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Probabilistic Principal Surfaces (PPS) offer very powerful visualization and classification capabilities and overcome most of the shortcomings of other neural tools such as SOM, GTM, etc. More specifically PPS build a probability density function of a given data set of patterns lying in a D-dimensional space (with D ≫ 3) which can be expressed in terms of a limited number of latent variables laying in a Q-dimensional space (Q is usually 2-3) which can be used to visualize the data in the latent space. PPS may also be arranged in ensembles to tackle very complex classification tasks. Competitive Evolution on Data (CED) is instead an evolutionary system in which the possible solutions (cluster centroids) compete to conquer the largest possible number of resources (data) and thus partition the input data set in clusters. We discuss the application of Spherical-PPS to two data sets coming, respectively, from astronomy (Great Observatory Origins Deep Survey) and from genetics (microarray data from yeast genoma) and of CED to the genetics data only.

Ensembles of Probabilistic Principal Surfaces and Competitive Evolution on Data: two different approaches to data classification