Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

Given a set of time series, it is of interest to discover subsets that share similar properties. For instance, this may be useful for identifying and estimating a single model that may fit conveniently several time series, instead of performing the usual identification and estimation steps for each one. On the other hand time series in the same cluster are related with respect to the measures assumed for cluster analysis and are suitable for building multivariate time series models. Though many approaches to clustering time series exist, in this view the most effective method seems to have to rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coe±cients, spectral measures or the eigenvectors of the covariance matrix. Some new indexes based on goodnessof-fit criteria will be proposed in this paper for fuzzy clustering of multivariate time series. A general purpose fuzzy clustering algorithm may be used to estimate the proper cluster structure according to some internal criteria of cluster validity. Such indexes are known to measure actually definite often conflicting cluster properties, compactness or connectedness, for instance, or distribution, orientation, size and shape. It is argued that the multiobjective optimization supported by genetic algorithms is a most effective choice in such a di±cult context. In this paper we use the Xie-Beni index and the C-means functional as objective functions to evaluate the cluster validity in a multiobjective optimization framework. The concept of Pareto optimality in multiobjective genetic algorithms is used to evolve a set of potential solutions towards a set of optimal non-dominated solutions. Genetic algorithms are well suited for implementing di±cult optimization problems where objective functions do not usually have good mathematical properties such as continuity, differentiability or convexity. In addition the genetic algorithms, as population based methods, may yield a complete Pareto front at each step of the iterative evolutionary procedure. The method is illustrated by means of a set of real data and an artificial multivariate time series data set.Fuzzy clustering, Internal criteria of cluster validity, Genetic algorithms, Multiobjective optimization, Time series, Pareto optimality

Clustering Z-information based on a system of fuzzy reference requirements

The paper develops a clustering model of multi-criteria object evaluations, taking into account the reliability of the results obtained. Clustering is based on a system of fuzzy reference requirements about the importance of the evaluated characteristics of objects for each of the clusters. Object evaluations are formalized on the basis of linguistic Z-numbers, both fuzzy numbers of which are the values of linguistic variables. Information for each object and each cluster is presented as a set of pairs (according to the number of characteristics) consisting of a fuzzy number (importance of a characteristic for the corresponding cluster) and a Z-number (an evaluation of the object within this characteristic and its reliability). Using this information, fuzzy ratings are determined for each object in accordance with fuzzy reference requirements for each cluster. Fuzzy ratings of objects, defined as fuzzy numbers, reflect the compliance of multi-criteria ratings of objects with fuzzy reference requirements. The comparative analysis of fuzzy ratings of all objects within one cluster proposed in the paper makes it possible to identify the best representative (or best representatives) of the cluster under consideration and determine the degree of belonging of the remaining objects to this cluster. The analysis is carried out for all clusters. A numerical example is given, which shows the effectiveness of the developed method under Z-information

Development of a Genetic Algorithm to Automate Clustering of a Dependency Structure Matrix

Much technology assessment and organization design data exists in Microsoft Excel spreadsheets. Tools are needed to put this data into a form that can be used by design managers to make design decisions. One need is to cluster data that is highly coupled. Tools such as the Dependency Structure Matrix (DSM) and a Genetic Algorithm (GA) can be of great benefit. However, no tool currently combines the DSM and a GA to solve the clustering problem. This paper describes a new software tool that interfaces a GA written as an Excel macro with a DSM in spreadsheet format. The results of several test cases are included to demonstrate how well this new tool works

Optimization of Unsupervised Classification by Evolutionary Strategies

ABSTRACT The kmeans algorithm is an unsupervised classification algorithm. This algorithm however, suffers from two difficulties which are the initialization phase and the local optimums. We present in this paper some improvements to this algorithm based on the evolutionary strategies in order to get around these two difficulties. We have designed a new evolutionist kmeans algorithm. We have proposed a new mutation operator in order for the algorithm to avoid local solutions and to converge to the global solution for a low computational time. This approach is validated on some simulation examples. The experimental results obtained confirm the rapidity of convergence and the good performances of the proposed algorithm

