Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Nearest neighbor classifier: simultaneous editing and feature selection
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to algorithms
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal Linear Representations of Images for Object Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Generalized low rank approximations of matrices
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
Discriminant Analysis with Tensor Representation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Neighborhood Preserving Embedding
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Two-stage optimal component analysis
Computer Vision and Image Understanding
Locality preserving nonnegative matrix factorization
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Local learning regularized nonnegative matrix factorization
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Document clustering using nonnegative matrix factorization
Information Processing and Management: an International Journal
Kernel Optimization in Discriminant Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Regularized Nonnegative Matrix Factorization for Data Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust nonnegative matrix factorization using L21-norm
Proceedings of the 20th ACM international conference on Information and knowledge management
Constrained Nonnegative Matrix Factorization for Image Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nearest neighbor pattern classification
IEEE Transactions on Information Theory
An optimization criterion for generalized discriminant analysis on undersampled problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The problem of dimensionality reduction is to map data from high dimensional spaces to low dimensional spaces. In the process of dimensionality reduction, the data structure, which is helpful to discover the latent semantics and simultaneously respect the intrinsic geometric structure, should be preserved. In this paper, to discover a low-dimensional embedding space with the nature of structure preservation and basis compactness, we propose a novel dimensionality reduction algorithm, called Structure Preserving Non-negative Matrix Factorization (SPNMF). In SPNMF, three kinds of constraints, namely local affinity, distant repulsion, and embedding basis redundancy elimination, are incorporated into the NMF framework. SPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. The convergence of the proposed update solutions is proved. Extensive experiments on both synthetic data and six real world data sets demonstrate the encouraging performance of the proposed algorithm in comparison to the state-of-the-art algorithms, especially some related works based on NMF. Moreover, the convergence of the proposed updating rules is experimentally validated.