References of "Likas, A."
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See detailA greedy EM algorithm for Gaussian mixture learning
Vlassis, Nikos UL; Likas, A.

in Neural Processing Letters (2002), 15(1), 77-87

Learning a Gaussian mixture with a local algorithm like EM can be difficult because (i) the true number of mixing components is usually unknown, (ii) there is no generally accepted method for parameter ... [more ▼]

Learning a Gaussian mixture with a local algorithm like EM can be difficult because (i) the true number of mixing components is usually unknown, (ii) there is no generally accepted method for parameter initialization, and (iii) the algorithm can get trapped in one of the many local maxima of the likelihood function. In this paper we propose a greedy algorithm for learning a Gaussian mixture which tries to overcome these limitations. In particular, starting with a single component and adding components sequentially until a maximum number k, the algorithm is capable of achieving solutions superior to EM with k components in terms of the likelihood of a test set. The algorithm is based on recent theoretical results on incremental mixture density estimation, and uses a combination of global and local search each time a new component is added to the mixture. [less ▲]

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Peer Reviewed
See detailA kurtosis-based dynamic approach to Gaussian mixture modeling
Vlassis, Nikos UL; Likas, A.

in IEEE Transactions on Systems, Man and Cybernetics. Part A, Systems and Humans (1999), 29(4), 393-399

We address the problem of probability density function estimation using a Gaussian mixture model updated with the expectation-maximization (EM) algorithm. To deal with the case of an unknown number of ... [more ▼]

We address the problem of probability density function estimation using a Gaussian mixture model updated with the expectation-maximization (EM) algorithm. To deal with the case of an unknown number of mixing kernels, we define a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kurtoses of the kernels. This measure provides an indication of how well the Gaussian mixture fits the data. Then we propose a new dynamic algorithm for Gaussian mixture density estimation which monitors the total kurtosis at each step of the Ehl algorithm in order to decide dynamically on the correct number of kernels and possibly escape from local maxima. We show the potential of our technique in approximating unknown densities through a series of examples with several density estimation problems. [less ▲]

Detailed reference viewed: 97 (1 UL)