München, Univ., Diss., 2003. / Computerdatei im Fernzugriff.

Deriving low-dimensional perceptual spaces from data consisting of many variables is of crucial interest in strategic market planning. A frequently used method in this context is Principal Components Analysis, which finds uncorrelated directions in the data. This methodology which supports the identification of competitive structures can gainfully be utilized for product (re)positioning or optimal product (re)design. In our paper, we investigate the usefulness of a novel technique, Independent Component Analysis, to discover market structures. Independent Component Analysis is an extension of Principal Components Analysis in the sense that it looks for directions in the data that are not only uncorrelated but also independent. Comparing the two approaches on the basis of an empirical data set, we find that Independent Component Analysis leads to clearer and sharper structures than Principal Components Analysis. Furthermore, the results of Independent Component Analysis have a reasonable marketing interpretation. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Konstanz, Univ., Bachelorarb., 2008.

This article deals with the recognition of recurring multivariate time series patterns modelled sample-point-wise by parametric fuzzy sets. An efficient classification-based approach for the online recognition of incompleted developing patterns in streaming time series is being presented. Furthermore, means are introduced to enable users of the recognition system to restrict results to certain stages of a pattern’s development, e. g. for forecasting purposes, all in a consistently fuzzy manner.

The present article dedicates itself to fuzzy modelling of data-inherent structures. In particular two main points are dealt with: the introduction of a fuzzy modelling framework and the elaboration of an automated, data-driven design strategy to model complex data-inherent structures within this framework. The innovation concerning the modelling framework lies in the fact that it is consistently built around a single, generic type of parametrical and convex membership function. In the first part of the article this essential building block will be defined and its assets and shortcomings will be discussed. The novelty regarding the automated, data-driven design strategy consist in the conservation of the modelling framework when modelling complex (nonconvex) data-inherent structures. Instead of applying current clustering methods the design strategy uses the inverse of the data structure in order to created a fuzzy model solely based on convex membership functions. Throughout the article the whole model design process is illustrated, section by section, with the help of an academic example.

This article proposes knowledge-based short-time prediction methods for multivariate streaming time series, relying on the early recognition of local patterns. A parametric, well-interpretable model for such patterns is presented, along with an online, classification-based recognition procedure. Subsequently, two options are discussed to predict time series employing the fuzzified pattern knowledge, accompanied by an example. Special emphasis is placed on comprehensible models and methods, as well as an easy interface to data mining algorithms.

