A classification EM algorithm for binned data

• Published in: Computational statistics & data analysis Vol. 51; no. 2; pp. 466 - 480
• Main Authors: Samé, Allou, Ambroise, Christophe, Govaert, Gérard
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.11.2006; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Binned data; CEM; Clustering; Exact sciences and technology; General topics; Histogram; Mathematics; Mixture model; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; Mixture model; EM; Histogram; CEM; Clustering; Binned data; Mixed distribution; Density estimation; Partition; Data analysis; Cluster analysis (statistics); High density; Acoustics; Real time; Surface; Numerical computation; Statistical computation; Experimental design; Law of large numbers; Greedy algorithm; Integral; EM algorithm
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2005.08.009

A real-time flaw diagnosis application for pressurized containers using acoustic emissions is described. The pressurized containers used are cylindrical tanks containing fluids under pressure. The surface of the pressurized containers is divided into bins, and the number of acoustic signals emanating from each bin is counted. Spatial clustering of high density bins using mixture models is used to detect flaws. A dedicated EM algorithm can be derived to select the mixture parameters, but this is a greedy algorithm since it requires the numerical computation of integrals and may converge only slowly. To deal with this problem, a classification version of the EM (CEM) algorithm is defined, and using synthetic and real data sets, the proposed algorithm is compared to the CEM algorithm applied to classical data. The two approaches generate comparable solutions in terms of the resulting partition if the histogram is sufficiently accurate, but the algorithm designed for binned data becomes faster when the number of available observations is large enough.