基于近似梯度算法的Fisher线性判别分析问题的求解研究

Fisher linear discriminant analysis based on the approximate gradient algorithm

Fisher线性判别分析(FLDA,Fisher linear discriminant analysis)是一种经典的线性降维方法,可归结为广义特征值问题的求解,但广义特征值问题的求解的复杂度较高.为了更好地求解FLDA问题,引入了近似梯度下降(PGD,proximal gradient descent)算法,并分析了该算法的收敛性.实验结果表明,相较于求解广义特征值等方法,PGD算法能更高效地求解FLDA问题.

Fisher linear discriminant analysis(FLDA) is a classic linear dimensionality reduction method,which can be reduced to the solution of a generalized eigenvalue problem,but the complexity of the generalized eigenvalue problem is conspicuous. In order to solve the FLDA problem better,the proximal gradient descent(PGD) method is discussed in this paper,and the convergence of the PGD algorithm is analyzed. Experimental results show that the PGD algorithm can solve the FLDA problem more efficiently than the traditional methods.