Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

Given a set of time series, it is of interest to discover subsets that share similar properties. For instance, this may be useful for identifying and estimating a single model that may fit conveniently several time series, instead of performing the usual identification and estimation steps for each one. On the other hand time series in the same cluster are related with respect to the measures assumed for cluster analysis and are suitable for building multivariate time series models. Though many approaches to clustering time series exist, in this view the most effective method seems to have to rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coe±cients, spectral measures or the eigenvectors of the covariance matrix. Some new indexes based on goodnessof-fit criteria will be proposed in this paper for fuzzy clustering of multivariate time series. A general purpose fuzzy clustering algorithm may be used to estimate the proper cluster structure according to some internal criteria of cluster validity. Such indexes are known to measure actually definite often conflicting cluster properties, compactness or connectedness, for instance, or distribution, orientation, size and shape. It is argued that the multiobjective optimization supported by genetic algorithms is a most effective choice in such a di±cult context. In this paper we use the Xie-Beni index and the C-means functional as objective functions to evaluate the cluster validity in a multiobjective optimization framework. The concept of Pareto optimality in multiobjective genetic algorithms is used to evolve a set of potential solutions towards a set of optimal non-dominated solutions. Genetic algorithms are well suited for implementing di±cult optimization problems where objective functions do not usually have good mathematical properties such as continuity, differentiability or convexity. In addition the genetic algorithms, as population based methods, may yield a complete Pareto front at each step of the iterative evolutionary procedure. The method is illustrated by means of a set of real data and an artificial multivariate time series data set.Fuzzy clustering, Internal criteria of cluster validity, Genetic algorithms, Multiobjective optimization, Time series, Pareto optimality

Clustering for binary data sets by using genetic algorithm-incremental K-means

This research was initially driven by the lack of clustering algorithms that specifically focus in binary data. To overcome this gap in knowledge, a promising technique for analysing this type of data became the main subject in this research, namely Genetic Algorithms (GA). For the purpose of this research, GA was combined with the Incremental Kmeans (IKM) algorithm to cluster the binary data streams. In GAIKM, the objective function was based on a few sufficient statistics that may be easily and quickly calculated on binary numbers. The implementation of IKM will give an advantage in terms of fast convergence. The results show that GAIKM is an efficient and effective new clustering algorithm compared to the clustering algorithms and to the IKM itself. In conclusion, the GAIKM outperformed other clustering algorithms such as GCUK, IKM, Scalable K-means (SKM) and K-means clustering and paves the way for future research involving missing data and outliers

Outliers in Time Series: an Empirical Likelihood Approach

The empirical likelihood method is known to be a flexible and effective approach for testing hypotheses and constructing confidence regions in a nonparametric setting. This framework is adopted here for dealing with the outlier problem in time series where conventional distributional assumptions may be inappropriate in most cases. The procedure is illustrated by a simulation experiment

Outliers in Time Series: an Empirical Likelihood Approach

The empirical likelihood method is known to be a flexible and effective approach for testing hypotheses and constructing confidence regions in a nonparametric setting. This framework is adopted here for dealing with the outlier problem in time series where conventional distributional assumptions may be inappropriate in most cases. The procedure is illustrated by a simulation experiment

Unsupervised classification of texture images by gray-level spatial dependence matrices and genetic algorithms

Recognition of objects and regions of interest in digital image processing often relies on texture classification. The source image is divided according to a rectangular grid to form textured regions each of which is characterized by some numerical significant measure called feature. A new approach is introduced that uses the gray-level spatial dependence matrices and the genetic clustering with unknown K algorithms to locate sets of homogeneous regions and enhance the discrimination amongst them. There is no need to select and compute complicated features transforms as the procedure is based on the optimal weighting of the simple basic features. A simulation experiment is performed using the well-known Brodatz textures to demonstrate that the new procedure is able to define well separated clusters according to the principle of strong internal cohesion and high inter-clusters separation

Evolutionary Computing in Statistical Data Analysis

Studies in Computational Intelligence vol. 20

Genetic search for threshold parameters in time series threshold models: algorithms and computer programs

Dipartimento di Statistica, Probabilita' e Statistiche Applicate, Working Paper 2009 - n. 10, URL: http://w3.uniroma1.it/statstsmeh/gasdtgarch05.pdf

Genetic algorithms-based approaches for clustering time series

Revised version of the selected paper presented at the biennal meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society which was held in Parma, June 6 - 8 , 2005. S. Zani, A. Cerioli, M. Riani and M. Vichi Editor