Domingo López-Rodríguez

Probabilistic PCA Self-Organizing Maps

In this paper, we present a probabilistic neural model, which extends Kohonens self-organizing map (SOM) by performing a probabilistic principal component analysis (PPCA) at each neuron. Several SOMs have been proposed in the literature to capture the local principal subspaces, but our approach offers a probabilistic model while it has a low complexity on the dimensionality of the input space. This allows to process very high-dimensional data to obtain reliable estimations of the probability densities which are based on the PPCA framework. Experimental results are presented, which show the map formation capabilities of the proposal with high-dimensional data, and its potential in image and video compression applications.

Graph partitioning via recurrent multivalued neural networks

In this work, the well-known Graph Partitioning (GP) problem for undirected weighted graphs has been studied from two points of view: maximizing (MaxCut) or minimizing (MinCut) the cost of the cut induced in the graph by the partition. An unified model, based on a neural technique for optimization problems, has been applied to these two concrete problems. A detailed description of the model is presented, and the technique to minimize an energy function, that measures the goodness of solutions, is fully described. Some techniques to escape from local optima are presented as well. It has proved to be a very competitive and efficient algorithm, in terms of quality of solutions and computational time, when compared to the state-of-the-art methods. Some simulation results are presented in this paper, to show the comparative efficiency of the methods.

Improving Neural Networks for Mechanism Kinematic Chain Isomorphism Identification

Detection of isomorphism among kinematic chains is essential in mechanical design, but difficult and computationally expensive. It has been shown that both traditional methods and previously presented neural networks still have a lot to be desired in aspects such as simplifying procedure of identification and adapting automatic computation. Therefore, a new algorithm based on a competitive Hopfield network is developed for automatic computation in the kinematic chain isomorphism problem. The neural approach provides directly interpretable solutions and does not demand tuning of parameters. We have tested the algorithm by solving problems reported in the recent mechanical literature. Simulation results show the effectiveness of the network that rapidly identifies isomorphic kinematic chains.

A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains

A lot of methods have been proposed for the kinematic chain isomorphism problem. However, the tool is still needed in building intelligent systems for product design and manufacturing. In this paper, we design a novel multivalued neural network that enables a simplified formulation of the graph isomorphism problem. In order to improve the performance of the model, an additional constraint on the degree of paired vertices is imposed. The resulting discrete neural algorithm converges rapidly under any set of initial conditions and does not need parameter tuning. Simulation results show that the proposed multivalued neural network performs better than other recently presented approaches.

Image compression by vector quantization with recurrent discrete networks

In this work we propose a recurrent multivalued network, generalizing Hopfields model, which can be interpreted as a vector quantifier. We explain the model and establish a relation between vector quantization and sum-of-squares clustering. To test the efficiency of this model as vector quantifier, we apply this new technique to image compression. Two well-known images are used as benchmark, allowing us to compare our model to standard competitive learning. In our simulations, our new technique clearly outperforms the classical algorithm for vector quantization, achieving not only a better distortion rate, but even reducing drastically the computational time.

K-pages graph drawing with multivalued neural networks

In this paper, the K-pages graph layout problem is solved by a new neural model. This model consists of two neural networks performing jointly in order to minimize the same energy function. The neural technique applied to this problem allows to reduce the energy function by changing outputs from both networks -outputs of first network representing location of nodes in the nodes line, while the outputs of the second one meaning the page where the edges are drawn. A detailed description of the model is presented, and the technique to minimize an energy function is fully described. It has proved to be a very competitive and efficient algorithm, in terms of quality of solutions and computational time, when compared to the state-of-the-art heuristic methods specifically designed for this problem. Some simulation results are presented in this paper, to show the comparative efficiency of the methods.

A Dipolar Competitive Neural Network for Video Segmentation

This paper present a video segmentation method which separate pixels corresponding to foreground from those corresponding to background. The proposed background model consists of a competitive neural network based on dipoles, which is used to classify the pixels as background or foreground. Using this kind of neural networks permits an easy hardware implementation to achieve a real time processing with good results. The dipolar representation is designed to deal with the problem of estimating the directionality of data. Experimental results are provided by using the standard PETS dataset and compared with the mixture of Gaussians and background subtraction methods.

A Study into the Improvement of Binary Hopfield Networks for Map Coloring

The map-coloring problem is a well known combinatorial optimization problem which frequently appears in mathematics, graph theory and artificial intelligence. This paper presents a study into the performance of some binary Hopfield networks with discrete dynamics for this classic problem. A number of instances have been simulated to demonstrate that only the proposed binary model provides optimal solutions. In addition, for large-scale maps an algorithm is presented to improve the local minima of the network by solving gradually growing submaps of the considered map. Simulation results for several n-region 4-color maps showed that the proposed neural algorithm converged to a correct colouring from at least 90% of initial states without the fine-tuning of parameters required in another Hopfield models.

Hebbian iterative method for unsupervised clustering with automatic detection of the number of clusters with discrete recurrent networks

In this paper, two important issues concerning pattern recognition by neural networks are studied: a new model of hebbian learning, as well as the effect of the network capacity when retrieving patterns and performing clustering tasks. Particularly, an explanation of the energy function when the capacity is exceeded: the limitation in pattern storage implies that similar patterns are going to be identified by the network, therefore forming different clusters. This ability can be translated as an unsupervised learning of pattern clusters, with one major advantage over most clustering algorithms: the number of data classes is automatically learned, as confirmed by the experiments. Two methods to reinforce learning are proposed to improve the quality of the clustering, by enhancing the learning of patterns relationships. As a related issue, a study on the net capacity, depending on the number of neurons and possible outputs, is presented, and some interesting conclusions are commented.

Shortest common superstring problem with discrete neural networks

In this paper, we investigate the use of artificial neural networks in order to solve the Shortest Common Superstring Problem. Concretely, the neural network used in this work is based on a multivalued model, MREM, very suitable for solving combinatorial optimization problems. We describe the foundations of this neural model, and how it can be implemented in the context of this problem, by taking advantage of a better representation than in other models, which, in turn, contributes to ease the computational dynamics of the model. Experimental results prove that our model outperforms other heuristic approaches known from the specialized literature.