Nonlinear Feature Extraction in a Logarithmic Space with Evolutionary Algorithms

The current paper presents a method to deliver non- linear projections of a data set that discriminate between existing labeled groups of data items. Inspired from traditional linear Projection Pursuit and Linear Discriminant Analysis, the new method seeks nonlinear combinations of attributes as polynomials that maximize Fisher’s criterion. The search for the monomials in a polynomial is conducted in a logarithmic space in order to reduce computational complexity. The selection of monomials and the optimization of weights that conduct to the nonlinear projection are performed with a multi-modal Genetic Algorithm hybridized with Differential Evolution. By alleviating the drawbacks driven from the linearity assumptions in traditional Projection Pursuit, the new method could gain a wide applicability in both unsupervised and supervised data analysis.