Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
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
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
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Projective Nonnegative Matrix Factorization (PNMF) is able to extract sparse features and provide good approximation for discrete problems such as clustering. However, the original PNMF optimization algorithm can not guarantee theoretical convergence during the iterative learning. We propose here an adaptive multiplicative algorithm for PNMF which is not only theoretically convergent but also significantly faster than the previous implementation. An adaptive exponent scheme has been adopted for our method instead of the old unitary one, which ensures the theoretical convergence and accelerates the convergence speed thanks to the adaptive exponent. We provide new multiplicative update rules for PNMF based on the squared Euclidean distance and the I-divergence. For the empirical contributions, we first provide a counter example on the monotonicity using the original PNMF algorithm, and then verify our proposed method by experiments on a variety of real-world data sets.