Evgenia Dimitriadou

An Examination of Indexes for Determining the Number of Clusters in Binary Data Sets.

The problem of choosing the correct number of clusters is as old as cluster analysis itself. A number of authors have suggested various indexes to facilitate this crucial decision. One of the most extensive comparative studies of indexes was conducted by Milligan and Cooper (1985). The present piece of work pursues the same goal under different conditions. In contrast to Milligan and Coopers work, the emphasis here is on high-dimensional empirical binary data. Binary artificial data sets are constructed to reflect features typically encountered in real-world data situations in the field of marketing research. The simulation includes 162 binary data sets that are clustered by two different algorithms and lead to recommendations on the number of clusters for each index under consideration. Index results are evaluated and their performance is compared and analyzed.

A quantitative comparison of functional MRI cluster analysis

The aim of this work is to compare the efficiency and power of several cluster analysis techniques on fully artificial (mathematical) and synthesized (hybrid) functional magnetic resonance imaging (fMRI) data sets. The clustering algorithms used are hierarchical, crisp (neural gas, self-organizing maps, hard competitive learning, k-means, maximin-distance, CLARA) and fuzzy (c-means, fuzzy competitive learning). To compare these methods we use two performance measures, namely the correlation coefficient and the weighted Jaccard coefficient (wJC). Both performance coefficients (PCs) clearly show that the neural gas and the k-means algorithm perform significantly better than all the other methods using our setup. For the hierarchical methods the ward linkage algorithm performs best under our simulation design. In conclusion, the neural gas method seems to be the best choice for fMRI cluster analysis, given its correct classification of activated pixels (true positives (TPs)) whilst minimizing the misclassification of inactivated pixels (false positives (FPs)), and in the stability of the results achieved.

A COMBINATION SCHEME FOR FUZZY CLUSTERING

In this paper we present a voting scheme for fuzzy cluster algorithms. This voting method allows us to combine several runs of cluster algorithms resulting in a common partition. This helps us to tackle the problem of choosing the appropriate clustering method for a data set where we have no a priori information about it. We mathematically derive the algorithm from theoretical considerations. Experiments show that the voting algorithm finds structurally stable results. Several cluster validity indexes show the improvement of the voting result in comparison to simple fuzzy voting.

Voting-Merging: An Ensemble Method for Clustering

In this paper we propose an unsupervised voting-merging scheme that is capable of clustering data sets, and also of finding the number of clusters existing in them. The voting part of the algorithm allows us to combine several runs of clustering algorithms resulting in a common partition. This helps us to overcome instabilities of the clustering algorithms and to improve the ability to find structures in a data set. Moreover, we develop a strategy to understand, analyze and interpret these results. In the second part of the scheme, a merging procedure starts on the clusters resulting by voting, in order to find the number of clusters in the data set.

A Combination Scheme for Fuzzy Clustering

In this paper we present a voting scheme for cluster algorithms. This voting method allows us to combine several runs of cluster algorithms resulting in a common partition. This helps us to tackle the problem of choosing the appropriate clustering method for a data set where we have no a priori information about it, and to overcome the problems of choosing an optimal result between different repetitions of the same method. Further on, we can improve the ability of a cluster algorithm to find structures in a data set and to validate the resulting partition.

Competitive learning for binary valued data

We propose a new approach for using online competitive learning on binary data. The usual Euclidean distance is replaced by binary distance measures, which take possible asymmetries of binary data into account and therefore provide a “different point of view” for looking at the data. The method is demonstrated on two artificial examples and applied on tourist marketing research data.

A Mixed Ensemble Approach for the Semi-supervised Problem

In this paper we introduce a mixed approach for the semi-supervised data problem. Our approach consists of an ensemble unsupervised learning part where the labeled and unlabeled points are segmented into clusters. Continuing, we take advantage of the a priori information of the labeled points to assign classes to clusters and proceed to predicting with the ensemble method new incoming ones. Thus, we can finally conclude classifying new data points according to the segmentation of the whole set and the association of its clusters to the classes.