K-means clustering via principal component analysis
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Co-clustering by block value decomposition
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Nonsmooth Nonnegative Matrix Factorization (nsNMF)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Orthogonal nonnegative matrix t-factorizations for clustering
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
A Generalized Divergence Measure for Nonnegative Matrix Factorization
Neural Computation
Multiplicative updates for non-negative projections
Neurocomputing
Fast Projection-Based Methods for the Least Squares Nonnegative Matrix Approximation Problem
Statistical Analysis and Data Mining
Computational Statistics & Data Analysis
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
Mixed Membership Stochastic Blockmodels
The Journal of Machine Learning Research
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
Linear and nonlinear projective nonnegative matrix factorization
IEEE Transactions on Neural Networks
Quadratic nonnegative matrix factorization
Pattern Recognition
Projective nonnegative matrix factorization for image compression and feature extraction
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
IEEE Transactions on Neural Networks - Part 1
Adaptive multiplicative updates for projective nonnegative matrix factorization
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
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In Nonnegative Matrix Factorization (NMF), a nonnegative matrix is approximated by a product of lower-rank factorizing matrices. Quadratic Nonnegative Matrix Factorization (QNMF) is a new class of NMF methods where some factorizing matrices occur twice in the approximation. QNMF finds its applications in graph partition, bi-clustering, graph matching, etc. However, the original QNMF algorithms employ constant multiplicative update rules and thus have mediocre convergence speed. Here we propose an adaptive multiplicative algorithm for QNMF which is not only theoretically convergent but also significantly faster than the original implementation. An adaptive exponent scheme has been adopted for our method instead of the old constant ones, which enables larger learning steps for improved efficiency. The proposed method is general and thus can be applied to QNMF with a variety of factorization forms and with the most commonly used approximation error measures. We have performed extensive experiments, where the results demonstrate that the new method is effective in various QNMF applications on both synthetic and real-world datasets.