Lagrangean-Based Combinatorial Optimization for Large-Scale S3VMs.

The process of manually labeling instances, essential to a supervised classifier, can be expensive and time-consuming. In such a scenario the semisupervised approach, which makes the use of unlabeled patterns when building the decision function, is a more appealing choice. Indeed, large amounts of unlabeled samples often can be easily obtained. Many optimization techniques have been developed in the last decade to include the unlabeled patterns in the support vector machines formulation. Two broad strategies are followed: continuous and combinatorial. The approach presented in this paper belongs to the latter family and is especially suitable when a fair estimation of the proportion of positive and negative samples is available. Our method is very simple and requires a very light parameter selection. Several medium- and large-scale experiments on both artificial and real-world data sets have been carried out proving the effectiveness and the efficiency of the proposed algorithm.

Clustering methods for the optimization of atomic cluster structure.

In this paper, we propose a revised global optimization method and apply it to large scale cluster conformation problems. In the 1990s, the so-called clustering methods were considered among the most efficient general purpose global optimization techniques; however, their usage has quickly declined in recent years, mainly due to the inherent difficulties of clustering approaches in large dimensional spaces. Inspired from the machine learning literature, we redesigned clustering methods in order to deal with molecular structures in a reduced feature space. Our aim is to show that by suitably choosing a good set of geometrical features coupled with a very efficient descent method, an effective optimization tool is obtained which is capable of finding, with a very high success rate, all known putative optima for medium size clusters without any prior information, both for Lennard-Jones and Morse potentials. The main result is that, beyond being a reliable approach, the proposed method, based on the idea of starting a computationally expensive deep local search only when it seems worth doing so, is capable of saving a huge amount of searches with respect to an analogous algorithm which does not employ a clustering phase. In this paper, we are not claiming the superiority of the proposed method compared to specific, refined, state-of-the-art procedures, but rather indicating a quite straightforward way to save local searches by means of a clustering scheme working in a reduced variable space, which might prove useful when included in many modern methods.