Normalized discriminant analysis for dimensionality reduction

In this paper, we propose the normalized discriminant analysis (NDA) technique for dimensionality reduction. NDA is built on the information of data point pairs that is implicitly encoded by using the pseudo-Riemannian metric tensor. This makes NDA to be easily adapted for unsupervised or supervised learning. It is also interesting to note that the solution of NDA will asymptotically converge to that of generalized linear discriminant analysis (GLDA) under proper conditions. This gives us some insights in understanding the evolving behavior of NDA. Extensive experiments on a simulated data, face images, character images, and UCI data sets are carried out to demonstrate the effectiveness of NDA.

► We develop normalized discriminant analysis (NDA) for dimensionality reduction. ► NDA is built on the information of data point pairs. ► NDA will converge to generalized LDA under proper conditions. ► Experiments on some data sets are conducted to evaluate the proposed method.