Face Recognition Using Average Invariant Factor

The recent developed intrinsic discriminate analysis (IDA) demonstrates superior recognition rate compared with classical methods such as PC A and LDA. The authors of IDA method explore the relative invariant of images through the total singular value decomposition (SVD) such that a face image is decomposed into three parts. Then the recognition rate is optimized by utilizing different mathematical properties of these three parts.In this paper, we not only re-prove the core theorem of IDA by using the simplified singular value decomposition from a new perspective, but also define the Average Invariant Factor (AIF) that generalizes IDA. And face recognition using Average Invariant Factor is presented.Moreover, we find an important property in IDA method. For the AIF matrix of IDA, the matrixes added to orthogonal vectors of null space are still AIF. Further more, our research shows that SVD decomposition is not the only way to structure Average Invariant Factor. We can also decompose a face image into three parts by means of QR decomposition and construct a series of methods based on AIF. So the theorem based on SVD and QR decompositions enlarge the application value of the AIF methods. The experiments show that these new methods represent better effectiveness in recognition phase. And the whole performance is held upon a stable levels.However, algorithms based on AIF inherit some inherent defects of IDA such as high time complexity and space complexity. Therefore, the kernel methods are presented to lower down the computational expenses and relax the linear assumption of the AIF methods. The theorems and illations in this paper prove the rationality of kernel methods based on AIF. A series of experiments on YALE and ORL sets demonstrate higher performance in terms of recognition rate and efficiency compared with classical statistical analysis methods (e.g., PCA, KPCA and2DPCA) and the IDA algorithm.