N. A. Vlassis, G. Papakonstantinou, and P. Tsanakas, "Mixture Density Estimation Based on Maximum Likelihood and Sequential Test Statistics," Neural Processing Letters, vol. 9, no. 1, pp. 63--76, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....that dynamically adjust the number of kernels. Specifying the number of basis functions is an important open research issue in RBF training and mixture modeling, and our aim is to check the adaptation and applicability of the several techniques proposed so far in the framework of the PRBF network [14], 15] ACKNOWLEDGMENT The authors would like to thank the anonymous referees for their useful suggestions. ....

N. A. Vlassis, G. Papakonstantinou, and P. Tsanakas, "Mixture density estimation based on maximum likelihood and test statistics," Neural Processing Lett., vol. 9, no. 1, 1999.

.... The techniques allowing for estimating the probability density function of a stationary (or quasi stationary) random process have found several applications in the field of adaptive data processing, as in statistical discriminant analysis and probabilistic clustering of variable s domain [17], time series prediction, forecasting and linear regression [1] and recently in blind source separation (see for instance [6, 19] and references therein) and in non destructive evaluation of materials [4] Among others, a popular estimation approach relies on the finite kernel mixture model ....

.... by means of an adjustable superposition of flexible kernels (for a review see [18] This method is very interesting in a neural network viewpoint because it may be directly implemented by means of network topologies like the classical multilayer perceptron and the probabilistic neural network [1, 9, 17]. However, when the samples of the random process under observation are obtained sequentially, that is no batch elaboration is concerned, this technique suffers from two related problems: 1) it is very difficult to estimate the number of kernels which guarantees the best performance, and 2) as a ....

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N.A. Vlassis, G. Papakonstantinou, and P. Tsanakas, Mixture Density Estimation Based on Maximum Likelihood and Sequential Test Statistics, Neural Processing Letters, Vol. 9, pp. 63 -- 76, Feb. 1999

....of the mixture, called total kurtosis, that indicates how well the Gaussian mixture ts the input data. This new measure is computed from the individual weighted sample kurtoses of the mixing kernels, de ned by analogy to the weighted means and variances of the kernels and rst introduced in [4] for on line density estimation. Based on the progressive change of the total kurtosis, our algorithm performs kernel splitting and increases the number of kernels of the mixture. This splitting aims at making the absolute value of the total kurtosis as small as possible. By performing dynamic ....

N. Vlassis, G. Papakonstantinou, and P. Tsanakas, \Mixture density estimation based on maximum likelihood and test statistics, " Neural Processing Letters, vol. 9, no. 1, pp. 63-76, Feb. 1999.

....of the mixture, called total kurtosis, that indicates how well the Gaussian mixture fits the input data. This new measure is computed from the individual weighted sample kurtoses of the mixing kernels, defined by analogy to the weighted means and variances of the kernels and first introduced in [4] for on line density estimation. Based on the progressive change of the total kurtosis, our algorithm performs kernel splitting and increases the number of kernels of the mixture. This splitting aims at making the absolute value of the total kurtosis as small as possible. By performing dynamic ....

N. Vlassis, G. Papakonstantinou, and P. Tsanakas, "Mixture density estimation based on maximum likelihood and test statistics, " Neural Processing Letters, vol. 9, no. 1, pp. 63--76, Feb. 1999.

....to compute the inputdependent variances as weighted squared distances between the targets and the means of each component, weighted by the posterior probabilities P (kjx n ; yn ) already computed from the E step. The priors are also computed based on the posterior values. It can be shown [10, 12] that when inputs arrive sequentially in a Gaussian mixture fitting problem, then the variances and priors can be estimated by the iterative formulas s 2 k (xn ) s 2 k (xn ) P (kjx n ; yn ) k (xn ) f[y n Gamma f k (xn ) 2 Gamma s 2 k (xn )g; 17) k (xn ) k (xn ) P ....

N. Vlassis, G. Papakonstantinou, and P. Tsanakas. Mixture density estimation based on maximum likelihood and test statistics. Neural Processing Letters, 9(1):63--76, Feb. 1999.

....estimates for the parameters of the kernel. On the hypothesis of normality we expect that the random variable k j q n j =96 (16) approximately follows Gaussian distribution N(0; 1) and thus we can split a kernel j if the absolute of this value becomes higher than a specific threshold, e.g. 3 [10]. After splitting a kernel we create two kernels with means j oe j and j Gamma oe j and variances and weights both equal to the original variance and weight, respectively. The weights of all kernels are renormalized to sum one. Similarly, we maintain that two kernels j and k can join in one ....

....thresholds, e.g. 1:5 and 3, respectively. Also we delete a kernel j if its weight j falls below 1=n, a threshold which ensures that the terms in (12) and (13) remain bounded. After join or deletion all kernels update their weights to unity. For more detailed derivations the reader may refer to [10]. We should note here that the number n in the above formulas is constant, e.g. n = 100. This has two effects: first, even nonstationary sensor distributions can be handled appropriately with our model, because the previous gradient descent method for maximizing the likelihood does not need to ....

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N. A. Vlassis, G. Papakonstantinou, and P. Tsanakas. Mixture density estimation based on maximum likelihood and test statistics. Neural Processing Letters, 9(1), Feb. 1999, to appear.

....of the mixture, called total kurtosis, that indicates how well the Gaussian mixture fits the input data. This new measure is computed from the individual weighted sample kurtoses of the mixing kernels, defined by analogy to the weighted means and variances of the kernels and first introduced in [4] for on line density estimation. Based on the progressive change of the total kurtosis, our algorithm performs kernel splitting and increases the number of kernels of the mixture. This splitting aims at making the absolute value of the total kurtosis as small as possible. By performing dynamic ....

N. Vlassis, G. Papakonstantinou, and P. Tsanakas, "Mixture density estimation based on maximum likelihood and test statistics, " Neural Processing Letters, vol. 9, no. 1, pp. 63--76, Feb. 1999.

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N. A. Vlassis, G. Papakonstantinou, and P. Tsanakas, "Mixture Density Estimation Based on Maximum Likelihood and Sequential Test Statistics," Neural Processing Letters, vol. 9, no. 1, pp. 63--76, 1999.

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