Multilinear Supervised Neighborhood Preserving Embedding Analysis of Local Descriptor Tensor
Xian‐Hua Han, Yen-Wei Che · InTech eBooks · 2012
Recently there are considerable interests in geometrically motivated approaches to visual analysis.Therein, the most popular ones include locality preserving projection by He et al. (2005), neighborhood preserving embedding, and so on, which cannot only preserve the local structure between samples but also obtain acceptable recognition rates for face recognition.In real applications, all these subspace learning methods need to firstly reshape the multilinear data into a 1D vector for analysis, which usually suffers an overfitting problem.Therefore, some researchers proposed to solve the curse-of-dimension problem with 2D subspace learning such as 2-D PCA and 2-D LDA by ming Wang et al. (2009) for analyzing directly on a 2D image matrix, which was proven to be suitable in some extend.However, all of the conventional methods usually perform subspace analysis directly on the reshaped vector or matrix of pixel-level intensity, which would be unstable under illumination and background variance.In this paper, we propose MSNPE for discriminant feature extraction on the local descriptor tensor.Unlike tensor discriminant analysis by Wang (2006), which equally deals with the samples in the same category, the proposed MSNPE uses neighbor similarity in the same category as a weight of minimizing the cost function for N th order tensor analysis, which is able to estimate geometrical and topological properties of the sub-manifold tensor from random points ("scattered data") lying on this unknown sub-manifold.In addition, compared with TensorFaces by Casilescu & D.Terzopoulos (2002) method, which also directly analyzes multi-dimensional data, the proposed multilinear supervised neighborhood preserving embedding uses supervised strategy and thus can extract more discriminant features for distinguishing different objects and, at the same time, can preserve samples' relationship of inner object instead of only dimension reduction in TensorFaces.We validate our proposed algorithm on different benchmark databases such as view-based object data sets and Facial image data sets (YALE and CMU PIE) by Belhumeur et al. (1997) andSim et al. (2001).