The Geodesic Classification Problem on Graphs

International audienceMotivated by the significant advances in integer optimization in the past decade, Bertsimas and Shioda developed an integer optimization method to the classical statistical problem of classification in a multi-dimensional space, delivering a software package called CRIO (Classification and Regression via Integer Optimization). Following those ideas, we define a new classification problem, exploring its combinatorial aspects. That problem is defined on graphs using the geodesic convexity as an analogy of the Euclidean convexity in the multidimensional space. We denote such a problem by Geodesic Classification (GC) problem. We propose an integer programming formulation for the GC problem along with a branch-and-cut algorithm to solve it. Finally, we show computational experiments in order to evaluate the combinatorial optimization efficiency and classification accuracy of the proposed approach

Integer Programming Models and Polyhedral Study for the Geodesic Classification Problem on Graphs

International audienceWe study a discrete version of the classical classification problem in the Euclidean space, to be called geodesic classification problem. It is defined on a graph, where some vertices are initially assigned a class and the remaining ones must be classified. This vertex partition into classes is grounded on the concept of geodesic convexity on graphs, as a replacement for the Euclidean convexity in the multidimensional space. We propose two new integer programming models along with branch-and-cut algorithms to solve them. We also carry out a polyhedral study of the associated polyhedra, which includes families of facet-defining inequalities and separation algorithms. Finally, we run computational experiments to evaluate the computational efficiency and the classification accuracy of the proposed approaches by comparing them with classic solution methods for the Euclidean convexity classification problem