Class-Incremental Generalized Discriminant Analysis-猫眼课题宝

类增量广义判别分析

DOI：

10.1162/neco.2006.18.4.979

发表时间：

2006

期刊：

Neural Computation

影响因子：

2.9

通讯作者：

中科院分区：

计算机科学4区

文献类型：

作者：

Wenming Zheng

Generalized discriminant analysis (GDA) is the nonlinear extension of the classical linear discriminant analysis (LDA) via the kernel trick. Mathematically, GDA aims to solve a generalized eigenequation problem, which is always implemented by the use of singular value decomposition (SVD) in the previously proposed GDA algorithms. A major drawback of SVD, however, is the difficulty of designing an incremental solution for the eigenvalue problem. Moreover, there are still numerical problems of computing the eigenvalue problem of large matrices. In this article, we propose another algorithm for solving GDA as for the case of small sample size problem, which applies QR decomposition rather than SVD. A major contribution of the proposed algorithm is that it can incrementally update the discriminant vectors when new classes are inserted into the training set. The other major contribution of this article is the presentation of the modified kernel Gram-Schmidt (MKGS) orthogonalization algorithm for implementing the QR decomposition in the feature space, which is more numerically stable than the kernel Gram-Schmidt (KGS) algorithm. We conduct experiments on both simulated and real data to demonstrate the better performance of the proposed methods.