Traven, H. (1991). A neural network approach to statistical pattern classification by semiparametric estimation of probability density functions. IEEE Trans. Neural Networks, Vol 2, 366-377.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(pdf s) In other words, to use new data in updating the previous estimate without modifying the structure of the previous model. The procedure was introduced by Nowlan [8] and explained in terms of the results by Neal and Hinton [9] Traven derived an Nmost recent window version of the procedure [10]. McKenna et al. [11,12,13] extended the result of Traven [10] to an L most recent window of the results from L batch EM runs and used it for tracking a multi colour foreground object. This parametric estimation approach can not run effectively without a good initial estimate (normally found by ....

....estimate without modifying the structure of the previous model. The procedure was introduced by Nowlan [8] and explained in terms of the results by Neal and Hinton [9] Traven derived an Nmost recent window version of the procedure [10] McKenna et al. [11,12,13] extended the result of Traven [10] to an L most recent window of the results from L batch EM runs and used it for tracking a multi colour foreground object. This parametric estimation approach can not run effectively without a good initial estimate (normally found by running the batch EM algorithm) The second group is that of ....

Traven, H. G. C., 21 neural network approach to statistical pattern classification by 5emiparametric' estimation ofprobability density functions. IEEE Transactions on Neural Networks, 1991.2(3): p. 366-77.

....samples to be stored for future use. The network size could grow substantially large in a continuous and dynamic environment modelling due to large amounts of training data are being fed into the network over a 6 long period. Some clustering algorithms have been proposed to overcome this problem [21 22]. Other than that, there is currently no intuitive method for selecting the optimal smoothing factor. The statistical method of determining smoothing factors is not suitable in dynamic and continuous modelling environment [18] Furthermore, GRNN requires many training samples in order to ....

....method based on the dynamic states of the plant, and without the need for statistical calculation. This scheme is able to assign the centre and width of the Gaussian kernel for each of the input variables effectively and with less computation procedures compared to other clustering method [21 22]. The initialisation of the sigma is based on the distance, i.e. the changing rate of the variable at the time when the new node was created. For the sigma of the variable (x i ) of the j pattern node created at the k sampling instant, the initialisation method can be written as follows: ....

Traven,H.G.C., A Neural network Approach to Statistical Pattern Classification by `Semiparametric Estimation of Probability Density function, IEEE Trans. On Neural Networks, Vol.2, May 1991, p366-377.

....of the input domain than sigmoidal ones through intermediate mappings. Some probabilistic neural networks, such as the Gaussian potential function network(GPFN) 11] the probabilistic neural network(PNN) 4] the probabilistic mapping networks (PMN) 7, 8] and the Gaussian clustering network(GCN)[12], have been developed using Gaussianlike nonlinear functions and appealed to our interests in classical pattern classi cation applications. However, there are no stochastic constraints imposed to the mixture weightings between the Gaussian basis units and the output units in the GPFN, so the ....

....evaluate the capacity of the network and remove the redundant training data, a large number of basis units will be involved for accurate density estimation of a distribution. Both the GCN and the PMN approximate the probability densities by a semi parametric estimation method with Gaussian kernels[12]. The PMN in [8] learns the model with MLE criterion, and gives an integrated method to learn all network parameters in one training phase for multiclass density estimation problems. However, the learning rule is derived by means of the principle of stochastic gradient descent searching, Some ....

H. G. C. Traven. A neural network approach to statistical pattern classi cation by semi-parametric estimation of probability density function. IEEE Trans on Neural Networks, 2(3):366377, May 1991.

....is chosen. 2. Non parametric Methods. When no such assumptions can be done, the densities need be estimated directly from the data. These are also known as kernel based estimators [12, 45, 46] 3. Semi parametric Methods. The densities are written as a mixture model whose parameters are estimated [12, 40, 50, 36, 48]. In the case of normal mixtures, this approach is equivalent to cluster based classification strategies like LVQ of Kohonen [24] and is similar to Gaussian radial basis function networks [32] 5 A decision rule as given in Eq. 1) has the effect of dividing the input space into mutually ....

....learning literature as there is no learning process but the computation is deferred up until recognition is done. Neural networks based on mixture models have also been proposed. Nowlan [36] considers them as soft variants of competitive approaches when used for vector quantization. Traven [50] proposes to use a mixture of Gaussians and calls this a a neural network approach and uses EM to optimize parameters without saying so. Statistics can also be used to improve the performance of neural techniques. Analysis of variances and using a preprocessing like z normalization or principal ....

