Robust Linear Projection: A Pattern Rejection Perspective

Linear projections have been extensively studied for pattern classification. In this paper, we examine them from another perspective: how well they can preserve rejection points. Here rejection points refer to those patterns whose class conditional probabilities are approximately tied. Although such patterns are often rejected in the decision process, due to their unique closeness to the class boundary, they may carry valuable information which we cannot mine from other patterns deep inside the classes. For instance, in support vector machines, the separating hyperplane is completely determined by those support vectors closest to the plane. Along this line, we present an experimental analysis of four commonly used projections with respect to two classical posterior estimators. Empirical results showed that projection robustness depends on the particular posterior estimator used. Finally we discuss the underlying factors that make a robust projection.