Javier Trejos

Optimization Strategies for Two-Mode Partitioning

Two-mode partitioning is a relatively new form of clustering that clusters both rows and columns of a data matrix. In this paper, we consider deterministic two-mode partitioning methods in which a criterion similar to k-means is optimized. A variety of optimization methods have been proposed for this type of problem. However, it is still unclear which method should be used, as various methods may lead to non-global optima. This paper reviews and compares several optimization methods for two-mode partitioning. Several known methods are discussed, and a new fuzzy steps method is introduced. The fuzzy steps method is based on the fuzzy c-means algorithm of Bezdek (1981) and the fuzzy steps approach of Heiser and Groenen (1997) and Groenen and Jajuga (2001). The performances of all methods are compared in a large simulation study. In our simulations, a two-mode k-means optimization method most often gives the best results. Finally, an empirical data set is used to give a practical example of two-mode partitioning.

Two-mode Partitioning: Review of Methods and Application of Tabu Search

As the special contribution of this paper we deal with an application of tabu search, to the problem of two-mode clustering for minimization of the two-mode variance criterion. States are two-mode partitions, neighborhoods are defined by transfers of a single row or column-mode object into a new class, and the tabu list contains the values of the criterion. We compare the results obtained with those of other methods, such as alternating exchanges, k-means, simulated annealing and a fuzzy-set approach.

Global Optimization Methods for Multidimensional Scaling Applied to Mobile Communications

The purpose of this paper is to present a short overview of recent developments of global optimization in least squares multidimensional scaling. Three promising candidates —the genetic algorithm, simulated annealing, and distance smoothing— are discussed in more detail and compared on a data set arising in mobile communication.

Global stochastic optimization techniques applied to partitioning

We have applied three global stochastic optimization techniques to the problem of partitioning: simulated annealing, genetic algorithms and tabu search. The criterion to be minimized is the within-variance. Results obtained are compared with those of classical algorithms and are shown to be better in nearly all cases.

Clustering by Ant Colony Optimization

We use the heuristic known as ant colony optimization in the partitioning problem for improving solutions of k-means method (McQueen (1967)). Each ant in the algorithm is associated with a partition, which is modified by the principles of the heuristic; that is, by the random selection of an element, and the assignment of another element which is chosen according to a probability that depends on the pheromone trail (related to the overall criterion: the maximization of the between-classes variance), and a local criterion (the distance between objects). The pheromone trail is reinforced for those objects that belong to the same class. We present some preliminary results, compared to results of other techniques, such as simulated annealing, genetic algorithms, tabu search, and k-means. Our results are as good as the best of the above methods.

Application of Simulated Annealing in some Multidimensional Scaling Problems

We apply simulated annealing as a combinatorial optimization heuristic in some multidimensional scaling (MDS) contexts for the minimization of Stress: metric MDS, MDS with restrictions in the configuration and INDSCAL parameter estimation. The application of this technique is based on a discretization of the representation space by a grid. Results obtained are compared to those of usual well-known algorithms and are shown to be better in most of the cases.