Journal ArticleDOI
Orthogonal locality minimizing globality maximizing projections for feature extraction
TLDR
Based on the analysis of the geometrical meaning of the shift-invariant LPP algorithm, two algorithms to minimize the locality and maximize the globality under an orthogonal projection matrix are proposed.Abstract:
Locality preserving projections (LPP) is a recently developed linear-feature extraction algorithm that has been frequently used in the task of face recognition and other applications. However, LPP does not satisfy the shift-invariance property, which should be satisfied by a linear-feature extraction algorithm. In this paper, we analyze the reason and derive the shift-invariant LPP algorithm. Based on the analysis of the geometrical meaning of the shift-invariant LPP algorithm, we propose two algorithms to minimize the locality and maximize the globality under an orthogonal projection matrix. Experimental results on face recognition are presented to demonstrate the effectiveness of the proposed algorithms.read more
Citations
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Journal ArticleDOI
Fast and Orthogonal Locality Preserving Projections for Dimensionality Reduction
TL;DR: A fast and orthogonal version of LPP, called FOLPP, is proposed, which simultaneously minimizes the locality and maximizes the globality under the Orthogonal constraint, so the computation burden of the proposed algorithm can be effectively alleviated compared with the OLPP algorithm.
Journal ArticleDOI
Feature Selective Projection with Low-Rank Embedding and Dual Laplacian Regularization
Chang Tang,Xinwang Liu,Xinzhong Zhu,Jian Xiong,Miaomiao Li,Jingyuan Xia,Xiangke Wang,Lizhe Wang +7 more
TL;DR: This paper designs an unsupervised linear feature selective projection (FSP) for feature extraction with low-rank embedding and dual Laplacian regularization, with the aim to exploit the intrinsic relationship among data and suppress the impact of noise.
Journal ArticleDOI
Robust Semi-Supervised Subspace Clustering via Non-Negative Low-Rank Representation
TL;DR: This paper proposes a robust semi-supervised subspace clustering method based on non-negative LRR (NNLRR) and introduces an efficient linearized alternating direction method with adaptive penalty to solve the corresponding optimization problem.
Journal ArticleDOI
Tensor Rank Preserving Discriminant Analysis for Facial Recognition
TL;DR: A new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained and discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition.
Journal ArticleDOI
Efficient Image Classification via Multiple Rank Regression
TL;DR: A novel multiple rank regression model (MRR) for matrix data classification is proposed, which employs multiple-rank left projecting vectors and right projecting vectors to regress each matrix data set to its label for each category.
References
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Journal ArticleDOI
Laplacian Eigenmaps for dimensionality reduction and data representation
Mikhail Belkin,Partha Niyogi +1 more
TL;DR: In this article, the authors proposed a geometrically motivated algorithm for representing high-dimensional data, based on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold and the connections to the heat equation.
Book
Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
Proceedings Article
Locality Preserving Projections
Xiaofei He,Partha Niyogi +1 more
TL;DR: These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold.
Journal ArticleDOI
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
TL;DR: A new supervised dimensionality reduction algorithm called marginal Fisher analysis is proposed in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizing the interclass separability.
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