Fractional-step dimensionality reduction

Linear projections for dimensionality reduction, computed using linear discriminant analysis (LDA), are commonly based on optimization of certain separability criteria in the output space. The resulting optimization problem is linear, but these separability criteria are not directly related to the classification accuracy in the output space. Consequently, a trial and error procedure has to be invoked, experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set. Often, even the best weighting function among the trial choices results in poor classification of data in the subspace. In this short paper, we introduce the concept of fractional dimensionality and develop an incremental procedure, called the fractional-step LDA (F-LDA) to reduce the dimensionality in fractional steps. The F-LDA algorithm is more robust to the selection of weighting function and for any given weighting function, it finds a subspace in which the classification accuracy is higher than that obtained using LDA.