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In many pattern recognition applications, feature space expansion is a key step for improving the performance of the classifier. In this paper, we (i) expand the discrete feature space by generating all orderings of values of k discrete attributes exhaustively, (ii) modify the well-known decision tree and rule induction classifiers (ID3, Quilan, 1986 [1] and Ripper, Cohen, 1995 [2]) using these orderings as the new attributes. Our simulation results on 15 datasets from UCI repository [3] show that the novel classifiers perform better than the proper ones in terms of error rate and complexity. This work has been supported by the Turkish Scientific Technical Research Council (TUBITAK) EEEAG 107E127 Publisher's Version Author Pre-Print

We deal in this paper with complex three-dimensional scenes, partitioned into several objects of any shape, and with varying local dimensions. We propose a consistent topological modeling of such scenes, based on a cellular model. We introduce a definition of simple elements for any adjacency graph-based geometrical structure. Then we prove a local characterization of simple cells of a cellular model, in the case of two objects, and of any number of objects. This characterization allows to define homotopic deformations of a complex scene.

The problem of dot clustering is studied from a model-based viewpoint. A set of “placement” processes is chosen, each of which associates a probability with each location in a discrete space; in other words, a placement is a probability mass function (pmf) on the space. A number of dots is then distributed in accordance with each of these pmfs; the pmf and its associated cardinality define a subpopulation of dots. This model is extremely general; the pmfs are arbitrary. Given a set of dots generated by such a model, maximum a posteriori (MAP) methods are applied to recover the most likely set of placements and cardinalities that could have given rise to the dots. This identification problem is different from the partitioning problem, which asks for the most likely partition of the dot population into subpopulations. It is shown how and why MAP methods are useful in cluster analysis, especially when the placement pmfs are non-Gaussian. It is also shown that although the general identification problem is intractable, there is a polynomial time solution if the number of subpopulations is bounded. It is shown that a similar result holds for the partitioning problem.