Topics in matrix analysis
Applied numerical linear algebra
Applied numerical linear algebra
Non-negative Matrix Factorization for Face Recognition
CCIA '02 Proceedings of the 5th Catalonian Conference on AI: Topics in Artificial Intelligence
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 based methods for object recognition
Pattern Recognition Letters
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Multiplicative Updates for Nonnegative Quadratic Programming
Neural Computation
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
SVD based initialization: A head start for nonnegative matrix factorization
Pattern Recognition
Non-negative Matrix Factorization on Manifold
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Graph Regularized Nonnegative Matrix Factorization for Data Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-negative matrix factorization with quasi-newton optimization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
On trivial solution and scale transfer problems in graph regularized NMF
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Metric learning with two-dimensional smoothness for visual analysis
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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Low rank approximation of matrices has been frequently applied in information processing tasks, and in recent years, Nonnegative Matrix Factorization (NMF) has received considerable attentions for its straightforward interpretability and superior performance. When applied to image processing, ordinary NMF merely views a p1×p2 image as a vector in p1×p2-dimensional space and the pixels of the image are considered as independent. It fails to consider the fact that an image displayed in the plane is intrinsically a matrix, and pixels spatially close to each other may probably be correlated. Even though we have p1×p2 pixels per image, this spatial correlation suggests the real number of freedom is far less. In this paper, we introduce a Spatially Correlated Nonnegative Matrix Factorization algorithm, which explicitly models the spatial correlation between neighboring pixels in the parts-based image representation. A multiplicative updating algorithm is also proposed to solve the corresponding optimization problem. Experimental results on benchmark image data sets demonstrate the effectiveness of the proposed method.