes complementary data as auxiliary matrices that share the row or column indices of the target matrix. The data sparseness is improved by decomposing the target and auxiliary matrices simultaneously, since auxiliary matrices provide information about the bases and coefficients. We formulate NMMF as a generalization of NMF, and then present a parameter estimation procedure derived from the multiplicative update rule. We examined NMMF in both synthetic and real data experiments. The effect of the auxiliary matrices appeared in the improved NMMF performance. We also confirmed that the bases that NMMF obtained from the real data were intuitive and reasonable thanks to the non-negative constraint.