Gaul Wolfgang A. - Challenges at the Interface of Data Analysis, Computer Science, and Optimization: Proceedings of the 34th Annual Conference of the Gesellschaft für Klassifikation e. V., Karlsruhe, July 21-23, 2010

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Part 1
Classification, Cluster Analysis, and Multidimensional Scaling

Wolfgang A. Gaul , Andreas Geyer-Schulz , Lars Schmidt-Thieme and Jonas Kunze (eds.) Studies in Classification, Data Analysis, and Knowledge Organization Challenges at the Interface of Data Analysis, Computer Science, and Optimization 2012 Proceedings of the 34th Annual Conference of the Gesellschaft fr Klassifikation e. V., Karlsruhe, July 21 - 23, 2010 10.1007/978-3-642-24466-7_1 Springer-Verlag Berlin Heidelberg 2012

Fuzzification of Agglomerative Hierarchical Crisp Clustering Algorithms

Mathias Bank 1

(1)

Faculty for Mathematics and Economics, University of Ulm, Ulm, Germany

(2)

Institute of Neural Information Processing, University of Ulm, Ulm, Germany

Mathias Bank (Corresponding author)

Email:

Friedhelm Schwenker

Email:

Abstract

User generated content from fora, weblogs and other social networks is a very fast growing data source in which different information extraction algorithms can provide a convenient data access. Hierarchical clustering algorithms are used to provide topics covered in this data on different levels of abstraction. During the last years, there has been some research using hierarchical fuzzy algorithms to handle comments not dealing with one topic but many different topics at once. The used variants of the well-known fuzzy c -means algorithm are nondeterministic and thus the cluster results are irreproducible. In this work, we present a deterministic algorithm that fuzzifies currently available agglomerative hierarchical crisp clustering algorithms and therefore allows arbitrary multi-assignments. It is shown how to reuse well-studied linkage metrics while the monotonic behavior is analyzed for each of them. The proposed algorithm is evaluated using collections of the RCV1 and RCV2 corpus.

Introduction

In recent years, the interest in user generated data out of fora, weblogs, social networks and recommendation systems has increased significantly. Many different methods are applied to extract relevant information out of this a priori unstructured data. One of the main tasks consists in topic detection. To group a large set of data in this case user comments according to underlying structures, cluster analysis techniques are applied. Especially hierarchical clustering algorithms have shown many advantages because they generate different levels of abstraction in which the user can decide on his own which one is the best for his individual information request.

Generally, user generated comments are not only dealing with one topic. Therefore, it must be possible to assign each document to more than one cluster. In literature, different methods have been proposed to generate hierarchical clusters with the possibility of multiple assignment. Next to pyramidal clusters (Diday ). These, however, suffer from the drawbacks of partitioning clustering algorithms. They are neither deterministic nor do they guarantee to create local optimal clusters due to random initialization. Additionally, it is necessary to predict the number of possible clusters.

In this work, we propose a new clustering method that fuzzifies well-known agglomerative hierarchical crisp clustering algorithms. The deterministic algorithm generates locally optimized clusters while well-known linkage methods can be reused with small modifications. The degree of branching can be specified with a fuzzifier f that is directly applied to the similarity matrix. It is shown that the generated clusters can still be monotonic depending on the used linkage measure even though the induced dissimilarity measures are no longer ultrametrics. Using the pairwise merged clusters, an additional shrinking process is proposed to generate topic related groups with more than two cluster elements.

The overall quality of the proposed clustering algorithm is analyzed using a cosine quality measure that indicates how well each element fits into the corresponding clusters. It is applied to text collections created out of the RCV1 and RCV2 (German) corpus.

Generalization of Agglomerative Crisp Clustering Algorithms

Overall Algorithm

The following listing presents an abstract overview of the complete algorithm. Each step is discussed in the following in detail. As the algorithm is based on a symmetric similarity matrix, the discussion and the algorithm are limited to the upper triangular matrix.

Input: similarity matrix S , linkage measure s , min. similarity While ( )Select and with Update Apply fuzzifier f to and Insert into S according to linkage measure s Calculate Fuzzy MembershipApply Shrinking Process for Topic Detection

Basic Concept

Similar to the crisp clustering process, the proposed agglomerative clustering algorithm starts with a symmetrical similarity matrix which is initially filled with all similarities between data points (singletons). At each iteration, the algorithm looks for the highest similarity value to select two clusters and , which are merged in the next step. An agglomerative hierarchical crisp clustering algorithm would delete all similarity entries and of these clusters. In contrast the proposed algorithm does not delete any entry but updates only the similarity value

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