Chih-Ching Hsiao

Robust support vector regression networks for function approximation with outliers

Support vector regression (SVR) employs the support vector machine (SVM) to tackle problems of function approximation and regression estimation. SVR has been shown to have good robust properties against noise. When the parameters used in SVR are improperly selected, overfitting phenomena may still occur. However, the selection of various parameters is not straightforward. Besides, in SVR, outliers may also possibly be taken as support vectors. Such an inclusion of outliers in support vectors may lead to seriously overfitting phenomena. In this paper, a novel regression approach, termed as the robust support vector regression (RSVR) network, is proposed to enhance the robust capability of SVR. In the approach, traditional robust learning approaches are employed to improve the learning performance for any selected parameters. From the simulation results, our RSVR can always improve the performance of the learned systems for all cases. Besides, it can be found that even the training lasted for a long period, the testing errors would not go up. In other words, the overfitting phenomenon is indeed suppressed.

Hybrid compensation control for affine TSK fuzzy control systems

The paper proposes a way of designing state feedback controllers for affine Takagi-Sugeno-Kang (TSK) fuzzy models. In the approach, by combining two different control design methodologies, the proposed controller is designed to compensate all rules so that the desired control performance can appear in the overall system. Our approach treats all fuzzy rules as variations of a nominal rule and such variations are individually dealt with in a Lyapunov sense. Previous approaches have proposed a similar idea but the variations are dealt with as a whole in a robust control sense. As a consequence, when fuzzy rules are distributed in a wide range, the stability conditions may not be satisfied. In addition, the control performance of the closed-loop system cannot be anticipated in those approaches. Various examples were conducted in our study to demonstrate the effectiveness of the proposed control design approach. All results illustrate good control performances as desired.

Radial Basis Function Networks With Linear Interval Regression Weights for Symbolic Interval Data

This paper introduces a new structure of radial basis function networks (RBFNs) that can successfully model symbolic interval-valued data. In the proposed structure, to handle symbolic interval data, the Gaussian functions required in the RBFNs are modified to consider interval distance measure, and the synaptic weights of the RBFNs are replaced by linear interval regression weights. In the linear interval regression weights, the lower and upper bounds of the interval-valued data as well as the center and range of the interval-valued data are considered. In addition, in the proposed approach, two stages of learning mechanisms are proposed. In stage 1, an initial structure (i.e., the number of hidden nodes and the adjustable parameters of radial basis functions) of the proposed structure is obtained by the interval competitive agglomeration clustering algorithm. In stage 2, a gradient-descent kind of learning algorithm is applied to fine-tune the parameters of the radial basis function and the coefficients of the linear interval regression weights. Various experiments are conducted, and the average behavior of the root mean square error and the square of the correlation coefficient in the framework of a Monte Carlo experiment are considered as the performance index. The results clearly show the effectiveness of the proposed structure.

A novel approach for TSK fuzzy modeling with outliers

The TSK type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications. In the literature, some approaches for modeling TSK fuzzy rules have been proposed. Most of them define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions. Recently, a new approach, fuzzy c-regression model (FCRM) clustering algorithm, is proposed to construct TSK fuzzy models. However, this approach does not take into account the training data with outliers. In order to overcome the effects of outliers, a robust TSK fuzzy modeling with outliers has been proposed. It is worth noting that this approach may need more computation time due to complicated formulas. Hence, a novel TSK fuzzy modeling approach with outliers is presented in this paper. In this approach, robust fuzzy regression (RFR) clustering algorithm is proposed to simultaneously define fuzzy subspaces and find the parameters in the consequent parts of TSK rules. In the clustering process, the similarity measure is used to reduce the redundant rules. To obtain a more precision model that is not affected by outliers, an annealing robust BP learning algorithm is employed. From the simulation results, the proposed TSK fuzzy model approach indeed showed superior performance.

