Nonlinear dimensionality reduction by locally linear inlaying
IEEE Transactions on Neural Networks
Linear-projection-based classification of human postures in time-of-flight data
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
A doubly weighted approach for appearance-based subspace learning methods
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Tensor distance based multilinear locality-preserved maximum information embedding
IEEE Transactions on Neural Networks
Orthogonal Complete Discriminant Locality Preserving Projections for Face Recognition
Neural Processing Letters
Graph descriptors from B-matrix representation
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
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Dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning. Linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze. In this paper, we propose an essentially linear projection technique, called locality-preserved maximum information projection (LPMIP), to identify the underlying manifold structure of a data set. LPMIP considers both the within-locality and the between-locality in the processing of manifold learning. Equivalently, the goal of LPMIP is to preserve the local structure while maximize the out-of-locality (global) information of the samples simultaneously. Different from principal component analysis (PCA) that aims to preserve the global information and locality-preserving projections (LPPs) that is in favor of preserving the local structure of the data set, LPMIP seeks a tradeoff between the global and local structures, which is adjusted by a parameter alpha, so as to find a sub- space that detects the intrinsic manifold structure for classification tasks. Computationally, by constructing the adjacency matrix, LPMIP is formulated as an eigenvalue problem. LPMIP yields orthogonal basis functions, and completely avoids the singularity problem as it exists in LPP. Further, we develop an efficient and stable LPMIP/QR algorithm for implementing LPMIP, especially, on high-dimensional data set. Theoretical analysis shows that conventional linear projection methods such as (weighted) PCA, maximum margin criterion (MMC), linear discriminant analysis (LDA), and LPP could be derived from the LPMIP framework by setting different graph models and constraints. Extensive experiments on face, digit, and facial expression recognition show the effectiveness of the proposed LPMIP method.