کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6939269 1449970 2018 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On convergence and parameter selection of the EM and DA-EM algorithms for Gaussian mixtures
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر چشم انداز کامپیوتر و تشخیص الگو
پیش نمایش صفحه اول مقاله
On convergence and parameter selection of the EM and DA-EM algorithms for Gaussian mixtures
چکیده انگلیسی
The expectation & maximization (EM) for Gaussian mixtures is popular as a clustering algorithm. However, the EM algorithm is sensitive to initial values, and so Ueda and Nakano [4] proposed the deterministic annealing EM (DA-EM) algorithm to improve it. In this paper, we investigate theoretical behaviors of the EM and DA-EM algorithms. We first derive a general Jacobian matrix of the DA-EM algorithm with respect to posterior probabilities. We then propose a theoretical lower bound for initialization of the annealing parameter in the DA-EM algorithm. On the other hand, some researches mentioned that the EM algorithm exhibits a self-annealing behavior, that is, the equal posterior probability with small random perturbations can avoid the EM algorithm to output the mass center for Gaussian mixtures. However, there is no theoretical analysis on this self-annealing property. Since the DA-EM will become the EM when the annealing parameter is 1, according to the Jacobian matrix of the DA-EM, we can prove the self-annealing property of the EM algorithm for Gaussian mixtures. Based on these results, we give not only convergence behaviors of the equal posterior probabilities and initialization lower bound of the temperature parameter of the DA-EM, but also a theoretical explanation why the EM algorithm for Gaussian mixtures exhibits a self-annealing behavior.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Pattern Recognition - Volume 77, May 2018, Pages 188-203
نویسندگان
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