A Linar Subspace Learning Approach via Sparse Coding线性子空间学习方法，通过稀疏编码.pptVIP

A Linear Subspace Learning Approach via Sparse Coding Lei Zhang et al. ICCV’11 7/10/11 Linear subspace learning (LSL) Most LSL methods directly compute statistics of original training sample (image) e.g. PCA, LDA Fail to exploit different contributions of different image components This paper proposed a LSL method by sparse coding and feature grouping The linear subspace can be computed simultaneously by preserving the more informative/discriminative components and suppressing the less informative/discriminative components Problems How to get feature images (components) Sparse coding based on image patches How to group feature images Variance and Fisher ratio How to reduce dimension Eigen value decomposition Flowchart Dictionary learning and sparse coding A patch based dictionary is learned Each patch is summation of k components Each training image is summation of k components: Feature images are concatenation of those Unsupervised subspace learning Feature grouping is based on variance Most discriminative part: Xa Less discriminative part: Xb Subspace learning Seek for a projection matrix P to maximize the energy Ea of Xa while minimizing energy Eb of Xb by solving the following optimization problem: When Sb is not explicitly expressed without sparse coding and feature grouping it reduces to PCA: Supervised subspace learning Feature grouping is based on Fisher ratio Subspace learning In the subspace, maximize between-class scatter matrix while minimizing within-class scatter matrix. Learning criterion is defined as follows: It becomes LDA, when alpha equals 1 without applying sparse coding and feature grouping Results * Each training sample is decomposed into feature images Feature images are grouped into two parts: MDP and LDP Projection is learned based on MDP and LDP , where *