Evolving linear transformations with a rotation-angles/scaling representation

Similarity between patterns is commonly used in many distance-based classification algorithms like KNN or RBF. Generalized Euclidean Distances (GED) can be optimized in order to improve the classification success rate in distance-based algorithms. This idea can be extended to any classification algorithm, because it can be shown that a GEDs is equivalent to a linear transformations of the dataset. In this paper, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is applied to the optimization of linear transformations represented as matrices. The method has been tested on several domains and results show that the classification success rate can be improved for some of them. However, in some domains, diagonal matrices get higher accuracies than full square ones. In order to solve this problem, we propose in the second part of the paper to represent linear transformations by means of rotation angles and scaling factors, based on the Singular Value Decomposition theorem (SVD). This new representation solves the problems found in the former part.