Robust back propagation learning algorithm based on near sets

The traditional robust learning algorithms are based on the estimated errors, which is not correct in the early stage of the training process. Therefore, the use of those approaches still cannot provide very decent learning performance in face of outliers unless a set of good initial weights is used. In this paper, a novel approach, termed as NRBP (Near set based Robust Back Propagation learning algorithm) is proposed. In this learning algorithm, the training (\estimated) data sets are separated into overlapping (or nonoverlapping) subsets of those data. It uses the set error measure instead of one-step error in robust back propagation based on near set. The set error measure is an estimated error measure between a subset of training data set and corresponding subset of estimated data set. Its benefit is it includes error messages and also reduces the outlier effect.

A Rough-set-based for fuzzy modeling with outlier

For high nonlinearly or unknown systems, the interest is toward data-driven methods for obtaining the system model. Fuzzy-rule-based modeling is a suitable tool that combines good approximation properties with a certain degree of inspects ability. The rough set theory is successes to deal with imprecise, incomplete or uncertain for information system. Fuzzy set and the rough set theories turned out to be particularly adequate for the analysis of various types of data, especially, when dealing with inexact, uncertain or vague knowledge. In this paper, we propose an novel algorithm, which termed as rough-based fuzzy C-regression model (RFCRM), that define fuzzy subspaces in a fuzzy regression manner and also include rough-set theory for TSK modeling with robust capability against outliers.

Robust Gaussian Kernel Based Approach for Feature Selection

The outlier problem of feature selection is rarely discussed in the most previous works. Moreover, there are no work has been reported in literature on symbolic interval feature selection in the supervised framework. In this paper, we will incorporate similarity margin concept and Gaussian kernel fuzzy rough sets to deal with the Symbolic Data Selection problem and it is also an optimizing problem. The advantage of this approach is it can easily introduce loss function and with robustness.

A rough-based robust support vector regression network for function approximation

Support vector regression (SVR) employs the support vector machine (SVM) to tackle problems of function approximation and regression estimation. SVR has been shown to have good robust properties against noise. Besides, in SVR, outliers may also possibly be taken as support vectors. Such an inclusion of outliers in support vectors may lead to seriously overfitting phenomena. The rough set theory is successes to deal with imprecise, incomplete or uncertain for information system. In this paper, a novel regression approach, termed as the Rough Margin Support Vector Regression (RMSVR) network, is proposed to enhance the robust capability of SVR. The basic idea of the approach is to adopt the concept of rough sets to construct the model obtained by SVR and fine tune it with a robust learning algorithm. Simulation results of the proposed approach have shown the effectiveness of the approximated function in discriminating against outliers.

An On-Line Fuzzy Predictor from Real-Time Data

The algorithm of online predictor from input-output data pairs will be proposed. In this paper, it proposed an approach to generate fuzzy rules of predictor from real-time input-output data by means of ARMA model concept for unknown system. It includes two phase: (1). generating fuzzy rules phase, (2). online learning phase; If the error between the real output and the predictors output is larger than the desired error, it means that the lack of the fuzzy rules. Thus, it will generate some new fuzzy rules for the fuzzy predictor or adding an output term in the premise part of fuzzy rules. From the generating fuzzy rules phase, it can online generate the fuzzy predictor. In another word, some redundant rules may be generated from bad information after learning. They may be incoming data include outliers, noises or uncertainties. Such bad rules will be discarded by a usage degree constant. To achieve good performance for this fuzzy predictor, the parameters of each fuzzy rule may be adjusted by on-line learning, when the prediction error into a pre-defined bound. In the simulation example, a nonlinear time-varying process operating in open loop is illustrated. Simulations and real-time results show the advantages of the proposed method.

A sliding manner compensation control for affine TSK fuzzy control systems

This work proposed a methodology of designing controllers for affine TSK fuzzy models. For hybrid compensation control (HCC) design technique in which fuzzy controllers share the same premise parts with the considered fuzzy systems and that can design controllers directly for affine fuzzy systems. On the other hand, the closed loop performance can also be theoretically anticipated. The modeling error always exists between real model and TSK fuzzy model. Hence, the HCC fuzzy controller can not achieve the performance in the real application. We added the third term to compensate the modeling error by sliding concept. Thus, the performance can be achieved with the real model by means of this three terms compensation fuzzy controller.