Traven, H. G.C. (1991) "A Neural Network Approach to Statistical Pattern Classification by `Semiparametric' Estimation of Probability Density Functions," IEEE Transactions on Neural Networks, 2(3), 366--377.

....to converge to the correct estimation. Another drawback of the EM algorithm is its batch operation, where all data has to be gathered before the estimation, and must be fully utilised in each estimating episode. Although an iterative version is obtainable by re arranging Eqns. 2) 5) see [5][6]) the learning rates have to follow an exact iterative updating procedure. This iterative form of the EM algorithm is really only a special case of the BSOM. The learning rates in the BSOM algorithm, however, can take much relaxed values. 3.2 Experiment (A) A Mixture of Three 2 D Gaussians ....

H. G. C. Traven. A neural network approach to statistical pattern classification by 'semiparametric' estimation of probability density functions, IEEE Trans. Neural Networks, vol. 2, pp. 366-377, 1991.

....labeled according to the most probable source density. However, mixture models are specially useful in nonparametric supervised learning situations. For instance, the class conditional densities required in Statistical Pattern Recognition were individually approximated in (Priebe Marchette 1991, Traven 1991) by finite mixtures; hierarchical mixtures of linear models were proposed in (Jordan Jacobs 1994, Peng et. al 1995) mixtures of factor analyzers have been developed in (Ghahramani Hinton 1996, Hinton, Dayan, Revow 1997) and mixture models have been also useful for feature selection (Pudil ....

Traven, H.G.C., (1991). "A Neural Network Approach to Statistical Pattern Classification by "Semiparametric" Estimation of Prob. Den. Func.". IEEE T Neural Networks, V2 N3.

....of K means and K nearest neighbor algorithms as the latter has an intrinsic limitation that all the function widths are identical for all input dimensions. The EM algorithm has been applied to estimate the parameters of Gaussian mixture models for speaker recognition [3] and phoneme classification [4]. It has also been combined with gradient based learning algorithms to train RBF like networks [5] Most of these studies, however, used diagonal covariance matrices in the networks. In this paper, we propose to use full covariance matrices in the basis functions, resulting in elliptical basis ....

Hans G. C. Traven. A neural network approach to statistical pattern classification by semiparametric estimation of probability density functions. IEEE Tran. on Neural Networks, 2(3):366-- 377, May 1991.

....to train the gating network parameters bears a close resemblance to the procedure of training the parameters of a mixture of Gaussian densities to model an unknown probability density [Duda and Hart (1973) which has attracted several attempts at on line versions. We take the approach of [Traven (1991)] to derive the on line algorithm to perform structural adaptation in the mixture of experts network. All equations in the EM update rule and the batch mode growing technique are of the general form fl t = P t k=1 hk fl(x k ) P t k=1 hk : For this form, it can be shown that fl t 1 = fl t t 1 ....

Traven, H. G. C., 1991, "A Neural Network Approach to Statistical Pattern Classification by "Semiparametric " Estimation of Probability Density Functions," IEEE Transactions on Neural Networks, Vol. 2.

....were computed for the n most recent above threshold frames, where n L. The threshold was set to T = Gamma koe, where k was a constant. 2 Setting L = t and ignoring terms based on frame t Gamma L Gamma 1 gives a stochastic algorithm for estimating a Gaussian mixture for a stationary signal [6, 21]. 6 Experiments In the following we describe a set of experiments in which colour mixture models were applied to object segmentation and tracking in dynamic scenes. All the experiments ran in real time (15 20Hz) on a standard 200MHz PC with a Matrox Meteor board. 6.1 Experiment 1: Colour based ....

H. G. C. Traven, "A neural network approach to statistical pattern classification by "semiparametric" estimation of probability density functions," IEEE Trans. Neural Networks, vol. 2, no. 3, pp. 366--378, 1991.

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Traven, H. (1991). A neural network approach to statistical pattern classification by semiparametric estimation of probability density functions. IEEE Trans. Neural Networks, Vol 2, 366-377.

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Traven H.G.C. "A Neural Network Approach to Statistical Pattern Classification by 'Semiparametric' Estimation of Probability Density Functions" IEEE Trans. Neur. Networks 3., (1991) pp. 366-377.

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