Fuzzy Particle Swarm Optimization Algorithm for a Supplier Clustering Problem

This paper presents a fuzzy decision-making approach to deal with a clustering supplier problem in a supply chain system. During recent years, determining suitable suppliers in the supply chain has become a key strategic consideration. However, the nature of these decisions is usually complex and unstructured. In general, many quantitative and qualitative factors, such as quality, price, and flexibility and delivery performance, must be considered to determine suitable suppliers. The aim of this study is to present a new approach using particle swarm optimization (PSO) algorithm for clustering suppliers under fuzzy environments and classifying smaller groups with similar characteristics. Our numerical analysis indicates that the proposed PSO improves the performance of the fuzzy c-means (FCM) algorithm

An Improved Fuzzy c

To organize the wide variety of data sets automatically and acquire accurate classification, this paper presents a modified fuzzy c-means algorithm (SP-FCM) based on particle swarm optimization (PSO) and shadowed sets to perform feature clustering. SP-FCM introduces the global search property of PSO to deal with the problem of premature convergence of conventional fuzzy clustering, utilizes vagueness balance property of shadowed sets to handle overlapping among clusters, and models uncertainty in class boundaries. This new method uses Xie-Beni index as cluster validity and automatically finds the optimal cluster number within a specific range with cluster partitions that provide compact and well-separated clusters. Experiments show that the proposed approach significantly improves the clustering effect

Proceedings / 17. Workshop Computational Intelligence [Elektronische Ressource] : Dortmund, 5. - 7. Dezember 2007

