Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.

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Survey of clustering algorithms

The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed. >

A validity measure for fuzzy clustering

Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in large data sets. It has been subject of wide research since it arises in many application domains in engineering, business and social sciences. Especially, in the last years the availability of huge transactional and experimental data sets and the arising requirements for data mining created needs for clustering algorithms that scale and can be applied in diverse domains.

This paper introduces the fundamental concepts of clustering while it surveys the widely known clustering algorithms in a comparative way. Moreover, it addresses an important issue of clustering process regarding the quality assessment of the clustering results. This is also related to the inherent features of the data set under concern. A review of clustering validity measures and approaches available in the literature is presented. Furthermore, the paper illustrates the issues that are under-addressed by the recent algorithms and gives the trends in clustering process.

/pdf/on-clustering-validation-techniques-8ov9z4uqbn.pdf

On Clustering Validation Techniques

The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples. >

http://systemaut.persiangig.com/Fuzzy/IEEE_00227387.pdf

A possibilistic approach to clustering

Clustering of time series data-a survey

This study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set. Assessment of cluster validity is based on performance measures using hypervolume and density criteria. An algorithm is derived from a combination of the fuzzy K-means algorithm and fuzzy maximum-likelihood estimation. The unsupervised fuzzy partition-optimal number of classes algorithm performs well in situations of large variability of cluster shapes, densities, and number of data points in each cluster. The algorithm was tested on different classes of simulated data, and on a real data set derived from sleep EEG signal. >

Unsupervised optimal fuzzy clustering

In 12 epileptic patients suffering from "absences" 8-channel EEG was recorded by telemetry. The autoregressive model was applied to the signal and the prediction coefficients being the basis for calculation of the poles of the predictor. The location of the poles in thez- ands-planes was described as a function of time for 0.1 s steps along the pre-seizure EEG. In 10 of the 12 patients, and in 25 of the 28 recorded seizures this presentation of the poles of the predictor showed specific pattern linked with the occurrence of the siezure. The trajectory of the "most mobile pole" during the pre-seizure period could aid in the prediction of the seizure by several seconds.

On the prediction of epileptic seizures

Multivariate spectral estimation based on parametric modelling has been applied to epileptic surface EEG in order to detect EEG changes that occur prior to the clinical outbreak of the seizure. A better time/frequency resolution has been achieved using residual energy ratios (Dickinson’s method). Prediction of oncoming seizures was based on detection of increased preictal synchronisation by calculation of coherence and pole trajectories. The method has been tested on simulated EEG data and on real EEG data from patients with primary generalised epilepsy. Prediction times of 1–6 s have been found in several seizures from five patients.

Prediction of epileptic seizures from two-channel EEG.

A new fuzzy clustering algorithm, designed to detect and characterize ring-shaped clusters and combinations of ring-shaped and compact spherical clusters, has been developed. This FKR algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric (intersected) combinations of clusters. Validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set. The FKR algorithm has been tested on a variety of simulated combinations of ring-shaped and compact spherical clusters, and its performance proved to be very good, both in identifying the input shapes and in recovering the input parameters. Application of the FKR algorithm to an MRI image of the heart's left ventricle was used to investigate the possibility of using this algorithm as an aid in image processing. >

Isak Gath

Papers

Unsupervised optimal fuzzy clustering

On the prediction of epileptic seizures

Prediction of epileptic seizures from two-channel EEG.

Detection and separation of ring-shaped clusters using fuzzy clustering

The effects of acoustic modification on the identification of familiar voices speaking isolated vowels