{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T03:10:12Z","timestamp":1719025812182},"reference-count":50,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[2017,9]]},"abstract":"<jats:p>In literature the references to EM estimation of product mixtures are not very frequent. The simplifying assumption of product components, e.g. diagonal covariance matrices in case of Gaussian mixtures, is usually considered only as a compromise because of some computational constraints or limited dataset. We have found that the product mixtures are rarely used intentionally as a preferable approximating tool. Probably, most practitioners do not \u201ctrust\u201d the product components because of their formal similarity to \u201cnaive Bayes models.\u201d Another reason could be an unrecognized numerical instability of EM algorithm in multidimensional spaces. In this paper we recall that the product mixture model does not imply the assumption of independence of variables. It is even not restrictive if the number of components is large enough. In addition, the product components increase numerical stability of the standard EM algorithm, simplify the EM iterations and have some other important advantages. We discuss and explain the implementation details of EM algorithm and summarize our experience in estimating product mixtures. Finally we illustrate the wide applicability of product mixtures in pattern recognition and in other fields.<\/jats:p>","DOI":"10.1142\/s0218001417500288","type":"journal-article","created":{"date-parts":[[2017,1,26]],"date-time":"2017-01-26T08:10:41Z","timestamp":1485418241000},"page":"1750028","source":"Crossref","is-referenced-by-count":3,"title":["Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial"],"prefix":"10.1142","volume":"31","author":[{"given":"Ji\u0159\u00ed","family":"Grim","sequence":"first","affiliation":[{"name":"Institute of Information Theory and Automation of the Czech Academy of Sciences, P. O. Box 18, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 4, CZ-18208 Prague 8, Czech Republic"}]}],"member":"219","published-online":{"date-parts":[[2017,1,26]]},"reference":[{"key":"S0218001417500288BIB001","volume-title":"Classification of Multivariate Observations","author":"Ajvazjan S. 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