Supervised Exponential Family Principal Component Analysis via Convex Optimization

Recently, supervised dimensionality reduction has been gaining attention, owing to the realization that data labels are often available and strongly suggest important underlying structures in the data. In this paper, we present a novel convex supervised dimensionality reduction approach based on exponential family PCA and provide a simple but novel form to project new testing data into the embedded space. This convex approach successfully avoids the local optima of the EM learning. Moreover, by introducing a sample-based multinomial approximation to exponential family models, it avoids the limitation of the prevailing Gaussian assumptions of standard PCA, and produces a kernelized formulation for nonlinear supervised dimensionality reduction. A training algorithm is then devised based on a subgradient bundle method, whose scalability can be gained through a coordinate descent procedure. The advantage of our global optimization approach is demonstrated by empirical results over both synthetic and real data.