Clustering Categories in Support Vector Machines

Support Vector Machines (SVM) is the state-of-the-art in Supervised Classification. In this paper the Cluster Support Vector Machines (CLSVM) methodology is proposed with the aim to reduce the complexity of the SVM classifier in the presence of categorical features. The CLSVM methodology lets categories cluster around their peers and builds an SVM classifier using the … Read more

Reformulation of a model for hierarchical divisive graph modularity maximization

Finding clusters, or communities, in a graph, or network is a very important problem which arises in many domains. Several models were proposed for its solution. One of the most studied and exploited is the maximization of the so called modularity, which represents the sum over all communities of the fraction of edges within these … Read more

A Branch-and-Price Approach to the k-Clustering Minimum Biclique Completion Problem

Given a bipartite graph G = (S , T , E ), we consider the problem of finding k bipartite subgraphs, called clusters, such that each vertex i of S appears in exactly one of them, every vertex j of T appears in each cluster in which at least one of its neighbors appears, and … Read more

Finding optimal realignments in sports leagues using a branch-and-cut-and-price approach

The sports team realignment problem can be modelled as $k$-way equipartition: given a complete graph $K_{n}=(V,E)$, with edge weight $c_{e}$ on each edge, partition the vertices $V$ into $k$ divisions that have exactly $S$ vertices, so as to minimize the total weight of the edges that have both endpoints in the same division. In this … Read more

A Tabu Search Algorithm for Partitioning

We present an original method for partitioning by automatic classi- fication, using the optimization technique of tabu search. The method uses a classical tabu search scheme based on transfers for the minimization of the within variance; it introduces in the tabu list the indicator of the object transfered. This method is compared with two stochastic … Read more

Branch-and-cut for the k-way equipartition problem

We investigate the polyhedral structure of a formulation of the k-way equipartition problem and a branch-and-cut algorithm for the problem. The k-way equipartition problem requires dividing the vertices of a weighted graph into k equally sized sets, so as to minimize the total weight of edges that have both endpoints in the same set. Applications … Read more