Ujjwal Maulik

Genetic algorithm-based clustering technique

Abstract A genetic algorithm-based clustering technique, called GA-clustering, is proposed in this article. The searching capability of genetic algorithms is exploited in order to search for appropriate cluster centres in the feature space such that a similarity metric of the resulting clusters is optimized. The chromosomes, which are represented as strings of real numbers, encode the centres of a fixed number of clusters. The superiority of the GA-clustering algorithm over the commonly used K-means algorithm is extensively demonstrated for four artificial and three real-life data sets.

Performance evaluation of some clustering algorithms and validity indices

In this article, we evaluate the performance of three clustering algorithms, hard K-Means, single linkage, and a simulated annealing (SA) based technique, in conjunction with four cluster validity indices, namely Davies-Bouldin index, Dunns index, Calinski-Harabasz index, and a recently developed index I. Based on a relation between the index I and the Dunns index, a lower bound of the value of the former is theoretically estimated in order to get unique hard K-partition when the data set has distinct substructures. The effectiveness of the different validity indices and clustering methods in automatically evolving the appropriate number of clusters is demonstrated experimentally for both artificial and real-life data sets with the number of clusters varying from two to ten. Once the appropriate number of clusters is determined, the SA-based clustering technique is used for proper partitioning of the data into the said number of clusters.

A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA

This paper describes a simulated annealing based multiobjective optimization algorithm that incorporates the concept of archive in order to provide a set of tradeoff solutions for the problem under consideration. To determine the acceptance probability of a new solution vis-a-vis the current solution, an elaborate procedure is followed that takes into account the domination status of the new solution with the current solution, as well as those in the archive. A measure of the amount of domination between two solutions is also used for this purpose. A complexity analysis of the proposed algorithm is provided. An extensive comparative study of the proposed algorithm with two other existing and well-known multiobjective evolutionary algorithms (MOEAs) demonstrate the effectiveness of the former with respect to five existing performance measures, and several test problems of varying degrees of difficulty. In particular, the proposed algorithm is found to be significantly superior for many objective test problems (e.g., 4, 5, 10, and 15 objective problems), while recent studies have indicated that the Pareto ranking-based MOEAs perform poorly for such problems. In a part of the investigation, comparison of the real-coded version of the proposed algorithm is conducted with a very recent multiobjective simulated annealing algorithm, where the performance of the former is found to be generally superior to that of the latter.

Validity index for crisp and fuzzy clusters

Abstract In this article, a cluster validity index and its fuzzification is described, which can provide a measure of goodness of clustering on different partitions of a data set. The maximum value of this index, called the PBM-index, across the hierarchy provides the best partitioning. The index is defined as a product of three factors, maximization of which ensures the formation of a small number of compact clusters with large separation between at least two clusters. We have used both the k-means and the expectation maximization algorithms as underlying crisp clustering techniques. For fuzzy clustering, we have utilized the well-known fuzzy c-means algorithm. Results demonstrating the superiority of the PBM-index in appropriately determining the number of clusters, as compared to three other well-known measures, the Davies–Bouldin index, Dunns index and the Xie–Beni index, are provided for several artificial and real-life data sets.

Genetic clustering for automatic evolution of clusters and application to image classification

Abstract In this article the searching capability of genetic algorithms has been exploited for automatically evolving the number of clusters as well as proper clustering of any data set. A new string representation, comprising both real numbers and the do not care symbol, is used in order to encode a variable number of clusters. The Davies–Bouldin index is used as a measure of the validity of the clusters. Effectiveness of the genetic clustering scheme is demonstrated for both artificial and real-life data sets. Utility of the genetic clustering technique is also demonstrated for a satellite image of a part of the city Calcutta. The proposed technique is able to distinguish some characteristic landcover types in the image.

An evolutionary technique based on K-means algorithm for optimal clustering in R N

A genetic algorithm-based efficient clustering technique that utilizes the principles of K-Means algorithm is described in this paper. The algorithm called KGA-clustering, while exploiting the searching capability of K-Means, avoids its major limitation of getting stuck at locally optimal values. Its superiority over the K-Means algorithm and another genetic algorithm-based clustering method, is extensively demonstrated for several artificial and real life data sets. A real life application of the KGA-clustering in classifying the pixels of a satellite image of a part of the city of Mumbai is provided.

Fuzzy partitioning using a real-coded variable-length genetic algorithm for pixel classification

The problem of classifying an image into different homogeneous regions is viewed as the task of clustering the pixels in the intensity space. Real-coded variable string length genetic fuzzy clustering with automatic evolution of clusters is used for this purpose. The cluster centers are encoded in the chromosomes, and the Xie-Beni index is used as a measure of the validity of the corresponding partition. The effectiveness of the proposed technique is demonstrated for classifying different landcover regions in remote sensing imagery. Results are compared with those obtained using the well-known fuzzy C-means algorithm.

Multiobjective Genetic Clustering for Pixel Classification in Remote Sensing Imagery

An important approach for unsupervised landcover classification in remote sensing images is the clustering of pixels in the spectral domain into several fuzzy partitions. In this paper, a multiobjective optimization algorithm is utilized to tackle the problem of fuzzy partitioning where a number of fuzzy cluster validity indexes are simultaneously optimized. The resultant set of near-Pareto-optimal solutions contains a number of nondominated solutions, which the user can judge relatively and pick up the most promising one according to the problem requirements. Real-coded encoding of the cluster centers is used for this purpose. Results demonstrating the effectiveness of the proposed technique are provided for numeric remote sensing data described in terms of feature vectors. Different landcover regions in remote sensing imagery have also been classified using the proposed technique to establish its efficiency

Nonparametric genetic clustering: comparison of validity indices

A variable-string-length genetic algorithm (GA) is used for developing a novel nonparametric clustering technique when the number of clusters is not fixed a-priori. Chromosomes in the same population may now have different lengths since they encode different number of clusters. The crossover operator is redefined to tackle the concept of variable string length. A cluster validity index is used as a measure of the fitness of a chromosome. The performance of several cluster validity indices, namely the Davies-Bouldin (1979) index, Dunns (1973) index, two of its generalized versions and a recently developed index, in appropriately partitioning a data set, are compared.

A Survey of Multiobjective Evolutionary Algorithms for Data Mining: Part I

The aim of any data mining technique is to build an efficient predictive or descriptive model of a large amount of data. Applications of evolutionary algorithms have been found to be particularly useful for automatic processing of large quantities of raw noisy data for optimal parameter setting and to discover significant and meaningful information. Many real-life data mining problems involve multiple conflicting measures of performance, or objectives, which need to be optimized simultaneously. Under this context, multiobjective evolutionary algorithms are gradually finding more and more applications in the domain of data mining since the beginning of the last decade. In this two-part paper, we have made a comprehensive survey on the recent developments of multiobjective evolutionary algorithms for data mining problems. In this paper, Part I, some basic concepts related to multiobjective optimization and data mining are provided. Subsequently, various multiobjective evolutionary approaches for two major data mining tasks, namely feature selection and classification, are surveyed. In Part II of this paper, we have surveyed different multiobjective evolutionary algorithms for clustering, association rule mining, and several other data mining tasks, and provided a general discussion on the scopes for future research in this domain.