These notes give a short introduction to Gaussian mixture models (GMMs) and the Expectation-Maximization (EM) algorithm, first for the specific case of GMMs, and then more generally. These notes assume you’re familiar with basic probability and basic calculus. If you’re interested in the full derivation (Section 3), some familiarity with entropy and KL divergence is useful but not strictly requ...

A fuzzy clustering based modification of Gaussian mixture models (GMMs) for speaker recognition is proposed. In this modification, fuzzy mixture weights are introduced by redefining the distances used in the fuzzy c-means (FCM) functionals. Their reestimation formulas are proved by minimising the FCM functionals. The experimental results show that the fuzzy GMMs can be used in speaker recogniti...

Recent results in the area of language identification have shown a significant improvement over previous systems. In this paper, we evaluate the related problem of dialect identification using one of the techniques recently developed for language identification, the Gaussian mixture models with shifted-delta-cepstral features. The system shown is developed using the same methodology followed fo...

Gaussian mixture models with eigen-decomposed covariance structures make up the most popular family of mixture models for clustering and classification, i.e., the Gaussian parsimonious clustering models (GPCM). Although the GPCM family has been used for almost 20 years, selecting the best member of the family in a given situation remains a troublesome problem. Likelihood ratio tests are develop...

background & aim: in the survival data with long-term survivors the event has not occurred for all the patients despite long-term follow-up, so the survival time for a certain percent is censored at the  end  of the  study.  mixture  cure  model  was  introduced  by boag,  1949  for  reaching  a  more efficient analysis of this set of data. because of some disadvantages of this model non-mixtur...

This paper presents a new modeling method of the continuous density Hidden Markov Model. As we know, speech signal is characterized by a hidden state sequence and each state is described by the mixture of weighted Gaussian density functions. Usually if we want to describe speech signal more precisely, we need to use more Gaussian functions for each state. But it will increase the computation si...

In recent years, a number of works have demonstrated that processing images using patch-based features provides more robust results than their pixel based counterparts. A contributing factor to their success is that image patches can be expressed sparsely in appropriately defined dictionaries, and these dictionaries can be tuned to a variety of applications. Yu, Sapiro and Mallat [24] demonstra...

The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extension of the Kullback-Leibler importance estimation procedure (KLIEP), an...

This article concerns the greedy learning of gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one after the other. We propose a heuristic for searching for the optimal component to insert. In a randomized manner, a set of candidate new components is generated. For each of these candidates, we find the locally optimal new component and insert it into th...