Showing papers on "Mixture theory published in 2010"

Model-Based Expectation-Maximization Source Separation and Localization

Abstract: This paper describes a system, referred to as model-based expectation-maximization source separation and localization (MESSL), for separating and localizing multiple sound sources from an underdetermined reverberant two-channel recording. By clustering individual spectrogram points based on their interaural phase and level differences, MESSL generates masks that can be used to isolate individual sound sources. We first describe a probabilistic model of interaural parameters that can be evaluated at individual spectrogram points. By creating a mixture of these models over sources and delays, the multi-source localization problem is reduced to a collection of single source problems. We derive an expectation-maximization algorithm for computing the maximum-likelihood parameters of this mixture model, and show that these parameters correspond well with interaural parameters measured in isolation. As a byproduct of fitting this mixture model, the algorithm creates probabilistic spectrogram masks that can be used for source separation. In simulated anechoic and reverberant environments, separations using MESSL produced on average a signal-to-distortion ratio 1.6 dB greater and perceptual evaluation of speech quality (PESQ) results 0.27 mean opinion score units greater than four comparable algorithms.

Model-based clustering of microarray expression data via latent Gaussian mixture models

Abstract: Motivation: In recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In this article, a family of eight mixture models which utilizes the factor analysis covariance structure is extended to 12 models and applied to gene expression microarray data. This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models. This family of models allows for the modelling of the correlation between gene expression levels even when the number of samples is small. Parameter estimation is carried out using a variant of the expectation–maximization algorithm and model selection is achieved using the Bayesian information criterion. This expanded family of Gaussian mixture models, known as the expanded parsimonious Gaussian mixture model (EPGMM) family, is then applied to two well-known gene expression data sets. Results: The performance of the EPGMM family of models is quantified using the adjusted Rand index. This family of models gives very good performance, relative to existing popular clustering techniques, when applied to real gene expression microarray data. Availability: The reduced, preprocessed data that were analysed are available at www.paulmcnicholas.info Contact: pmcnicho@uoguelph.ca

Simplifying Mixture Models Through Function Approximation

Abstract: The finite mixture model is widely used in various statistical learning problems. However, the model obtained may contain a large number of components, making it inefficient in practical applications. In this paper, we propose to simplify the mixture model by minimizing an upper bound of the approximation error between the original and the simplified model, under the use of the L 2 distance measure. This is achieved by first grouping similar components together and then performing local fitting through function approximation. The simplified model obtained can then be used as a replacement of the original model to speed up various algorithms involving mixture models during training (e.g., Bayesian filtering, belief propagation) and testing [e.g., kernel density estimation, support vector machine (SVM) testing]. Encouraging results are observed in the experiments on density estimation, clustering-based image segmentation, and simplification of SVM decision functions.

General coupling of porous flows and hyperelastic formulations -- From thermodynamics principles to energy balance

Abstract: We formulate a general poromechanics model --~within the framework of a two-phase mixture theory --~compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles --~namely, essential conservation and thermodynamics laws --~and we thus obtain a Clausius-Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential --~with additional viscous effects --~which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid-structure interaction problem written in an Arbitrary Lagrangian-Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation.

Video Foreground Detection Based on Symmetric Alpha-Stable Mixture Models

Abstract: Background subtraction (BS) is an efficient technique for detecting moving objects in video sequences. A simple BS process involves building a model of the background and extracting regions of the foreground (moving objects) with the assumptions that the camera remains stationary and there exist no movements in the background. These assumptions restrict the applicability of BS methods to real-time object detection in video. In this letter, we propose an extended cluster BS technique with a mixture of symmetric alpha-stable (SαS) distributions. An online self-adaptive mechanism is presented that allows automated estimation of the model parameters using the log moment method. Results over real video sequences from indoor and outdoor environments, with data from static and moving video cameras are presented. The SαS mixture model is shown to improve the detection performance compared with a cluster BS method using a Gaussian mixture model and the method of Li et al.

Development of a Generalized Version of the Poisson-Nernst-Planck Equations Using the Hybrid Mixture Theory : Presentation of 2D Numerical Examples

Abstract: A numerical scheme for the transient solution of a generalized version of the Poisson–Nernst–Planck (PNP) equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The PNP equations represent a set of diffusion equations for charged species, i.e. dissolved ions, present in the pore solution of a rigid porous material in which the surface charge can be assumed neglectable. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst–Planck equations describing the diffusion of the ionic species and Gauss’ law in use are, however, coupled in both directions. The governing set of equations is derived from a simplified version of the so-called hybrid mixture theory (HMT). The simplifications used here mainly concerns ignoring the deformation and stresses in the porous material in which the ionic diffusion occurs. The HMT is a special version of the more ‘classical’ continuum mixture theories in the sense that it works with averaged equations at macroscale and that it includes the volume fractions of phases in its structure. The background to the PNP equations can by the HMT approach be described by using the postulates of mass conservation of constituents together with Gauss’ law used together with consistent constitutive laws. The HMT theory includes the constituent forms of the quasistatic version of Maxwell’s equations making it suitable for analyses of the kind addressed in this work. Within the framework of HTM, constitutive equations have been derived using the postulate of entropy inequality together with the technique of identifying properties by Lagrange multipliers. These results will be used in obtaining a closed set of equations for the present problem.

