This proposal is to study a novel method for dimensionality reduction and feature extraction of data in matrix form,called Structural Principal Component Analysis (S-PCA).The basic idea of S-PCA is: First, matrix space is decomposed into some low-dimensional subspaces, each of which has some different geometrical structure, by a complementary structures decomposition,then matrix data are mapped into the structural subspaces,and a PCA with structure preserving property is carried out. S-PCA has the following advantages:(1) The low dimensionality of the structure subspaces makes it more computational efficient than the standard PCA. (2) The PCA with structure preserving makes it more robust than the standard PCA.(3) In contrast to the K-PCA, S-PCA transforms the high-dimensional data into the low-dimensional structural subspaces by the structures decomposition, and does not involve any nonlinear optimization in the reconstruction process.(4) S-PCA has lower dimensionality than the GLRA does under the same information loss rate. The key issues of this proposal include: S-PCA algorithm, Symmetrical S-PCA, Structure selection, and applications of S-PCA in computer vision.
