Fuzzy C-regression Research Articles

클러스터 생성을 이용한 자기구성 퍼지 모델링

본 논문에서는 상대적으로 큰 퍼지 엔트로피를 갖는 입력-출력 데이터 집단에 다중 회귀 분석을 적용하여 다차원 평면 클러스터를 생성하고, 이 클러스터를 새로운 퍼지 모델의 규칙으로 추가한 후 모델 파라미터의 개략 동조와 정밀 동조를 반복 수행하는 자기구성 퍼지 모델링을 제안한다 Weighted recursive least squared 알고리즘과 fuzzy C-regression model 클러스터링에 의해 퍼지 모델의 파라미터를 개략적으로 동조한 후 gradient descent 알고리즘에 의해 파라미터를 정밀 동조하면서 감수분열 유전 알고리즘을 이용하여 최적의 학습률을 탐색한다. 그리고, 자기구성 퍼지 모델링 기법을 이용하여 Box-Jenkins의 가스로 데이터, 비선형 다변수 정적 함수의 데이터, 하수처리 활성오니 공정과 Mackey-Glass 시계열 데이터의 모델링을 수행하고, 기존의 방법에 의한 모델링 결과와 비교하여 그 성능을 입증한다. This paper proposes a self-organizing fuzzy modeling which can create a new hyperplane-shaped cluster by applying multiple regression to input/output data with relatively large fuzzy entropy, add the new cluster to fuzzy rule base and adjust parameters of the fuzzy model in repetition. Tn the coarse tuning, weighted recursive least squared algorithm and fuzzy C-regression model clustering are used and in the fine tuning, gradient descent algorithm is used to adjust parameters of the fuzzy model precisely And learning rates are optimized by utilizing meiosis-genetic algorithm. To check the effectiveness and feasibility of the suggested algorithm, four representative examples for system identification are examined and the performance of the identified fuzzy model is demonstrated in comparison with that of the conventional fuzzy models.

A load curve based fuzzy modeling technique for short-term load forecasting

A modeling method is suggested in this paper that permits building fuzzy models for short-term load forecasting (STLF). The model building process is divided in three parts: (a) the structure identification based on a fuzzy C-regression method, (b) selection of the proper model inputs which is achieved using a genetic algorithm based selection mechanism, and (c) fine tuning by means of a hybrid genetic/least squares algorithm. To obtain simple and efficient models we employ two descriptions for the load curves ( LC's), namely, the feature description for the premise part and the cubic B-spline curve for the consequent part of the rules. The simulation results demonstrate that the suggested model exhibits very good forecast capabilities. The suggested model is favorably compared with the ANN model in terms of prediction accuracy, robustness and model complexity.

Fuzzy clustering and switching regression models using ambiguity and distance rejects

This paper examines how reject options can be used in performing fuzzy clustering and switching regression models. We define an objective function in which reject options are introduced to optimization of certain clustering models. This approach can be directly applied to any clustering model which can be represented as a functional dependent upon a set of cluster centers. The approach can be further generalized for models that require parameters other than the cluster centers. Two types of reject have been included: (1) the ambiguity reject which concerns patterns lying near the cluster boundaries or in the case of switching regression problems, the data points which fit several models equally well; (2) the distance or error reject dealing with patterns that are far away from all the clusters. Clustering and fuzzy c-regression algorithms such as FcM (fuzzy c-means) and FcRM (fuzzy c-regression models) which use calculus-based optimization methods suffer from several drawbacks. They are very sensitive to the presence of noise. Moreover, the memberships are relative numbers. The membership of a point in a cluster depends on the membership of the point in all other clusters. So, the cluster centers or estimates for the parameters are poor. This can be a serious problem in situations where one wishes to generate membership functions from training data. This paper provides answers to these problems: to avoid the memberships to be spread across the clusters and to allow the distinction between “equally likely” and “unknown”, we define partial ambiguity rejects which introduce a discounting process between the classical FcM or FcRM membership functions; to improve the performance of our algorithm in the presence of noise, we use an amorphous noise cluster defined in Demko et al. (Actes des sixièmes rencontres del la société francophone de classification, Montpellier, France, September 1998). To compute these rejects, we propose an extension of FcRM algorithm (Hathaway and Bezdek, IEEE Trans. Fuzzy Systems 1 (3) (1993) 195–203). This algorithm is called the fuzzy (c+2)-regression model (Fc+2RM). Preliminary computational experiences on the developed algorithm are encouraging and compare favorably with results from other methods as FcRM and AFC algorithms on the same data sets.

Simultaneous Approach to Fuzzy Clustering, Principal Component and Multiple Regression Analysis

Hathaway and Bezdek's Fuzzy c-Regression Models (FCRM) is regarded as a simultaneous analysis of clustering and multiple regression. In high dimensional setting, the regression techniques do not perform well for reasonable sample sizes because of the inherent sparsity of samples in the cluster. This paper proposes a simultaneous approach to the clustering, principal component analysis and multiple regression analysis. Aiming at knowledge discovery from POS data that are recorded automatically into the cash register transactions, we analyze the relationship between meteorological information and sales of perishables.

A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm.

Switching regression models and fuzzy clustering

A family of objective functions called fuzzy c-regression models, which can be used too fit switching regression models to certain types of mixed data, is presented. Minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models, together with a fuzzy c-partitioning of the data. A general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed. The approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models. >