Maximal Data Piling in Discrimination

In a binary discrimination problem, a linear classifier finds a linear hyperplane that separates two classes by partitioning the data space. Especially in a High Dimension Low Sample Size (HDLSS) setting, there are linear separating hyperplanes such that the projections of the training data points onto their normal direction vectors are identically zero, or some non-zero constant. Of interest in this paper is a linear separating hyperplane such that the projections of the training data points from each class onto its normal direction vector have two distinct values, one for each class. This direction vector is uniquely defined in the subspace generated by the data. A simple formula is given to find this direction. In non-HDLSS settings, this direction vector is the same as the Fisher Linear Discrimination direction vector.