Fast orthogonal linear discriminant analysis with applications to image classification

Orthogonalized variant of Linear Discriminant Analysisis (LDA) is an effective statistical learning tool for dimension reduction. However, existing orthogonalized LDA algorithms suffer from various drawbacks, including the requirement for expensive computing time. This paper develops an efficient algorithm for dimension reduction, referred to as Fast Orthogonal Linear Discriminant Analysis (FOLDA), which adopts an iterative procedure to extract the orthogonal projection vectors. Different from previous efforts, this new approach applies QR decomposition and regression to solve for a new projection vector in each time of iterations, leading to the by far cheaper computational cost. FOLDA can achieve comparable recognition rates to existing orthogonal LDA algorithms. Experimental results on image databases, such as MNIST, COIL20, MEPG-7, and OUTEX, show the effectiveness and efficiency of FOLDA.