We offer three algorithms for the generation of topographic mappings to the practitioner of unsupervised data analysis. The algorithms are each based on the minimization of a cost function which is performed using an ...
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We offer three algorithms for the generation of topographic mappings to the practitioner of unsupervised data analysis. The algorithms are each based on the minimization of a cost function which is performed using an em algorithm and deterministic annealing. The soft topographic vector quantization algorithm (STVQ) - like the original self-organizing map (SOM) - provides a tool for the creation of self-organizing maps of Euclidean data. Its optimization scheme, however, offers an alternative to the heuristic stepwise shrinking of the neighborhood width in the SOM and makes it possible to use a fixed neighborhood function solely to encode desired neighborhood relations between nodes. The kernel-based soft topographic mapping (STMK) is a generalization of STVQ and introduces new distance measures in data space, based on kernel functions. Using the new distance measures corresponds to performing the STVQ in a high-dimensional feature space, which is related to data space by a nonlinear mapping. This preprocessing can reveal structure in the data which may go unnoticed if the STVQ is performed in the standard Euclidean space. The soft topographic mapping for proximity data (STMP) is another generalization of STVQ that enables the user to generate topographic maps for data which are given in terms of pairwise proximities. It thus offers a flexible alternative to multidimensional scaling methods and opens up a new range of applications for SOMs. Both STMK and STMP share the robust optimization properties of STVQ due to the application of deterministic annealing. In our contribution we discuss the algorithms together with their implementation and provide detailed pseudo-code and explanations. (C) 1998 Elsevier Science B.V. All rights reserved.
We consider the probabilistic neural network (PNN) that is a mixture of Gaussian basis functions having different variances. Such a Gaussian heteroscedastic PNN is more economic, in terms of the number of kernel funct...
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We consider the probabilistic neural network (PNN) that is a mixture of Gaussian basis functions having different variances. Such a Gaussian heteroscedastic PNN is more economic, in terms of the number of kernel functions required, than the Gaussian mixture PNN of a common variance. The expectation-maximisation (em) algorithm, although a powerful technique for constructing maximum likelihood (ML) homoscedastic PNNs, often encounters numerical difficulties when training heteroscedastic PNNs. We combine a robust statistical technique known as the Jack-knife with the em algorithm to provide a robust ML training algorithm. An artificial-data case, the two-dimensional XOR problem, and a real-data case, success or failure prediction of UK private construction companies, are used to evaluate the performance of this robust learning algorithm. (C) 1998 Elsevier Science Ltd. All rights reserved.
Visualization has proven to be a powerful and widely-applicable tool for the analysis and interpretation of multivariate data. Most visualization algorithms aim to find a projection from the data space down to a two-d...
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Visualization has proven to be a powerful and widely-applicable tool for the analysis and interpretation of multivariate data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space, it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and subclusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach on a toy data set, and we then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multiphase flows in oil pipelines, and to data in 36 dimensions derived from satellite images. A Matlab software implementation of the algorithm is publicly available from the World Wide Web.
This paper deals with the matrix rate of convergence of the ECME algorithm, a simple extention of em and ECM algorithms proposed recently by Liu and Rubin. We establish a general formula for the matrix rate of converg...
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This paper deals with the matrix rate of convergence of the ECME algorithm, a simple extention of em and ECM algorithms proposed recently by Liu and Rubin. We establish a general formula for the matrix rate of convergence of ECME which is a generalization of the result of Liu and Rubin. (C) 1998 Elsevier Science B.V.
We extend our previously proposed quasi-Bayes adaptive learning framework to cope with the correlated continuous density hidden Markov models (HMM's) with Gaussian mixture state observation densities in which all ...
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We extend our previously proposed quasi-Bayes adaptive learning framework to cope with the correlated continuous density hidden Markov models (HMM's) with Gaussian mixture state observation densities in which all mean vectors are assumed to be correlated and have a joint prior distribution. A successive approximation algorithm is proposed to implement the correlated mean vectors' updating. As an example, by applying the method to on-line speaker adaptation application, the algorithm is experimentally shown to be asymptotically convergent as well as being able to enhance the efficiency and the effectiveness of the Bayes learning by taking into account the correlation information between different model parameters. The technique can be used to cope with the time-varying nature of some acoustic and environmental variabilities, including mismatches caused by changing speakers, channels, transducers, environments, and so on.
We derive and investigate a variant of AIC, the Akaike information criterion, for model selection in settings where the observed data is incomplete. Our variant is based on the motivation provided for the PDIO ('p...
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We derive and investigate a variant of AIC, the Akaike information criterion, for model selection in settings where the observed data is incomplete. Our variant is based on the motivation provided for the PDIO ('predictive divergence for incomplete observation models') criterion of Shimodaira (1994, in: Selecting Models from Data: Artificial Intelligence and Statistics IV, Lecture Notes in Statistics, vol. 89, Springer, New York, pp. 21-29). However, our variant differs from PDIO in its 'goodness-of-fit' term. Unlike AIC and PDIO, which require the computation of the observed-data empirical log-likelihood, our criterion can be evaluated using only complete-data tools, readily available through the em algorithm and the Sem ('supplemented' em) algorithm of Meng and Rubin (Journal of the American Statistical Association 86 (1991) 899-909). We compare the performance of our AIC variant to that of both AIC and PDIO in simulations where the data being modeled contains missing values. The results indicate that our criterion is less prone to overfitting than AIC and less prone to underfitting than PDIO. (C) 1998 Elsevier Science B.V. All rights reserved.
