Optimizing Linear and Quadratic Data Transformations for Classification Tasks

Many classification algorithms use the concept of distance or similarity between patterns. Previous work has shown that it is advantageous to optimize general Euclidean distances (GED). In this paper, we optimize data transformations, which is equivalent to searching for GEDs, but can be applied to any learning algorithm, even if it does not use distances explicitly. Two optimization techniques have been used: a simple Local Search (LS) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). CMA-ES is an advanced evolutionary method for optimization in difficult continuous domains. Both diagonal and complete matrices have been considered. The method has also been extended to a quadratic non-linear transformation. Results show that in general, the transformation methods described here either outperform or match the classifier working on the original data.