Ignacio Rojas

Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation

This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of input-output pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process. These new operators are based on two well-known matrix transformations: singular value decomposition (SVD) and orthogonal least squares (OLS), which have been used to define new mutation operators that produce local or global modifications in the radial basis functions (RBFs) of the networks (the individuals in the population in the evolutionary procedure). After analyzing the efficiency of the different operators, we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the RBFNNs.

Self-organized fuzzy system generation from training examples

In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. The paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms.

Time series analysis using normalized PG-RBF network with regression weights

This paper proposes a framework for constructing and training a radial basis function (RBF) neural network. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. The structure of the Gaussian functions is modified using a pseudo-Gaussian function (PG) in which two scaling parameters σ are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. Other important characteristics of the proposed neural system are that the activation of the hidden neurons is normalized which, as described in the bibliography, provides a better performance than nonnormalization and instead of using a single parameter for the output weights, these are functions of the input variables which leads to a significant reduction in the number of hidden units compared to the classical RBF network. Finally, we examine the result of applying the proposed algorithm to time series prediction.

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.

A systematic approach to a self-generating fuzzy rule-table for function approximation

In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.

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.

Window Size Impact in Human Activity Recognition

Signal segmentation is a crucial stage in the activity recognition process; however, this has been rarely and vaguely characterized so far. Windowing approaches are normally used for segmentation, but no clear consensus exists on which window size should be preferably employed. In fact, most designs normally rely on figures used in previous works, but with no strict studies that support them. Intuitively, decreasing the window size allows for a faster activity detection, as well as reduced resources and energy needs. On the contrary, large data windows are normally considered for the recognition of complex activities. In this work, we present an extensive study to fairly characterize the windowing procedure, to determine its impact within the activity recognition process and to help clarify some of the habitual assumptions made during the recognition system design. To that end, some of the most widely used activity recognition procedures are evaluated for a wide range of window sizes and activities. From the evaluation, the interval 1–2 s proves to provide the best trade-off between recognition speed and accuracy. The study, specifically intended for on-body activity recognition systems, further provides designers with a set of guidelines devised to facilitate the system definition and configuration according to the particular application requirements and target activities.

Statistical analysis of the main parameters involved in the design of a genetic algorithm

Most genetic algorithm (GA) users adjust the main parameters of the design of a GA (crossover and mutation probability, population size, number of generations, crossover, mutation, and selection operators) manually. Nevertheless, when GA applications are being developed it is very important to know which parameters have the greatest influence on the behavior and performance of a GA. The purpose of this study was to analyze the dynamics of GAs when confronted with modifications to the principal parameters that define them, taking into account the two main characteristics of GAs; their capacity for exploration and exploitation. Therefore, the dynamics of GAs have been analyzed from two viewpoints. The first is to study the best solution found by the system, i.e., to observe its capacity to obtain a local or global optimum. The second viewpoint is the diversity within the population of GAs; to examine this, the average fitness was calculated. The relevancy and relative importance of the parameters involved in GA design are investigated by using a powerful statistical tool, the analysis of the variance (ANOVA).

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).

Dealing with the Effects of Sensor Displacement in Wearable Activity Recognition

Most wearable activity recognition systems assume a predefined sensor deployment that remains unchanged during runtime. However, this assumption does not reflect real-life conditions. During the normal use of such systems, users may place the sensors in a position different from the predefined sensor placement. Also, sensors may move from their original location to a different one, due to a loose attachment. Activity recognition systems trained on activity patterns characteristic of a given sensor deployment may likely fail due to sensor displacements. In this work, we innovatively explore the effects of sensor displacement induced by both the intentional misplacement of sensors and self-placement by the user. The effects of sensor displacement are analyzed for standard activity recognition techniques, as well as for an alternate robust sensor fusion method proposed in a previous work. While classical recognition models show little tolerance to sensor displacement, the proposed method is proven to have notable capabilities to assimilate the changes introduced in the sensor position due to self-placement and provides considerable improvements for large misplacements.