In this correspondence, an algorithm to jointly estimate signal directions and signal parameters for a class of analogue communications signals collected by a uniform linear array is presented. It has been shown that ...
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In this correspondence, an algorithm to jointly estimate signal directions and signal parameters for a class of analogue communications signals collected by a uniform linear array is presented. It has been shown that for the combination of quadrature baseband model and linear Gauss-Markov sources, the expectation maximization (em) algorithm can be used to jointly estimate both signal directions of arrival and signal parameters. The em algorithm presented uses fixed interval smoothing in the E-step, and an exact M-step for a two sensor array. Having an exact M-step for an em algorithm significantly reduces computation. An iterative method to estimate an empirical Fisher information matrix (FIM) is applied to calculate the Cramer-Rao bound (CRB). For the algorithm presented, several important properties such as robust performance are identified through computer simulations, while the estimated CRB is used to indicate performance. (C) 1998 Elsevier Science B.V. All rights reserved.
The authors propose a new model parameter compensation algorithm based on parallel model combination (PMC). If differs from PMC in that the amount of adaption for the parameters is varied depending on the states and m...
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The authors propose a new model parameter compensation algorithm based on parallel model combination (PMC). If differs from PMC in that the amount of adaption for the parameters is varied depending on the states and mixture components of continuous density HMM. A state-dependent association factor which determines the adaption is employed and obtained by an em algorithm.
The population pharmacokinetics of teicoplanin in plasma and tonsillar tissue in children was determined following intramuscular administration. Thirty seven patients in all received either a single 5 mg/kg dose;2 dos...
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The population pharmacokinetics of teicoplanin in plasma and tonsillar tissue in children was determined following intramuscular administration. Thirty seven patients in all received either a single 5 mg/kg dose;2 doses of 5 mg/kg, 12 h apart;3 doses of 5 mg/kg, 12 h apart;or, a single 10 mg/kg dose. Limited data, comprising a maximum of 2 blood samples and 1 tonsillar sample were taken from each patient, with the maximum time being 48 h after the first dose of teicoplanin (in the 3X5 mg/kg dosing schedule). All plasma data were analyzed simultaneously by a maximum likelihood method employing a modified em algorithm. A first-order absorption, one-compartment disposition model was fitted to the data. Mean parameter values (with lower and upper 95% confidence intervals) were: clearance/bioavailability, 0.024 L h(-1) kg(-1) (0.020-0.027);volume of distribution/bioavailability, 0.61 L kg(-1) (0.54-0.70);absorption rate constant, 0.43 h(-1) (0.31-0.61). A first-order transfer model for distribution of teicoplanin between plasma and tonsillar tissue was fitted to the tonsil data. The mean parameter values (95% confidence intervals) were: transfer rate constant between plasma and tonsils 0.49 h(-1) (0.35-0.67);transfer rate constant between tonsils and plasma 0.73 h(-1) (0.52-1.03). These rate constants correspond to a distribution half-life of 0.95 h and an equilibrium distribution concentration ratio between tonsillar tissue and plasma of 0.67. After normalising clearance and volume of distribution for body weight, there was no further influence of body weight on the pharmacokinetic parameters. Also, there was no effect of dose, and as two formulations were used, one for the 5 mg/kg dose and the other for the 10 mg/kg dose, no effect of formulation on the pharmacokinetics of teicoplanin after im (intramuscular) administration was found. (C) 1998 Elsevier Science B.V. All rights reserved.
Analysis of convergence of the algebraic reconstruction technique (ART) shows it to be predisposed to converge to a solution faster than simultaneous methods, such as those of the Cimmino-Landweber type, the expectati...
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Analysis of convergence of the algebraic reconstruction technique (ART) shows it to be predisposed to converge to a solution faster than simultaneous methods, such as those of the Cimmino-Landweber type, the expectation maximization maximum likelihood method for the Poisson model (emML), and the simultaneous multiplicative ART (SMART), which use all the data at each step, Although choice of ordering of the data and of relaxation parameters are important, as Herman and Meyer have shown, they are not the full story, The analogous multiplicative ART (MART), which applies only to systems y = Pr in which y > 0, P greater than or equal to 0 and a nonnegative solution is sought, is also sequential (or "row-action"), rather than simultaneous, but does not generally exhibit the same accelerated convergence relative to its simultaneous version, SMART. By dividing each equation by the maximum of the corresponding row of P, we find that this rescaled MART (RMART) does converge faster, when solutions exist, significantly so in cases in which the row maxima are substantially less than one, Such cases arise frequently in tomography and when the columns of P have been normalized to have sum one. Between simultaneous methods, which use all the data at each step, and sequential (or row-action) methods, which use only a single data value at each step, there are the block-iterative (or ordered subset) methods, in which a single block or subset of the data is processed at each step. The ordered subset em (OSem) of Hudson et al, is significantly faster than the emML, but often fails to converge. The "rescaled block-iterative" emML RBI-emML) is an accelerated block-iterative version of emML that converges, in the consistent case, to a solution, for any choice of subsets;it reduces to OSem when the restrictive "subset balanced" condition holds, Rescaled block-iterative versions of SMART and MART also exhibit accelerated convergence.
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