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33
Modified Gath–Geva clustering for fuzzy segmentation of multivariate timeseries
, 2005
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Model Order Selection of Nonlinear InputOutput Models  A Clustering Based Approach
, 2003
"... Selecting the order of an inputoutput model of a dynamical system is a key step toward the goal of system identification. The false nearest neighbors algorithm (FNN) is a useful tool for the estimation of the order of linear and nonlinear systems. While advanced FNN uses nonlinear inputoutput data ..."
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Cited by 8 (2 self)
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Selecting the order of an inputoutput model of a dynamical system is a key step toward the goal of system identification. The false nearest neighbors algorithm (FNN) is a useful tool for the estimation of the order of linear and nonlinear systems. While advanced FNN uses nonlinear inputoutput data based models for the modelbased selection of the threshold constant that is used to compute the percentage of false neighbors, the computational e#ort of the method increases along with the number of data and the dimension of the model. To increase the e#ciency of this method, in this paper we propose a clusteringbased algorithm. Clustering is applied to the product space of the input and output variables. The model structure is then estimated on the basis of the cluster covariance matrix eigenvalues. The main advantage of the proposed solution is that it is modelfree. This means that no particular model needs to be constructed in order to select the order of the model, while most other techniques are `wrapped' around a particular model construction method. This saves the computational e#ort and avoids a possible bias due to the particular construcPreprint submitted to Elsevier Science 3 December 2003 tion method used. Three simulation examples are given to illustrate the proposed technique: estimation of the model structure for a linear system, a polymerization reactor and the van der Vusse reactor.
Fuzzy Clustering Based Segmentation of TimeSeries
 Lecture Notes in Computer Science
, 2003
"... The segmentation of timeseries is a constrained clustering problem: the data points should be grouped by their similarity, but with the constraint that all points in a cluster must come from successive time points. The changes of the variables of a timeseries are usually vague and do not focus ..."
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Cited by 7 (1 self)
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The segmentation of timeseries is a constrained clustering problem: the data points should be grouped by their similarity, but with the constraint that all points in a cluster must come from successive time points. The changes of the variables of a timeseries are usually vague and do not focused on any particular time point. Therefore it is not practical to define crisp bounds of the segments. Although fuzzy clustering algorithms are widely used to group overlapping and vague objects, they cannot be directly applied to timeseries segmentation. This paper proposes a clustering algorithm for the simultaneous identification of fuzzy sets which represent the segments in time and the local PCA models used to measure the homogeneity of the segments. The algorithm is applied to the monitoring of the production of highdensity polyethylene.
Using fuzzy logic to improve a clustering technique for function approximation, Neurocomputing 70
, 2007
"... Clustering algorithms have been applied in several disciplines successfully. 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) algorit ..."
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Cited by 5 (2 self)
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Clustering algorithms have been applied in several disciplines successfully. 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 algorithm’s 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 has 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.
Compact TSFuzzy Models through Clustering and OLS plus FIS Model Reduction
 In Proc. of IEEE international
, 2001
"... The identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy logic models are often a good choice to describe such systems, however in many cases these become complex soon. Generally, too less effort is put into variable selection and in the creation of suitab ..."
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Cited by 3 (2 self)
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The identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy logic models are often a good choice to describe such systems, however in many cases these become complex soon. Generally, too less effort is put into variable selection and in the creation of suitable local rules. Moreover, in general no model reduction is applied, while this may simplify the model by removing redundant information. This paper proposes a combined method that handles these issues in order to create compact TakagiSugeno (TS) models that can be effectively used to represent complex systems. A new fuzzy clustering method is proposed for the identification of compact TSfuzzy models. The most relevant consequent variables of the TS model are selected by an orthogonal least squares method based on the obtained clusters. For the selection of the relevant antecedent (scheduling) variables a new method has been developed based on Fisher's interclass separability criteria. This overall approach is demonstrated by means of the MPG (miles per gallon) nonlinear regression benchmark. The results are compared with results obtained by standard linear, neurofuzzy and advanced fuzzy clustering based identification tools.
Automatic ClusteringBased Identification of Autoregressive Fuzzy Inference Models for Time Series
"... We analyze the use of clustering methods for the automatic identification of fuzzy inference models for autoregressive prediction of time series. A methodology that combines fuzzy methods and residual variance estimation techniques is followed. A nonparametric residual variance estimator is used for ..."