Dieser Tagungsband enthält die Beiträge des 17. Workshops „Computational Intelligence“ des Fachausschusses 5.14 der VDI/VDE-Gesellschaft für Mess- und Automatisierungstechnik (GMA) und der Fachgruppe „Fuzzy-Systeme und Soft-Computing“ der Gesellschaft für Informatik (GI), der vom 5. – 7. Dezember 2007 im Haus Bommerholz bei Dortmund stattfindet. Der GMA-Fachausschuss 5.14 „Computational Intelligence“ entstand 2005 aus den bisherigen Fachausschüssen „Neuronale Netze und Evolutionäre Algorithmen“ (FA 5.21) sowie „Fuzzy Control“ (FA 5.22). Der Workshop steht in der Tradition der bisherigen Fuzzy-Workshops, hat aber seinen Fokus in den letzten Jahren schrittweise erweitert. Die Schwerpunkte sind Methoden, Anwendungen und Tools für • Fuzzy-Systeme, • Künstliche Neuronale Netze, • Evolutionäre Algorithmen und • Data-Mining-Verfahren sowie der Methodenvergleich anhand von industriellen und Benchmark-Problemen. INHALTSVERZEICHNIS T. Fober, E. Hüllermeier, M. Mernberger (Philipps-Universität Marburg): Evolutionary Construction of Multiple Graph Alignments for the Structural Analysis of Biomolecules G. Heidemann, S. Klenk (Universität Stuttgart): Visual Analytics for Image Retrieval F. Rügheimer (OvG-Universität Magdeburg): A Condensed Representation for Distributions over Set-Valued Attributes T. Mrziglod (Bayer Technology Services GmbH, Leverkusen): Mit datenbasierten Technologien und Versuchsplanung zu erfolgreichen Produkten H. Schulte (Bosch Rexroth AG, Elchingen): Approximationsgenauigkeit und dynamisches Fehlerwachstum der Modellierung mit Takagi-Sugeno Fuzzy Systemen C. Burghart, R. Mikut, T. Asfour, A. Schmid, F. Kraft, O. Schrempf, H. Holzapfel, R. Stiefelhagen, A. Swerdlow, G. Bretthauer, R. Dillmann (Universität Karlsruhe, Forschungszentrum Karlsruhe GmbH): Kognitive Architekturen für humanoide Roboter: Anforderungen, Überblick und Vergleich R. Mikut, C. Burghart, A. Swerdlow (Forschungszentrum Karlsruhe GmbH, Universität Karlsruhe): Ein Gedankenexperiment zum Entwurf einer integrierten kognitiven Architektur für humanoide Roboter G. Milighetti, H.-B. Kuntze (FhG IITB Karlsruhe): Diskret-kontinuierliche Regelung und Überwachung von Robotern basierend auf Aktionsprimitiven und Petri-Netzen N. Rosemann, W. Brockmann (Universität Osnabrück): Kontrolle dynamischer Eigenschaften des Online-Lernens in Neuro-Fuzzy-Systemen mit dem SILKE-Ansatz A. Hans, D. Schneegaß, A. Schäfer, S. Udluft (Siemens AG, TU Ilmenau): Sichere Exploration für Reinforcement-Learning-basierte Regelung Th. Bartz-Beielstein, M. Bongards, C. Claes, W. Konen, H. Westenberger (FH Köln): Datenanalyse und Prozessoptimierung für Kanalnetze und Kläranlagen mit CI-Methoden S. Nusser, C. Otte, W. Hauptmann (Siemens AG, OvG-Universität Magdeburg): Learning Binary Classifiers for Applications in Safety-Related Domains W. Jakob, A. Quinte, K.-U. Stucky, W. Süß, C. Blume (Forschungszentrum Karlsruhe GmbH; FH Köln, Campus Gummersbach) Schnelles Resource Constrained Project Scheduling mit dem Evolutionären Algorithmus GLEAM M. Preuß, B. Naujoks (Universität Dortmund): Evolutionäre mehrkriterielle Optimierung bei Anwendungen mit nichtzusammenhängenden Pareto-Mengen G. Rudolph, M. Preuß (Universität Dortmund): in mehrkriterielles Evolutionsverfahren zur Bestimmung des Phasengleichgewichts von gemischten Flüssigkeiten Y. Chen, O. Burmeister, C. Bauer, R. Rupp, R. Mikut (Universität Karlsruhe, Forschungszentrum Karlsruhe GmbH, Orthopädische Universitätsklinik Heidelberg): First Steps to Future Applications of Spinal Neural Circuit Models in Neuroprostheses and Humanoid Robots F. Hoffmann, J. Braun, T. Bertram, S. Hölemann (Universität Dortmund, RWTH Aachen): Multikriterielle Optimierung mit modellgestützten Evolutionsstrategien S. Piana, S. Engell (Universität Dortmund): Evolutionäre Optimierung des Betriebs von rohrlosen Chemieanlagen T. Runkler (Siemens AG, CT IC 4): Pareto Optimization of the Fuzzy c–Means Clustering Model Using a Multi–Objective Genetic Algorithm H. J. Rommelfanger (J.W. Goethe-Universität Frankfurt am Main): Die Optimierung von Fuzzy-Zielfunktionen in Fuzzy (Mehrziel-) LPSystemen - Ein kritischer Überblick D. Gamrad, D. Söffker (Universität Duisburg-Essen): Formalisierung menschlicher Interaktionen durch Situations-Operator- Modellbildung S. Ritter, P. Bretschneider (FhG AST Ilmenau): Optimale Planung und Betriebsführung der Energieversorgung im liberalisierten Energiemarkt R. Seising (Medizinische Universität Wien): Heinrich Hertz, Ludwig Wittgenstein und die Fuzzy-Strukturen - Eine kleine „Bildergeschichte“ zur Erkenntnisphilosophie J. Limberg, R. Seising (Medizinische Universität Wien): Sequenzvergleiche im Fuzzy-Hypercube M. Steinbrecher, R. Kruse (OvG-Universität Magdeburg): Visualisierung temporaler Abhängigkeiten in Bayesschen Netzen M. Schneider, R. Tillmann, U. Lehmann, J. Krone, P. Langbein, U. Stark, J. Schrickel, Ch. Ament, P. Otto (FH Südwestfalen, Airbus Deutschland GmbH, Hamburg, TU Ilmenau): Künstliches Neuronales Netz zur Analyse der Geometrie von großflächig gekrümmten Bauteilen C. Frey (FhG IITB Karlsruhe): Prozessdiagnose und Monitoring feldbusbasierter Automatisierungsanlagen mittels selbstorganisierender Karte