Multivariate Direction Scoring for Dimensionality Reduction in Classification Problems

Dimensionality reduction is the process of reducing the number of features in a data set. In a classification problem, the proposed formula allows to sort a set of directions to be used for data projection, according to a score that estimates their capability of discriminating the different data classes. A reduction in the number of features can be obtained by taking a subset of these directions and projecting data on this space. The projecting vectors can be derived from a spectral representation or other choices. If the vectors are eigenvectors of the data covariance matrix, the proposed score is aimed to take the place of the eigenvalues in eigenvector ordering