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We analyze the use of clustering methods for the automatic identification of fuzzy inference models for autoregressive prediction of time series. A methodology that combines fuzzy methods and residual variance estimation techniques is followed. A nonparametric residual variance estimator is used for a priori input and model selection. A simple scheme for initializing the widths of the input membership functions of fuzzy inference systems is proposed for the Improved Clustering for Function Approximation algorithm (ICFA), previously introduced for initializing RBF networks. This extension to the ICFA algorithm is shown to provide the most accurate predictions among a wide set of clustering algorithms. The method is applied to a diverse set of time series benchmarks. Its advantages in terms of accuracy and computational requirements are shown as compared to leastsquares support vector machines (LSSVM), the multilayer perceptron (MLP) and two variants of the extreme learning machine (ELM).
GathGeva Specification and Genetic Generalization of TakagiSugenoKang Fuzzy Models
"... Abstract—This paper introduces a fuzzy inference system, based on the TakagiSugenoKang model, to achieve efficient and reliable classification in the domain of ubiquitous computing, and in particular for smart or contextaware, sensoraugmented devices. As these are typically deployed in unpredict ..."
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Abstract—This paper introduces a fuzzy inference system, based on the TakagiSugenoKang model, to achieve efficient and reliable classification in the domain of ubiquitous computing, and in particular for smart or contextaware, sensoraugmented devices. As these are typically deployed in unpredictable environments and have a large amount of correlated sensor data, we propose to use a GathGeva clustering specification as well as a genetic algorithm approach to improve the model’s robustness. Experiments on data from such a sensoraugmented device show that accuracy is boosted from 83 % to 97 % with these optimizations under normal conditions, and for more challenging data from 54 % to 79%. I.
On Generating Fuzzy Systems based on Pareto Multiobjective Cooperative Coevolutionary Algorithm
"... Abstract: An approach to construct multiple interpretable and precise fuzzy systems based on the Pareto Multiobjective Cooperative Coevolutionary Algorithm (PMOCCA) is proposed in this paper. First, a modified fuzzy clustering algorithm is used to construct antecedents of fuzzy system, and conseque ..."
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Abstract: An approach to construct multiple interpretable and precise fuzzy systems based on the Pareto Multiobjective Cooperative Coevolutionary Algorithm (PMOCCA) is proposed in this paper. First, a modified fuzzy clustering algorithm is used to construct antecedents of fuzzy system, and consequents are identified separately to reduce computational burden. Then, the PMOCCA and the interpretabilitydriven simplification techniques are executed to optimize the initial fuzzy system with three objectives: the precision performance, the number of fuzzy rules and the number of fuzzy sets; thus both the precision and the interpretability of the fuzzy systems are improved. In order to select the best individuals from each species, we generalize the NSGAII algorithm from one species to multispecies, and propose a new nondominated sorting technique and collaboration mechanism for cooperative coevolutionary algorithm. Finally, the proposed approach is applied to two benchmark problems, and the results show its validity.
Rule weights in a neurofuzzy system with a hierarchical domain partition
 INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE
, 2010
"... The paper discusses the problem of rule weight tuning in neurofuzzy systems with parameterized consequences in which rule weights and the activation of the rules are not interchangeable. Some heuristic methods of rule weight computation in neurofuzzy systems with a hierarchical input domain partit ..."
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The paper discusses the problem of rule weight tuning in neurofuzzy systems with parameterized consequences in which rule weights and the activation of the rules are not interchangeable. Some heuristic methods of rule weight computation in neurofuzzy systems with a hierarchical input domain partition and parameterized consequences are proposed. Several heuristics with experimental results showing the advantage of their usage are presented.
State estimation of the threetank system using a multiple model
"... Abstract—This paper addresses the exact transformation of nonlinear systems into a multiple model form with unmeasurable premise variables. The multiple model structure serves to treat the observability and the state estimation problem of nonlinear systems. Using a method with no information loss, ..."
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Abstract—This paper addresses the exact transformation of nonlinear systems into a multiple model form with unmeasurable premise variables. The multiple model structure serves to treat the observability and the state estimation problem of nonlinear systems. Using a method with no information loss, a nonlinear system is transformed into a multiple model, depending on the choice of premise variables. It is a key point, since it allows to choose, between different multiple model forms, the one that has suitable structure and properties, in order to design an observer. The convergence conditions of the state estimation error are expressed in LMI formulation using the Lyapunov method. These proposals are investigated and applied to the threetank system. I.