Cross-weighted Fisher discriminant analysis for visualization of DNA microarray data

Fisher discriminant analysis (DA) has recently shown promise in dimensionality reduction of high dimensional DNA data. However, the 1D projection provided by this method is an optimal Bayesian classifier only when the intraclass data patterns are purely Gaussian distributed. Unfortunately, it has been well recognized that most DNA expression data are much more realistically represented by a Gaussian mixture model (GMM), which allows for multiple cluster centroids per class. When a data set from such a GMM is projected onto a 1D subspace, its inherent multi-modal nature may be partially or completely obscured. Consequently, traditional Fisher DA is quite inadequate when higher dimensional visualization (e.g. 2D or 3D) is necessary. The proposed technique addresses this problem and makes use of combined supervised and unsupervised learning techniques for several DNA microarray signal processing functions, including intraclass cluster discovery, optimal projection, and identification/selection of responsible gene groups. In particular, a cross-weighted Fisher DA is proposed and its abilities to reduce dimensionality and to visualize data sets are evaluated.