Discriminant Projective Non-Negative Matrix Factorization

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W-T X as their coefficients, i.e., X approximate to WWT X. Since PNM

Supervised Sparsity Preserving Projections for Face Recognition

Recently feature extraction methods have commonly been used as a principled approach to understand the intrinsic structure hidden in high-dimensional data. In this paper, a novel supervised learning method, called Supervised Sparsity Preserving Projections (SSPP), is proposed. SSPP attempts to preserve the sparse representation structure of the data when identifying an efficient discriminant subspace. First, SSPP creates a concatenated dictionary by class-wise PCA decompositions and learns the sparse representation structure of each sample under the constructed dictionary using the least squares method. Second, by maximizing the ratio of non-local scatter to local scatter, a Laplacian discriminant function is defined to characterize the separability of the samples in the different sub-manifolds. Then, to achieve improved recognition results, SSPP integrates the learned sparse representation structure as a regular term into the Laplacian discriminant function. Finally, the proposed method is converted into a generalized eigenvalue problem. The extensive and promising experimental results on several popular face databases validate the feasibility and effectiveness of the proposed approach

Discriminant feature extraction: exploiting structures within each sample and across samples.

Zhang, Wei.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 95-109).Abstract also in Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Area of Machine Learning --- p.1Chapter 1.1.1 --- Types of Algorithms --- p.2Chapter 1.1.2 --- Modeling Assumptions --- p.4Chapter 1.2 --- Dimensionality Reduction --- p.4Chapter 1.3 --- Structure of the Thesis --- p.8Chapter 2 --- Dimensionality Reduction --- p.10Chapter 2.1 --- Feature Extraction --- p.11Chapter 2.1.1 --- Linear Feature Extraction --- p.11Chapter 2.1.2 --- Nonlinear Feature Extraction --- p.16Chapter 2.1.3 --- Sparse Feature Extraction --- p.19Chapter 2.1.4 --- Nonnegative Feature Extraction --- p.19Chapter 2.1.5 --- Incremental Feature Extraction --- p.20Chapter 2.2 --- Feature Selection --- p.20Chapter 2.2.1 --- Viewpoint of Feature Extraction --- p.21Chapter 2.2.2 --- Feature-Level Score --- p.22Chapter 2.2.3 --- Subset-Level Score --- p.22Chapter 3 --- Various Views of Feature Extraction --- p.24Chapter 3.1 --- Probabilistic Models --- p.25Chapter 3.2 --- Matrix Factorization --- p.26Chapter 3.3 --- Graph Embedding --- p.28Chapter 3.4 --- Manifold Learning --- p.28Chapter 3.5 --- Distance Metric Learning --- p.32Chapter 4 --- Tensor linear Laplacian discrimination --- p.34Chapter 4.1 --- Motivation --- p.35Chapter 4.2 --- Tensor Linear Laplacian Discrimination --- p.37Chapter 4.2.1 --- Preliminaries of Tensor Operations --- p.38Chapter 4.2.2 --- Discriminant Scatters --- p.38Chapter 4.2.3 --- Solving for Projection Matrices --- p.40Chapter 4.3 --- Definition of Weights --- p.44Chapter 4.3.1 --- Contextual Distance --- p.44Chapter 4.3.2 --- Tensor Coding Length --- p.45Chapter 4.4 --- Experimental Results --- p.47Chapter 4.4.1 --- Face Recognition --- p.48Chapter 4.4.2 --- Texture Classification --- p.50Chapter 4.4.3 --- Handwritten Digit Recognition --- p.52Chapter 4.5 --- Conclusions --- p.54Chapter 5 --- Semi-Supervised Semi-Riemannian Metric Map --- p.56Chapter 5.1 --- Introduction --- p.57Chapter 5.2 --- Semi-Riemannian Spaces --- p.60Chapter 5.3 --- Semi-Supervised Semi-Riemannian Metric Map --- p.61Chapter 5.3.1 --- The Discrepancy Criterion --- p.61Chapter 5.3.2 --- Semi-Riemannian Geometry Based Feature Extraction Framework --- p.63Chapter 5.3.3 --- Semi-Supervised Learning of Semi-Riemannian Metrics --- p.65Chapter 5.4 --- Discussion --- p.72Chapter 5.4.1 --- A General Framework for Semi-Supervised Dimensionality Reduction --- p.72Chapter 5.4.2 --- Comparison to SRDA --- p.74Chapter 5.4.3 --- Advantages over Semi-supervised Discriminant Analysis --- p.74Chapter 5.5 --- Experiments --- p.75Chapter 5.5.1 --- Experimental Setup --- p.76Chapter 5.5.2 --- Face Recognition --- p.76Chapter 5.5.3 --- Handwritten Digit Classification --- p.82Chapter 5.6 --- Conclusion --- p.84Chapter 6 --- Summary --- p.86Chapter A --- The Relationship between LDA and LLD --- p.89Chapter B --- Coding Length --- p.91Chapter C --- Connection between SRDA and ANMM --- p.92Chapter D --- From S3RMM to Graph-Based Approaches --- p.93Bibliography --- p.9