Alberto Guillén

Soft-computing techniques and ARMA model for time series prediction

The challenge of predicting future values of a time series covers a variety of disciplines. The fundamental problem of selecting the order and identifying the time varying parameters of an autoregressive moving average model (ARMA) concerns many important fields of interest such as linear prediction, system identification and spectral analysis. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional ARMA structure. These linear models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. This study was designed: (a) to investigate a hybrid methodology that combines ANN and ARMA models; (b) to resolve one of the most important problems in time series using ARMA structure and Box-Jenkins methodology: the identification of the model. In this paper, we present a new procedure to predict time series using paradigms such as: fuzzy systems, neural networks and evolutionary algorithms. Our goal is to obtain an expert system based on paradigms of artificial intelligence, so that the linear model can be identified automatically, without the need of human expert participation. The obtained linear model will be combined with ANN, making up an hybrid system that could outperform the forecasting result.

Hybridization of intelligent techniques and ARIMA models for time series prediction

Traditionally, the autoregressive moving average (ARMA) model has been one of the most widely used linear models in time series prediction. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional ARMA structure. These linear models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. In this paper we propose a hybridization of intelligent techniques such as ANNs, fuzzy systems and evolutionary algorithms, so that the final hybrid ARIMA-ANN model could outperform the prediction accuracy of those models when used separately. More specifically, we propose the use of fuzzy rules to elicit the order of the ARMA or ARIMA model, without the intervention of a human expert, and the use of a hybrid ARIMA-ANN model that combines the advantages of the easy-to-use and relatively easy-to-tune ARIMA models, and the computational power of ANNs.

Adaptive fuzzy controller: Application to the control of the temperature of a dynamic room in real time

This paper presents a direct adaptive fuzzy controller for unknown monotonic nonlinear systems, thus not requiring the system model, but only a little information about it: the plant monotonicity and its delay. Without any off-line pre-training, the algorithm achieves very high control performance through a three-stage algorithm: (1) output scale factor, (2) adaptation of the fuzzy rule consequents and (3) optimization of the position of the membership functions. The design is simple, in the sense that both the membership functions and the rule-base can be initialized from arbitrary values. It can be applied to a large class of monotonic dynamic or static plants, due the fact that the system is able to modify its behaviour in real time, i.e., during the control process.

Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this paper a multi-objective evolutionary approach is proposed to determine a Pareto-optimum set of fuzzy systems with different compromises between their accuracy and complexity. In particular, two fundamental and competing objectives concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained system. Another key aspect of the algorithm presented in this work is the use of some new expert evolutionary operators, specifically designed for the problem of fuzzy function approximation, that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm.

Yield development in potatoes as influenced by cultivar and the timing and level of nitrogen fertilization

Path-coefficient analysis based on an ontogenetic model was used to study the relationships between tuber yield and yield components as influenced by cultivar and nitrogen fertilization. Four experiments were carried out from 1987 to 1989 in Granada, southern Spain. Two of these experiments used six potato cultivars with a single N rate, while the other two experiments used one cultivar and nine levels of N, split between planting and top-dressing. Variation in tuber yield between cultivars resulted mainly from differences in stem number per m2 followed by tubers per stem and, to a lesser extent, average tuber weight. In N experiments, however, average tuber weight was the only yield component that showed a significant direct effect on yield, while the number of stems per m2 and tubers per stem had negligible direct effects. In addition, the ontogenetic model used indicated compensatory mechanisms during the formation of the three yield components in the potato, which resulted stronger in the N experiments.CompendioPara estudiar las relaciones entre la producción de tubérculos y los componentes del rendimiento en función de la variedad y fertilización nitrogenada en el cultivo de patata, se ha realizadado un análisis mediante coeficientes de sendero (path-coefficient analysis) basado en un diagrama ontogénico. Se han llevado a cabo para ello cuatro experimentos entre 1987 y 1989 en Granada, Sur de España. Dos de ellos con seis variedades, y otros dos con nueve dosis de N total, repartido entre fondo y cobertera. Las variaciones en la producción de tubérculos debidas a la variedad han dependido principalmente del número de tallos por m2, del número de tubérculos por tallo y en menor proporción del peso medio de los tubérculos. Sin embargo, en los experimentos de aplicación de N, el peso medio por tubérculo fue el único componente del rendimiento que mostró un efecto directo significativo sobre la producción final, mientras que el número de tallos por m2 y el número de tubérculos por tallo sólo ejercieron efectos directes insignificantes. El diagrama ontogénico utilizado reveló también la existencia de mecanismos de compensación durante la formación de los tres componentes del rendimiento en la patata, que resultaron más pronunciados en los experimentos de N

Parallel multiobjective memetic RBFNNs design and feature selection for function approximation problems

