Fuzzy clustering with volume prototypes and adaptive cluster merging

Two extensions to the objective function-based fuzzy clustering are proposed. First, the (point) prototypes are extended to hypervolumes, whose size can be fixed or can be determined automatically from the data being clustered. It is shown that clustering with hypervolume prototypes can be formulated as the minimization of an objective function. Second, a heuristic cluster merging step is introduced where the similarity among the clusters is assessed during optimization. Starting with an overestimation of the number of clusters in the data, similar clusters are merged in order to obtain a suitable partitioning. An adaptive threshold for merging is proposed. The extensions proposed are applied to Gustafson–Kessel and fuzzy c-means algorithms, and the resulting extended algorithm is given. The properties of the new algorithm are illustrated by various examples

Neuroengineering of Clustering Algorithms

Cluster analysis can be broadly divided into multivariate data visualization, clustering algorithms, and cluster validation. This dissertation contributes neural network-based techniques to perform all three unsupervised learning tasks. Particularly, the first paper provides a comprehensive review on adaptive resonance theory (ART) models for engineering applications and provides context for the four subsequent papers. These papers are devoted to enhancements of ART-based clustering algorithms from (a) a practical perspective by exploiting the visual assessment of cluster tendency (VAT) sorting algorithm as a preprocessor for ART offline training, thus mitigating ordering effects; and (b) an engineering perspective by designing a family of multi-criteria ART models: dual vigilance fuzzy ART and distributed dual vigilance fuzzy ART (both of which are capable of detecting complex cluster structures), merge ART (aggregates partitions and lessens ordering effects in online learning), and cluster validity index vigilance in fuzzy ART (features a robust vigilance parameter selection and alleviates ordering effects in offline learning). The sixth paper consists of enhancements to data visualization using self-organizing maps (SOMs) by depicting in the reduced dimension and topology-preserving SOM grid information-theoretic similarity measures between neighboring neurons. This visualization\u27s parameters are estimated using samples selected via a single-linkage procedure, thereby generating heatmaps that portray more homogeneous within-cluster similarities and crisper between-cluster boundaries. The seventh paper presents incremental cluster validity indices (iCVIs) realized by (a) incorporating existing formulations of online computations for clusters\u27 descriptors, or (b) modifying an existing ART-based model and incrementally updating local density counts between prototypes. Moreover, this last paper provides the first comprehensive comparison of iCVIs in the computational intelligence literature --Abstract, page iv

Extended Fuzzy Clustering Algorithms

Fuzzy clustering is a widely applied method for obtaining fuzzy models from data. Ithas been applied successfully in various fields including finance and marketing. Despitethe successful applications, there are a number of issues that must be dealt with in practicalapplications of fuzzy clustering algorithms. This technical report proposes two extensionsto the objective function based fuzzy clustering for dealing with these issues. First, the(point) prototypes are extended to hypervolumes whose size is determined automaticallyfrom the data being clustered. These prototypes are shown to be less sensitive to a biasin the distribution of the data. Second, cluster merging by assessing the similarity amongthe clusters during optimization is introduced. Starting with an over-estimated number ofclusters in the data, similar clusters are merged during clustering in order to obtain a suitablepartitioning of the data. An adaptive threshold for merging is introduced. The proposedextensions are applied to Gustafson-Kessel and fuzzy c-means algorithms, and the resultingextended algorithms are given. The properties of the new algorithms are illustrated invarious examples.fuzzy clustering;cluster merging;similarity;volume prototypes

Dynamic Clustering of Histogram Data Based on Adaptive Squared Wasserstein Distances

This paper deals with clustering methods based on adaptive distances for histogram data using a dynamic clustering algorithm. Histogram data describes individuals in terms of empirical distributions. These kind of data can be considered as complex descriptions of phenomena observed on complex objects: images, groups of individuals, spatial or temporal variant data, results of queries, environmental data, and so on. The Wasserstein distance is used to compare two histograms. The Wasserstein distance between histograms is constituted by two components: the first based on the means, and the second, to internal dispersions (standard deviation, skewness, kurtosis, and so on) of the histograms. To cluster sets of histogram data, we propose to use Dynamic Clustering Algorithm, (based on adaptive squared Wasserstein distances) that is a k-means-like algorithm for clustering a set of individuals into $K$ classes that are apriori fixed. The main aim of this research is to provide a tool for clustering histograms, emphasizing the different contributions of the histogram variables, and their components, to the definition of the clusters. We demonstrate that this can be achieved using adaptive distances. Two kind of adaptive distances are considered: the first takes into account the variability of each component of each descriptor for the whole set of individuals; the second takes into account the variability of each component of each descriptor in each cluster. We furnish interpretative tools of the obtained partition based on an extension of the classical measures (indexes) to the use of adaptive distances in the clustering criterion function. Applications on synthetic and real-world data corroborate the proposed procedure

Incremental Predictive Process Monitoring: How to Deal with the Variability of Real Environments

A characteristic of existing predictive process monitoring techniques is to first construct a predictive model based on past process executions, and then use it to predict the future of new ongoing cases, without the possibility of updating it with new cases when they complete their execution. This can make predictive process monitoring too rigid to deal with the variability of processes working in real environments that continuously evolve and/or exhibit new variant behaviors over time. As a solution to this problem, we propose the use of algorithms that allow the incremental construction of the predictive model. These incremental learning algorithms update the model whenever new cases become available so that the predictive model evolves over time to fit the current circumstances. The algorithms have been implemented using different case encoding strategies and evaluated on a number of real and synthetic datasets. The results provide a first evidence of the potential of incremental learning strategies for predicting process monitoring in real environments, and of the impact of different case encoding strategies in this setting

Clustering analysis of railway driving missions with niching

A wide number of applications requires classifying or grouping data into a set of categories or clusters. Most popular clustering techniques to achieve this objective are K-means clustering and hierarchical clustering. However, both of these methods necessitate the a priori setting of the cluster number. In this paper, a clustering method based on the use of a niching genetic algorithm is presented, with the aim of finding the best compromise between the inter-cluster distance maximization and the intra-cluster distance minimization. This method is applied to three clustering benchmarks and to the classification of driving missions for railway applications