Luis Javier Herrera

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.

Color difference thresholds in dentistry

PURPOSE The aim of this prospective multicenter study was to determine 50:50% perceptibility threshold (PT) and 50:50% acceptability threshold (AT) of dental ceramic under simulated clinical settings. MATERIALS AND METHODS The spectral radiance of 63 monochromatic ceramic specimens was determined using a non-contact spectroradiometer. A total of 60 specimen pairs, divided into 3 sets of 20 specimen pairs (medium to light shades, medium to dark shades, and dark shades), were selected for psychophysical experiment. The coordinating center and seven research sites obtained the Institutional Review Board (IRB) approvals prior the beginning of the experiment. Each research site had 25 observers, divided into five groups of five observers: dentists-D, dental students-S, dental auxiliaries-A, dental technicians-T, and lay persons-L. There were 35 observers per group (five observers per group at each site ×7 sites), for a total of 175 observers. Visual color comparisons were performed using a viewing booth. Takagi-Sugeno-Kang (TSK) fuzzy approximation was used for fitting the data points. The 50:50% PT and 50:50% AT were determined in CIELAB and CIEDE2000. The t-test was used to evaluate the statistical significance in thresholds differences. RESULTS The CIELAB 50:50% PT was ΔEab  = 1.2, whereas 50:50% AT was ΔEab  = 2.7. Corresponding CIEDE2000 (ΔE00 ) values were 0.8 and 1.8, respectively. 50:50% PT by the observer group revealed differences among groups D, A, T, and L as compared with 50:50% PT for all observers. The 50:50% AT for all observers was statistically different than 50:50% AT in groups T and L. CONCLUSION A 50:50% perceptibility and ATs were significantly different. The same is true for differences between two color difference formulas ΔE00 /ΔEab . Observer groups and sites showed high level of statistical difference in all thresholds. CLINICAL SIGNIFICANCE Visual color difference thresholds can serve as a quality control tool to guide the selection of esthetic dental materials, evaluate clinical performance, and interpret visual and instrumental findings in clinical dentistry, dental research, and subsequent standardization. The importance of quality control in dentistry is reinforced by increased esthetic demands of patients and dental professionals.

TaSe, a Taylor series-based fuzzy system model that combines interpretability and accuracy

Typically, Takagi-Sugeno-Kang (TSK) fuzzy rules have been used as a powerful tool for function approximation problems, since they have the capability of explaining complex relations among variables using rule consequents that are functions of the input variables. But they present the great drawback of the lack of interpretability, which makes them not to be so suitable for a wide range of problems where interpretability of the obtained model is a fundamental key. In this paper, we present a novel approach that extends the work by Bikdash (IEEE Trans. Fuzzy Systems 7 (6) (1999) 686-696), in order to obtain an interpretable and accurate model for function approximation from a set of I/O data samples, which make use of the Taylor Series Expansion of a function around a point to approximate the function using a low number of rules. Our approach also provides an automatic methodology for obtaining the optimum structure of our Taylor series-based (TaSe) fuzzy system as well as its pseudo-optimal rule-parameters (both antecedents and consequents).

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.

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.

Studying possibility in a clustering algorithm for RBFNN design for function approximation

The function approximation problem has been tackled many times in the literature by using radial basis function neural networks (RBFNNs). In the design of these neural networks there are several stages where, the most critical stage is the initialization of the centers of each RBF since the rest of the steps to design the RBFNN strongly depend on it. The improved clustering for function approximation (ICFA) algorithm was recently introduced and proved successful for the function approximation problem. In the ICFA algorithm, a fuzzy partition of the input data is performed but, a fuzzy partition can behave inadequately in noise conditions. Possibilistic and mixed approaches, combining fuzzy and possibilistic partitions, were developed in order to improve the performance of a fuzzy partition. In this paper, a study of the influence of replacing the fuzzy partition used in the ICFA algorithm with the possibilistic and the fuzzy-possibilistic partitions will be done. A comparative analysis of each kind of partition will be performed in order to see if the possibilistic approach can improve the performance of the ICFA algorithm both in normal and in noise conditions. The results will show how the employment of a mixed approach combining fuzzy and possibilistic approach can lead to improve the results when designing RBFNNs.