Constraint optimized weight adaptation for Gaussian mixture reduction

Abstract: Gaussian mixture model (GMM) has been used in many applications for dynamic state estimation such as target tracking or distributed fusion. However, the number of components in the mixture distribution tends to grow rapidly when multiple GMMs are combined. In order to keep the computational complexity bounded, it is necessary to approximate a Gaussian mixture by one with reduced number of components. Gaussian mixture reduction is traditionally conducted by recursively selecting two components that appear to be most similar to each other and merging them. Different definitions on similarity measure have been used in literature. For the case of one-dimensional Gaussian mixtures, Kmeans algorithms and some variations are recently proposed to cluster Gaussian mixture components in groups, use a center component to represent all in each group, readjust parameters in the center components, and finally perform weight optimization. In this paper, we focus on multi-dimensional Gaussian mixture models. With a variety of reduction algorithms and possible combinations, we developed a hybrid algorithm with constraint optimized weight adaptation to minimize the integrated squared error (ISE). In additions, with extensive simulations, we showed that the proposed algorithm provides an efficient and effective Gaussian mixture reduction performance in various random scenarios.

Modeling of active transmembrane transport in a mixture theory framework.

Abstract: This study formulates governing equations for active transport across semi-permeable membranes within the framework of the theory of mixtures. In mixture theory, which models the interactions of any number of fluid and solid constituents, a supply term appears in the conservation of linear momentum to describe momentum exchanges among the constituents. In past applications, this momentum supply was used to model frictional interactions only, thereby describing passive transport processes. In this study, it is shown that active transport processes, which impart momentum to solutes or solvent, may also be incorporated in this term. By projecting the equation of conservation of linear momentum along the normal to the membrane, a jump condition is formulated for the mechano-electrochemical potential of fluid constituents which is generally applicable to nonequilibrium processes involving active transport. The resulting relations are simple and easy to use, and address an important need in the membrane transport literature.

Mechanics and Thermodynamics of Fluid-Saturated Highly Elastic Materials

Abstract: We consider a mixture that consists of a highly elastic material and a liquid dissolved in this material. Using the laws of classical thermodynamics, we state a variational principle describing the mixture equilibrium under static loading conditions. From this principle, we derive equilibrium equations and a system of constitutive relations characterizing the mixture elastic and thermodynamic properties. We state problems describing the stress-strain state of a swollen material and a statically loaded material in thermodynamic equilibrium with the liquid. We consider the case of incompressible mixture. The general theory is illustrated by examples concerned with the deformation behavior of inhomogeneously swollen cross-linked polymers and with their thermodynamics of strains and swelling in solvent media.

On Pore Fluid Pressure and Effective Solid Stress in the Mixture Theory of Porous Media

Abstract: In this paper we briefly review a typical example of a mixture of elastic materials, in particular, an elastic solid-fluid mixture as a model for porous media. Application of mixture theories to porous media rests upon certain physical assumptions and appropriate interpretations in order to be consistent with some better-known notions in engineering applications. We shall discuss, for instance, the porosity, pore fluid pressure, effective solid stress and Darcy’s law in this paper.

A comparison of distance metrics between mixture distributions

Abstract: Many applications require measuring the distance between mixture distributions. For example in the content-based image retrieval (CBIR) systems and audio speech identification a distance measure between mixture models are often required. This is also an important element for multisensor tracking and fusion where different types of state representations employed by distributed agents need to be correlated. Various distance metrics have been developed to serve this purpose. The performance of these metrics can be evaluated by comparing probabilities of correct correlation verses false detection as a function of a pre-determined threshold on the calculated distance. In this paper, we compare several distance metrics for mixtures distributions. Specifically, we focus on three such distance measures, namely the Integral Square Error distance, the Bhattacharyya distance and the Kullback Leibler distance. To ensure that these techniques can be applied for general distributions, not just for Gaussian mixture model (GMM), we use these techniques in conjunction with a specific distance metric designed for mixture type, called general mixture distance (GMD). For evaluation purpose, we use GMM in the simulation as a test example of mixture models.

An Introduction to Mixture Theory

Abstract: We have already remarked that the simplified models of continuum mechanics (perfect and viscous fluids, elastic systems, etc.) do not always accurately describe the complex phenomenology exhibited by real materials. In Chap. 2 we discussed a nonstandard model that includes (along with the usual elastic properties) microrotation, revealing internal microstructure. There are other situations in which we must derive more complex models to recover some phenomenological features related to internal structure that is erased by the continuous model. For instance, in Chap. 3 the model of a continuum with an interface was proposed in order to produce a macroscopic description of phase transitions in simple materials.

Un graphe génératif pour la classification semi-supervisée

Abstract: We introduce a new semi-supervised algorithm based on a generative model. This model combines a Gaussian mixture model and a generative graph built on the components of this mixture. The combination corresponds to refit the class membership of the mixture component with a propagation process. Both models can be optimized under the maximum likelihood framework and the only hyper-parameter (number of components of the mixture) can be selected with a statistical criterion. Experimental results show that we achieve accuracies comparable to those of rival state-of-the-art algorithms when few labeled data are available. Moreover, it offers the advantage of defining an objective statistical criterion for tuning its parameters, cancelling the need for arbitrary hand-tuning.

A method for recognizing the shape of a Gaussian mixture from a sparse sample set

Abstract: The motivating application for this research is the problem of recognizing a planar object consisting of points from a noisy observation of that object. Given is a planar Gaussian mixture model ρT (x) representing an object along with a noise model for the observation process (the template). Also given are points representing the observation of the object (the query). We propose a method to determine if these points were drawn from a Gaussian mixture ρQ(x) with the same shape as the template. The method consists in comparing samples from the distribution of distances of ρT (x )a ndρQ(x), respectively. The distribution of distances is a faithful representation of the shape of generic Gaussian mixtures. Since it is invariant under rotations and translations of the Gaussian mixture, it provides a workaround to the problem of aligning objects before recognizing their shape without sacrificing accuracy. Experiments using synthetic data show a robust performance against type I errors, and few type II errors when the given template Gaussian mixtures are well distinguished.