The design of radial basis function neural networks (RBFNNs) still remains as a difficult task when they are applied to classification or to regression problems. The difficulty arises when the parameters that define an RBFNN have to be set, these are: the number of RBFs, the position of their centers and the length of their radii. Another issue that has to be faced when applying these models to real world applications is to select the variables that the RBFNN will use as inputs. The literature presents several methodologies to perform these two tasks separately, however, due to the intrinsic parallelism of the genetic algorithms, a parallel implementation will allow the algorithm proposed in this paper to evolve solutions for both problems at the same time. The parallelization of the algorithm not only consists in the evolution of the two problems but in the specialization of the crossover and mutation operators in order to evolve the different elements to be optimized when designing RBFNNs. The subjacent genetic algorithm is the non-sorting dominated genetic algorithm II (NSGA-II) that helps to keep a balance between the size of the network and its approximation accuracy in order to avoid overfitted networks. Another of the novelties of the proposed algorithm is the incorporation of local search algorithms in three stages of the algorithm: initialization of the population, evolution of the individuals and final optimization of the Pareto front. The initialization of the individuals is performed hybridizing clustering techniques with the mutual information (MI) theory to select the input variables. As the experiments will show, the synergy of the different paradigms and techniques combined by the presented algorithm allow to obtain very accurate models using the most significant input variables.

New method for instance or prototype selection using mutual information in time series prediction

The problem of selecting the patterns to be learned by any model is usually not considered by the time of designing the concrete model but as a preprocessing step. Information theory provides a robust theoretical framework for performing input variable selection thanks to the concept of mutual information. Recently the computation of the mutual information for regression tasks has been proposed so this paper presents a new application of the concept of mutual information not to select the variables but to decide which prototypes should belong to the training data set in regression problems. The proposed methodology consists in deciding if a prototype should belong to or not to the training set using as criteria the estimation of the mutual information between the variables. The novelty of the approach is to focus in prototype selection for regression problems instead of classification as the majority of the literature deals only with the last one. Other element that distinguishes this work from others is that it is not proposed as an outlier detector but as an algorithm that determines the best subset of input vectors by the time of building a model to approximate it. As the experiment section shows, this new method is able to identify a high percentage of the real data set when it is applied to highly distorted data sets.

Using fuzzy logic to improve a clustering technique for function approximation

Clustering algorithms have been successfully applied in several disciplines. One of those applications is the initialization of radial basis function (RBF) centers composing a neural network, designed to solve functional approximation problems. The Clustering for Function Approximation (CFA) algorithm was presented as a new clustering technique that provides better results than other clustering algorithms that were traditionally used to initialize RBF centers. Even though CFA improves performance against other clustering algorithms, it has some flaws that can be improved. Within those flaws, it can be mentioned the way the partition of the input data is done, the complex migration process, the algorithms speed, the existence of some parameters that have to be set in order to obtain good solutions, and the convergence is not guaranteed. In this paper, it is proposed an improved version of this algorithm that solves the problems that its predecessor have using fuzzy logic successfully. In the experiments section, it will be shown how the new algorithm performs better than its predecessor and how important is to make a correct initialization of the RBF centers to obtain small approximation errors.

Output value-based initialization for radial basis function neural networks

The use of Radial Basis Function Neural Networks (RBFNNs) to solve functional approximation problems has been addressed many times in the literature. When designing an RBFNN to approximate a function, the first step consists of the initialization of the centers of the RBFs. This initialization task is very important because the rest of the steps are based on the positions of the centers. Many clustering techniques have been applied for this purpose achieving good results although they were constrained to the clustering problem. The next step of the design of an RBFNN, which is also very important, is the initialization of the radii for each RBF. There are few heuristics that are used for this problem and none of them use the information provided by the output of the function, but only the centers or the input vectors positions are considered. In this paper, a new algorithm to initialize the centers and the radii of an RBFNN is proposed. This algorithm uses the perspective of activation grades for each neuron, placing the centers according to the output of the target function. The radii are initialized using the center’s positions and their activation grades so the calculation of the radii also uses the information provided by the output of the target function. As the experiments show, the performance of the new algorithm outperforms other algorithms previously used for this problem.

Minimising the delta test for variable selection in regression problems

The problem of selecting an adequate set of variables from a given data set of a sampled function becomes crucial by the time of designing the model that will approximate it. Several approaches have been presented in the literature although recent studies showed how the delta test is a powerful tool to determine if a subset of variables is correct. This paper presents new methodologies based on the delta test such as tabu search, genetic algorithms and the hybridisation of them, to determine a subset of variables which is representative of a function. The paper considers as well the scaling problem where a relevance value is assigned to each variable. The new algorithms were adapted to be run in parallel architectures so better performances could be obtained in a small amount of time, presenting great robustness and scalability.