A new and fast implementation for null space based linear discriminant analysis

In this paper we present a new implementation for the null space based linear discriminant analysis. The main features of our implementation include: (i) the optimal transformation matrix is obtained easily by only orthogonal transformations without computing any eigendecomposition and singular value decomposition (SVD), consequently, our new implementation is eigendecomposition-free and SVD-free; (ii) its main computational complexity is from a economic QR factorization of the data matrix and a economic QR factorization of a n×n matrix with column pivoting, here n is the sample size, thus our new implementation is a fast one. The effectiveness of our new implementation is demonstrated by some real-world data sets.