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Abstract:
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In HDLSS classification, projecting data points onto the normal direction vector of a separating hyperplane often gives useful information about the classifier. We present an interesting discriminant direction vector called maximal data piling (MDP), onto which data points project to only two distinct values, one for each class. It only exists in general when the dimensionality of the data is larger than the sample size. There exist many such directions in the data space, however, the MDP direction has the longest distance between the projections. We investigate mathematical and geometrical properties of the MDP direction and compare its performance as a classification method with other methods such as Fisher's linear discrimination and support vector machine.
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