Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonsmooth Nonnegative Matrix Factorization (nsNMF)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Non-negative Matrix Factorization on Manifold
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Learning with structured sparsity
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Group lasso with overlap and graph lasso
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Model-based compressive sensing
IEEE Transactions on Information Theory
Projective nonnegative graph embedding
IEEE Transactions on Image Processing
Structured Variable Selection with Sparsity-Inducing Norms
The Journal of Machine Learning Research
Topology Preserving Non-negative Matrix Factorization for Face Recognition
IEEE Transactions on Image Processing
IEEE Transactions on Neural Networks
Manifold Regularized Discriminative Nonnegative Matrix Factorization With Fast Gradient Descent
IEEE Transactions on Image Processing
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Non-negativity matrix factorization (NMF) and its variants have been explored in the last decade and are still attractive due to its ability of extracting non-negative basis images. However, most existing NMF based methods are not ready for encoding higher-order data information. One reason is that they do not directly/explicitly model structured data information during learning, and therefore the extracted basis images may not completely describe the ''parts'' in an image [1] very well. In order to solve this problem, the structured sparse NMF has been recently proposed in order to learn structured basis images. It however depends on some special prior knowledge, i.e. one needs to exhaustively define a set of structured patterns in advance. In this paper, we wish to perform structured sparsity learning as automatically as possible. To that end, we propose a pixel dispersion penalty (PDP), which effectively describes the spatial dispersion of pixels in an image without using any manually predefined structured patterns as constraints. In PDP, we consider each part-based feature pattern of an image as a cluster of non-zero pixels; that is the non-zero pixels of a local pattern should be spatially close to each other. Furthermore, by incorporating the proposed PDP, we develop a spatial non-negative matrix factorization (Spatial NMF) and a spatial non-negative component analysis (Spatial NCA). In Spatial NCA, the non-negativity constraint is only imposed on basis images and such constraint on coefficients is released, so both subtractive and additive combinations of non-negative basis images are allowed for reconstructing any images. Extensive experiments are conducted to validate the effectiveness of the proposed pixel dispersion penalty. We also experimentally show that Spatial NCA is more flexible for extracting non-negative basis images and obtains better and more stable performance.