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Methods for clustering univariate time series often rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coefficients, spectral measures, time delays at some selected frequencies and special characteristics such as trend, seasonality, etc. In this context some interesting features based on indexes of goodness-of-fit seem worth of special attention. Similar approaches have been suggested for clustering sets of multivariate time series. For example, clusters of regional economies may be formed based on sets of macroeconomic time series for each country. In a multivariate framework, however, the features of interest are more difficult to extract than for univariate time series. Indeed multivariate time series may differ not only for structure or pairwise correlation but for dimensionality and internal correlation as well. We propose some measures of predictability and interpolability as indexes of goodness-of-fit for multivariate time series that may serve as useful features to find clusters in the data. The capability of a clustering methods in distinguishing clusters of multivariate time series may be evaluated by using several cluster internal validity criteria. As each criterion is known to measure some special characteristics of the extracted features, multiobjective clustering methods and a genetic algorithm implementation are used to perform such evaluation. The concept of Pareto optimality in multiobjective genetic algorithms is used to perform simultaneous search over multiple criteria. The advantage in using genetic algorithms for multiobjective optimization resides in the circumstance that genetic algorithms maintain a population of solutions most of them non-dominated in the Pareto sense so that the whole Pareto front may be provided in a single run. The effectiveness of the measures of predictability and interpolability in conjunction with the multiobjective genetic optimization procedure for outlining the cluster structure of a set of multivariate time series will be studied on a set of real time series data. Furthermore, a simulation experiment will be presented to compare the performance of the proposed procedure with procedures arising from alternative approaches.

A genetic algorithmic methodology, termed a genetic algorithm with chromosome differentiation (GACD), is described which incorporates chromosome differentiation for evolutionary process. Chromosomes are distinguished into two categories of population over the generations based on the value contained in the two class bits. These are initially generated based on maximum hamming distance between them. Crossover (mating) is allowed only between individuals belonging to these categories. Theoretical analysis shows that the basic tenet of genetic algorithms holds for GACD as well; above average, short, low order schema will receive increasing number of trials in subsequent generations. It is also shown that in certain situations, the lower bound of the number of instances of a schema sampled by GACD is greater than or equal to that of the conventional genetic algorithm. Experimental results on a large number of function optimization and pattern classification problems demonstrate the significantly better performance of GACD over the conventional ones.

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.

We evaluate the performance of two fuzzy cluster validity indices, including a recently developed index, PBMF. The effectiveness of variable string length genetic algorithm (VGA) is used in conjunction with the fuzzy indices to determine the number of clusters present in a data set as well as the proper fuzzy cluster configuration. The utility of the fuzzy partitioning is tested on a number of artificial and real life data sets. The results of the fuzzy VGA algorithm are compared with those obtained by the well known FCM (fuzzy C-means) algorithm which is applicable only when the number of clusters is known a priori. The performance of the two fuzzy cluster validity indices is also tested for the pixel classification of a remotely sensed image of the race-course ground of Kolkata.

This article deals with the development of an unsupervised pattern classification technique that exploits the searching capability of genetic algorithms for automatically clustering a given data set into an appropriate number of clusters. Since the number of clusters is not known a priori, a modified string representation, comprising both real numbers and the don't care symbols, is used in order to encode a variable number of clusters. The Dunn's index is used as a measure of the fitness of a chromosome. Effectiveness of the genetic clustering scheme is demonstrated for several artificial and real-life data sets with the number of dimensions ranging from two to nine, and the number of clusters ranging from two to six.

The three-dimensional structure being critical for the function of a protein is usually conserved during evolution. It holds a wealth of information which can be harnessed to understand various aspects of proteins including sequence- structure function and evolutionary relationships. The understanding of these complex relationships is facilitated by a simplistic one-dimensional representation of the tertiary structure like a string of letters. The advantage is an easier visualization without losing much of the vital information due to dimension reduction. Using various methodologies, local structural patterns that can be combined to generate the desired backbone conformation, have been identified that use atomic coordinates characterising three-dimensional structures of proteins. Protein Blocks (PBs) is a set of 16 such local structural descriptors, denoted by letters a .. p that has been derived using unsupervised machine learning algorithms and can approximate the three dimensional space of proteins. Each letter corresponds to a entapeptide with distinct values of 8 dihedral angles (phi, psi). We demonstrate the use of PBs to characterize structural variations in enzymes using kinases as the case study. A protein kinase undergoes structural alterations as it switches to its active conformation from its inactive form. Crystal structures of several protein kinases are available in different enzymatic states. Firstly, we have applied PBs approach in distinguishing between conformation changes and rigid body displacements between the structures of active and inactive forms of a kinase. Secondly, we have performed a comparison of conformational patterns of active forms of a kinase with the active and inactive forms of a closely related kinase. Thirdly, we have studied the structural differences in the active states of homologous kinases. Such studies might help in understanding the structural differences among these enzymes at a different level as well as guide in making drug targets for a specific kinase. The first section gives a brief introduction on PBs and protein kinases followed by the analyses on conformational plasticity in kinases using Protein Blocks.