{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T00:30:01Z","timestamp":1785198601372,"version":"3.55.0"},"reference-count":14,"publisher":"MIT Press","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p>\u03b1-integration and \u03b1-GMM have been recently proposed for integrated stochastic modeling. However, there has not been an approach to date for estimating model parameters for \u03b1-GMM in a statistical way, based on a set of training data. In this letter, parameter updating formulas are mathematically derived based on maximum likelihood criterion using an adapted expectation-maximization algorithm. With this method, model parameters for \u03b1-GMM are reestimated in an iterative way. The updating formulas were found to be simple and systematically compatible with the GMM equations. This advantage renders the \u03b1-GMM a superset of the GMM but with similar computational complexity. This method has been effectively applied to realistic speaker recognition applications.<\/jats:p>","DOI":"10.1162\/neco.2008.04-08-776","type":"journal-article","created":{"date-parts":[[2008,11,19]],"date-time":"2008-11-19T22:51:05Z","timestamp":1227135065000},"page":"1776-1795","source":"Crossref","is-referenced-by-count":13,"title":["Parameter Estimation for \u03b1-GMM Based on Maximum Likelihood Criterion"],"prefix":"10.1162","volume":"21","author":[{"given":"Dalei","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, York University, Toronto, Ontario, M3J 1P3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.10.2780"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697196"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1968.27.211"},{"key":"B4","unstructured":"Bilmes, J. A. (1997). A gentle tutorial of the EM algorithm and its application to parameter estimation for gaussian mixture and hidden Markov models (Tech. Rep. tr-97-021) Berkeley: University of California."},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.1999.759799"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729330"},{"key":"B7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"Dempster A. P.","year":"1977","journal-title":"Journal of the Royal Statistical Society B"},{"key":"B8","first-page":"93","volume-title":"Proceedings of DARPA Workshop on Speech Recognition","author":"Fisher W. M.","year":"1986"},{"key":"B9","volume-title":"Inequalities","author":"Hardy G. H.","year":"1952","edition":"2"},{"key":"B10","volume-title":"A general formulation for discriminative learning of generative graphical models","author":"Jiang H.","year":"2007"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1137\/050621906"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1109\/97.372913"},{"key":"B15","first-page":"72","volume-title":"Nonlinear Analyses and Algorithms for Speech Processing Part II","author":"Wu D.","year":"2005"},{"key":"B16","volume-title":"The HTK book","author":"Young S.","year":"2002"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco.2008.04-08-776","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T00:46:51Z","timestamp":1738543611000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/direct.mit.edu\/neco\/article\/21\/6\/1776-1795\/7445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":14,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1162\/neco.2008.04-08-776"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1162\/neco.2008.04-08-776","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}