F. X. Albizuri

Genetic algorithms: bridging the convergence gap

In this paper we consider the extension of genetic algorithms (GAs) with a probabilistic Boltzmann reduction operator and prove their convergence to the optimum. The algorithm can be seen as a hybridisation between GAs and simulated annealing (SA), i.e. a SA-like GA. The “temperature” parameter allows us to control the size of the entries of the probabilistic transition matrix of the corresponding Markov chain. In the limit case of temperature zero, the reduction operator becomes a kind of strong elitism. Convergence to the optimum is shown under very mild conditions for the sequence of temperatures {ck}. This means that the proposed algorithm is quite robust, and can be expected to perform well on practical applications.

The high-order Boltzmann machine: learned distribution and topology

In this paper we give a formal definition of the high-order Boltzmann machine (BM), and extend the well-known results on the convergence of the learning algorithm of the two-order BM. From the Bahadur-Lazarsfeld expansion we characterize the probability distribution learned by the high order BM. Likewise a criterion is given to establish the topology of the BM depending on the significant correlations of the particular probability distribution to be learned.

A Sensitivity Analysis of the Self Organizing Maps as an AdaptiveOne-pass Non-stationary Clustering Algorithm: the Case of ColorQuantization of Image Sequences

In this paper we study the sensitivity of the Self Organizing Map to several parameters in the context of the one-pass adaptive computation of cluster representatives over non-stationary data. The paradigm of Non-stationary Clustering is represented by the problem of Color Quantization of image sequences.

Convex Coordinates From Lattice Independent Sets for Visual Pattern Recognition

One of the key processes in nowadays intelligent systems is feature extraction. It pervades applications from computer vision to bioinformatics and data mining. The purpose of this chapter is to introduce a new feature extraction process based on the detection of extremal points on the cloud of points that represent the high dimensional data sample. These extremal points are assumed to define an approximation to the convex hull covering the data sample points. The features extracted are the coordinates of the data points relative to the extremal points, the convex coordinates. We have experimented this approach in several applications that will be summarized in the chapter.

Experiments of Fast Learning with High Order Boltzmann Machines

This work reports the results obtained with the application of High Order Boltzmann Machines without hidden units to construct classifiers for some problems that represent different learning paradigms. The Boltzmann Machine weight updating algorithm remains the same even when some of the units can take values in a discrete set or in a continuous interval. The absence of hidden units and the restriction to classification problems allows for the estimation of the connection statistics, without the computational cost involved in the application of simulated annealing. In this setting, the learning process can be sped up several orders of magnitude with no appreciable loss of quality of the results obtained.

Morphological Neural Networks for Real-time Vision Based Self-Localization

In this paper we present some real time results of the implementation on a mobile robot of visual self-localization algorithms based on Morphological Heteroassociative Memories (MHM). We propose a dual set of min/max MHM storing the views that serve as landmarks for self localization. The binarized input images are subject to erosion in order to increase the robustness of the recall process. We present some empirical results on basic navigation experiments in an indoor environment. We use as the measure of performance of our approach the rate of false recognition, conditioned to some landmark being recognized.

Face localization based on the morphological multiscale fingerprints

Abstract Face localization is a previous step for face recognition systems. We propose morphological multiscale fingerprints (MMF) as a holistic feature extraction technique for face localization. The MMF is computed as the local maxima and minima preserved up to a certain scale in a multiscale analysis based on morphological erosion and dilation. We do not consider any geometrical model of the face features. As an initial validation of our approach, we have compared it with principal component analysis (PCA) over a small custom image database. Afterwards, we have tested it over the CMU image database, with good results. Finally, we present the receiving operator curve (ROC) results as well as some instances of face detection.

A Comparison of Experimental Results with an Evolution Strategy and Competitive Neural Networks for Near Real-Time Color Quantization of Image Sequences

Color quantization of image sequences is a case of non-stationary clustering problem. The approach we adopt to deal with this kind of problems is to propose adaptive algorithms to compute the cluster representatives. We have studied the application of Competitive Neural Networks and Evolution Strategies to the one-pass adaptive solution of this problem. One-pass adaptation is imposed by the near real-time constraint that we try to achieve. In this paper we propose a simple and effective evolution strategy for this task. Two kinds of competitive neural networks are also applied. Experimental results show that the proposed evolution strategy can produce results comparable to that of competitive neural networks.

Structure of the high-order Boltzmann machine from independence maps

In this paper we consider the determination of the structure of the high-order Boltzmann machine (HOBM), a stochastic recurrent network for approximating probability distributions. We obtain the structure of the HOBM, the hypergraph of connections, from conditional independences of the probability distribution to model. We assume that an expert provides these conditional independences and from them we build independence maps, Markov and Bayesian networks, which represent conditional independences through undirected graphs and directed acyclic graphs respectively. From these independence maps we construct the HOBM hypergraph. The central aim of this paper is to obtain a minimal hypergraph. Given that different orderings of the variables provide in general different Bayesian networks, we define their intersection hypergraph. We prove that the intersection hypergraph of all the Bayesian networks (N!) of the distribution is contained by the hypergraph of the Markov network, it is more simple, and we give a procedure to determine a subset of the Bayesian networks that verifies this property. We also prove that the Markov network graph establishes a minimum connectivity for the hypergraphs from Bayesian networks.

Competitive stochastic neural networks for Vector Quantization of images

Abstract A stochastic approximation to the nearest neighbour (NN) classification rule is proposed. This approximation is called Local Stochastic Competition (LSC). Some convergence properties of LSC are discussed, and experimental results are presented. The approach shows a great potential for speeding up the codification process, with an affordable loss of codification quality.