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This is an excellent and informative work, th...Hi, <br />This is an excellent and informative work, this will really helpful for me in future. I like the way you start and then conclude your thoughts. I completely agree with the points you have shared here about estimating the density or clustering. Thanks for this information. I really appreciate your work, keep it up.<br /><br /><a href="http://www.customessaywriting.net" rel="nofollow">Essay Writing Service</a>Custom Essay Writinghttp://www.customessaywriting.netnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-36638886113741964722010-06-23T22:40:52.613-06:002010-06-23T22:40:52.613-06:00Really trustworthy blog. Please keep updating with...Really trustworthy blog. Please keep updating with great posts like this one. 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I like your ideas for the future.<br /><a href="http://www.jacksonvillebeach-cosmeticdentist.com" rel="nofollow">jacksonville beach cosmetic dentist</a>gamefan12https://www.blogger.com/profile/17700305176595632282noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-66470951671637546442009-10-31T03:00:33.541-06:002009-10-31T03:00:33.541-06:00where they consider a variant where points are ass...where they consider a variant where points are assigned probabilistically rather than either hard or soft.<br /><a rel="follow" href="http://www.thedissertation.co.uk/" rel="nofollow">Dissertation</a> | <a rel="follow" href="http://www.theessay.co.uk/" rel="nofollow">Essay</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-27073498064583203452009-10-31T03:00:06.407-06:002009-10-31T03:00:06.407-06:00there is little hope to get anything more than a h...there is little hope to get anything more than a heuristic from a finite sample.<br /><a rel="follow" href="http://www.theassignments.co.uk/" rel="nofollow">Assignment</a> | <a rel="follow" href="http://www.thecoursework.co.uk/" rel="nofollow">Coursework</a> | <a rel="follow" href="http://www.theonlinethesis.co.uk/" rel="nofollow">Thesis</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-14261263615389035852009-03-05T07:35:00.000-07:002009-03-05T07:35:00.000-07:00Have you considered the relation between EM with G...Have you considered the relation between EM with Gaussian Mixtures and the original k-means clustering algorithm (isodata), where k-means can can be seen as a limiting form of EM-GM. Also, see an old paper by Mike Kearns on this topic, where they consider a variant where points are assigned probabilistically rather than either hard or soft.bjhttps://www.blogger.com/profile/11731812843589737087noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-31039781955121171642009-03-04T18:19:00.000-07:002009-03-04T18:19:00.000-07:00On a related note -- I think we often forget that ...On a related note -- I think we often forget that the EM theorem says that EM converges to a local max in likelihood, and says nothing about convergence of the parameters. If the parameters are nonidentifiable there's no reason to expect them to converge (I've seen this with multinomial mixture models).Mark Johnsonhttps://www.blogger.com/profile/05951121491616376798noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-22684371096849058042009-03-04T07:15:00.000-07:002009-03-04T07:15:00.000-07:00I believe that the problem of non-identifiability ...I believe that the problem of non-identifiability is well-understood in the literature, e.g., On the exponential value of labeled samples by Castelli and Cover. Of course if the mixture is not identifiable, it is hard to do anything at all. <BR/><BR/>But I think that the following question is at the heart of the problem: <BR/><BR/>given a probability density p, what is a good clustering? <BR/><BR/>If we cannot answer this (at least under some conditions), there is little hope to get anything more than a heuristic from a finite sample.<BR/><BR/>misha bAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-1472023768524817912009-03-03T11:08:00.000-07:002009-03-03T11:08:00.000-07:00Here's the abstract from Dempster, Laird and Rubin...Here's the abstract from Dempster, Laird and Rubin (1977), in which they describe EM as producing maximum likelihood estimates in the face of missing data (where the missing data in the mixture case is the mixture assignment): <BR/><BR/><I>A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived.<BR/><BR/>Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.<BR/></I>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-2932071258886126552009-03-03T03:08:00.000-07:002009-03-03T03:08:00.000-07:00I usually also think that if you want X, go for it...I usually also think that if you want X, go for it. But the question of identifiability is not existing (i mean solved) under classical hypothesis, in the gaussian case, right ?<BR/><BR/>Nice thing with gaussian mixtures is that the theoretical framework under which you fall makes things much easier than many clustering algorithms...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-4816594554492022402009-03-03T00:27:00.000-07:002009-03-03T00:27:00.000-07:00nice pic. maybe in another post you can expand on ...nice pic. maybe in another post you can expand on the EM vs ME issueSuresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.com