Die Arbeit ordnet sich in das Gebiet der unscharfen Klassifikation ein und stellt im Detail eine Weiterführung der Forschung zur Fuzzy-Pattern-Klassifikation dar. Es handelt sich dabei um eine leistungsfähige systemtheoretische Methodik zur klassifikatorischen Modellierung komplexer, hochdimensionaler, technischer oder nichttechnischer Systeme auf der Basis von metrischen Messgrößen und/oder nichtmetrischen Experten-Bewertungen. Die Beschreibung der Unschärfe von Daten, Zuständen und Strukturen wird hierbei durch einen einheitlichen Typ einer Zugehörigkeitsfunktion des Potentialtyps realisiert. Ziel der Betrachtungen ist die weiterführende Nutzung des bestehenden Klassenmodells zur unscharfen Beschreibung nichtkonvexer Objektmengenmorphologien. Ausgehend vom automatischen datengetriebenen Aufbau der konvexen Klassenbeschreibung, deren vorteilhaften Eigenschaften sowie Defiziten wird im Rahmen der Arbeit eine Methodik vorgestellt, die eine Modellierung beliebiger Objektmengenmorphologien erlaubt, ohne das bestehende Klassifikationskonzept zu verlassen. Kerngedanken des Vorgehens sind: 1.) Die Aggregation von Fuzzy-Pattern-Klassen auf der Basis so genannter komplementärer Objekte. 2.) Die sequentielle Verknüpfung von Fuzzy-Pattern-Klassen und komplementären Klassen im Sinne einer unscharfen Mengendifferenz. 3.) Die Strukturierung des Verknüpfungsprozesses durch die Clusteranalyse von Komplementärobjektmengen und damit der Verwendung von Konfigurationen aus komplementären Fuzzy-Pattern-Klassen. Das dabei gewonnene nichtkonvexe Fuzzy-Klassifikationsmodell impliziert eine Vernetzung von Fuzzy-Klassifikatoren in Form von Klassifikatorbäumen. Im Ergebnis entstehen Klassifikatorstrukturen mit hoher Transparenz, die - neben der üblichen zustandsorientierten klassifikatorischen Beschreibung in den Einzelklassifikatoren - zusätzliche Informationen über den Ablauf der Klassifikationsentscheidungen erfassen. Der rechnergestützte Entwurf und die Eigenschaften der entstehenden Klassifikatorstruktur werden an akademischen Teststrukturen und realen Daten demonstriert. Die im Rahmen der Arbeit dargestellte Methodik wird in Zusammenhang mit dem Fuzzy-Pattern-Klassifikationskonzept realisiert, ist jedoch aufgrund ihrer Allgemeingültigkeit auf eine beliebige datenbasierte konvexe Klassenbeschreibung übertragbar. / This work contributes to the field of fuzzy classification. It dedicates itself to the subject of "Fuzzy-Pattern-Classification", a versatile method applied for classificatory modeling of complex, high dimensional systems based on metric and nonmetric data, i.e. sensor readings or expert statements. Uncertainties of data, their associated morphology and therewith classificatory states are incorporated in terms of fuzziness using a uniform and convex type of membership function. Based on the properties of the already existing convex Fuzzy-Pattern-Class models and their automatic, data-driven setup a method for modeling nonconvex relations without leaving the present classification concept is introduced. Key points of the elaborated approach are: 1.) The aggregation of Fuzzy-Pattern-Classes with the help of so called complementary objects. 2.) The sequential combination of Fuzzy-Pattern-Classes and complementary Fuzzy-Pattern-Classes in terms of a fuzzy set difference. 3.) A clustering based structuring of complementary Fuzzy-Pattern-Classes and therewith a structuring of the combination process. A result of this structuring process is the representation of the resulting nonconvex fuzzy classification model in terms of a classifier tree. Such a nonconvex Fuzzy-Classifier features high transparency, which allows a structured understanding of the classificatory decision in working mode. Both the automatic data-based design as well as properties of such tree-like fuzzy classifiers will be illustrated with the help of academic and real word data. Even though the proposed method is introduced for a specific type of membership function, the underlying idea may be applied to any convex membership function.

Zugl.: Regensburg, Universiẗat, Diss., 1998.

This article deals with the recognition of recurring multivariate time series patterns modelled sample-point-wise by parametric fuzzy sets. An efficient classification-based approach for the online recognition of incompleted developing patterns in streaming time series is being presented. Furthermore, means are introduced to enable users of the recognition system to restrict results to certain stages of a pattern’s development, e. g. for forecasting purposes, all in a consistently fuzzy manner.

The present article dedicates itself to fuzzy modelling of data-inherent structures. In particular two main points are dealt with: the introduction of a fuzzy modelling framework and the elaboration of an automated, data-driven design strategy to model complex data-inherent structures within this framework. The innovation concerning the modelling framework lies in the fact that it is consistently built around a single, generic type of parametrical and convex membership function. In the first part of the article this essential building block will be defined and its assets and shortcomings will be discussed. The novelty regarding the automated, data-driven design strategy consist in the conservation of the modelling framework when modelling complex (nonconvex) data-inherent structures. Instead of applying current clustering methods the design strategy uses the inverse of the data structure in order to created a fuzzy model solely based on convex membership functions. Throughout the article the whole model design process is illustrated, section by section, with the help of an academic example.