Hani Hamdan

Mixture Model Clustering of Uncertain Data

This paper addresses the problem of fitting mixture densities to uncertain data using the EM algorithm. Uncertain data are modelled by multivariate uncertainty zones which constitute a generalization of multivariate interval-valued data. We develop an EM algorithm to treat uncertainty zones around points of Ropfp in order to estimate the parameters of a mixture model defined on Ropfp and obtain a fuzzy clustering or partition. This EM algorithm requires the evaluation of multidimensional integrals over each uncertainty zone at each iteration. In the diagonal Gaussian mixture model case, these integrals can be computed by simply using the one-dimensional normal cumulative distribution function. Results on simulated data indicate that the proposed algorithm can estimate the true underlying density better than the classical EM algorithm applied to the imprecise data, especially when the imprecision degree is high

Self-organizing map based on L 2 distance for interval-valued data

The Self-Organizing Maps have been widely used as multidimensional unsupervised classifiers. The aim of this paper is to develop a self-organizing map for interval data. Due to the increasing use of such data in Data Mining, many clustering methods for interval data have been proposed this last decade. In this paper, we propose an algorithm to train the self-organizing map for interval data. We use an extension of the Euclidian distance to compare two vectors of intervals. In order to show the usefulness of our approach, we apply the proposed algorithm on real interval data issued from meteorological stations in China.

Interval data clustering using self-organizing maps based on adaptive Mahalanobis distances

The self-organizing map is a kind of artificial neural network used to map high dimensional data into a low dimensional space. This paper presents a self-organizing map for interval-valued data based on adaptive Mahalanobis distances in order to do clustering of interval data with topology preservation. Two methods based on the batch training algorithm for the self-organizing maps are proposed. The first method uses a common Mahalanobis distance for all clusters. In the second method, the algorithm starts with a common Mahalanobis distance per cluster and then switches to use a different distance per cluster. This process allows a more adapted clustering for the given data set. The performances of the proposed methods are compared and discussed.

Self-organizing map based on hausdorff distance for interval-valued data

The Self-Organizing Maps have been widely used as multidimensional unsupervised classifiers. The aim of this paper is to develop a self-organizing map for interval data. Due to the increasing use of such data in Data Mining, many clustering methods for interval data have been proposed this last decade. In this paper, we propose an algorithm to train the self-organizing map for interval data. We use the Hausdorff distance to compare two vectors of intervals. In order to show the usefulness of our approach, we apply the self-organizing map on real interval data issued from meteorological stations in China.

Int-EM-CEM algorithm for imprecise data. Comparison with the CEM algorithm using Monte Carlo simulations

This paper addresses the problem of fitting mixture model based-clustering to imprecise data using the CEM algorithm. Imprecise data are modelled by multivariate uncertainty zones, which constitute a generalization of multivariate interval-valued data. To estimate simultaneously the mixture model parameters and the partition from uncertainty zone data, we propose an adapted version of the CEM algorithm. Results on simulated data compare the proposed algorithm with the classical one (applied to the raw data then to the uncertain data).

CEM algorithm for imprecise data. Application to flaw diagnosis using acoustic emission

This paper addresses the problem of fitting mixture model based-clustering to imprecise data using the CEM algorithm. Imprecise data are modelled by multivariate uncertainty zones, which constitute a generalization of multivariate interval-valued data. To estimate simultaneously the mixture model parameters and the partition from uncertainty zone data, we propose an adapted version of the CEM algorithm. The paper concludes with a brief description of an application of this approach to flaw diagnosis, on pressure equipments, using acoustic emission, in the context of imprecise bivariate measurements of localization of acoustic emission signals

Self-Organizing Map Based on City-Block Distance for Interval-Valued Data

The Self-Organizing Maps have been widely used as multidimensional unsupervised classifiers. The aim of this paper is to develop a self-organizing map for interval data. Due to the increasing use of such data in Data Mining, many clustering methods for interval data have been proposed this last decade. In this paper, we propose an algorithm to train the self-organizing map for interval data. We use the city-block distance to compare two vectors of intervals. In order to show the usefulness of our approach, we apply the self-organizing map on real interval data issued from meteorological stations in France.

A neural networks approach to interval-valued data clustering. Applicationto Lebanese meteorological stations data

The Self-Organizing Maps have been widely used as multidimensional unsupervised classifiers. The aim of this paper is to develop a self-organizing map for interval data. Due to the increasing use of such data in Data Mining, many clustering methods for interval data have been proposed this last decade. In this paper, we propose an algorithm to train the self-organizing map for interval data. We use the Euclidian distance to compare two vectors of intervals. In order to show the usefulness of our approach, we apply the self-organizing map on real interval data issued from meteorological stations in Lebanon.

Parsimonious Gaussian mixture models of general family for binned data clustering: Mixture approach

Binning data provides a solution in deducing computation expense in cluster analysis. According to former study, basing cluster analysis on Gaussian mixture models has become a classical and power approach. Mixture approach is one of the most common model-based approaches, which estimates the model parameters by maximizing the likelihood by EM algorithm. According to eigenvalue composition of the variance matrices of the mixture components, parsimonious models are generated. Choosing a right parsimonious model is crucial in obtaining a good result. In this paper, we address the problem of applying mixture approach to binned data (binned-EM algorithm). Six general models are studied and the difference in the performances of six general models is analyzed.

EM algorithm of spherical models for binned data

In cluster analysis, dealing with large quantity of data is computational expensive. And binning data can be efficient in solving this problem. In the former study, basing cluster analysis on Gaussian mixture models becomes a classical and powerful approach. EM and CEM algorithm are commonly used in mixture approach and classification approach respectively. According to the parametrization of the variance matrices (allowing some of the features of clusters be the same or different: orientation, shape and volume), 14 Gaussian parsimonious models can be generated. Choosing the right parsimonious model is important in obtaining a good result. According to the existing study, Binned-EM algorithm was performed for the most general and diagonal model. In this paper, we apply binned-EM algorithm on spherical models. Two spherical models are studied and their performances on simulated data are compared. The influence of the size of bins in binned-EM algorithm is analyzed. Practical application is shown by applying on Iris data.