Feature selection based on linear separability and a CPL criterion function

Linear separability of data sets is one of the basic concepts in the theory of neural networks and pattern recognition. Data sets are often linearly separable because of their high dimensionality. Such is the case of genomic data, in which a small number of cases is represented in a space with extremely high dimensionality. An evaluation of linear separability of two data sets can be combined with feature selection and carried out through minimisation of a convex and piecewise-linear (CPL) criterion function. The perceptron criterion function belongs to the CPL family. The basis exchange algorithms allow us to find minimal values of CPL functions efficiently, even in the case of large, multidimensional data sets.