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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 Pro- jection 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 unsuper- vised and supervised data analysis.

Cross-clustering asks for a Boolean matrix to be brought to a quasi-canonical form. The problem has many applications in image processing, circuit design, archaeology, ecology etc. The heuristics currently used to solve it rely on either topological sorting or quasi-random search. We present here two evolutionary approaches to this problem: a permutation-based solution and a clustering one. The results on both real data and randomly generated, scalable, test data show very good convergence and encouraging efficiency properties, mainly for our second approach.

The current work proposes and investigates a new method to identify outliers in multivariate numerical data, driving its roots in projection pursuit. Projection pursuit is basically a method to deliver meaningful linear combinations of attributes. The novelty of our approach resides in introducing nonlinear combinations, able to model more complex interactions among attributes. The exponential increase of the search space with the increase of the polynomial degree is tackled with a genetic algorithm that performs monomial selection. Synthetic test cases highlight the benefits of the new approach over classical linear projection pursuit.