Mixture theory

About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.

Unsupervised Learning of Correlated Multivariate Gaussian Mixture Models Using MML

Abstract: Mixture modelling or unsupervised classification is the problem of identifying and modelling components (or clusters, or classes) in a body of data. We consider here the application of the Minimum Message Length (MML) principle to a mixture modelling problem of multivariate Gaussian distributions. Earlier work in MML mixture modelling includes the multinomial, Gaussian, Poisson, von Mises circular, and Student t distributions and in these applications all variables in a component are assumed to be uncorrelated with each other. In this paper, we propose a more general type of MML mixture modelling which allows the variables within a component to be correlated. Two MML approximations are used. These are the Wallace and Freeman (1987) approximation and Dowe’s MMLD approximation (2002). The former is used for calculating the relative abundances (mixing proportions) of each component and the latter is used for estimating the distribution parameters involved in the components of the mixture model. The proposed method is applied to the analysis of two real-world datasets – the well-known (Fisher) Iris and diabetes datasets. The modelling results are then compared with those obtained using two other modelling criteria, AIC and BIC (which is identical to Rissanen’s 1978 MDL), in terms of their probability bit-costings, and show that the proposed MML method performs better than both these criteria. Furthermore, the MML method also infers more closely the three underlying Iris species than both AIC and BIC.

Infiltration through Deformable Porous Media

Abstract: The equations driving the flow of an incompressible fluid through a porous deformable medium are derived in the framework of the mixture theory. This mechanical system is described as a binary saturated mixture of incompressible components. The mathematical problem is characterized by the presence of two moving boundaries, the material boundaries of the solid and the fluid, respectively. The boundary and interface conditions to be supplied to ensure the well-posedness of the initial boundary value problem are inspired by typical processes in the manufacturing of composite materials. They are discussed in their connections with the nature of the partial stress tensors. Then the equations are conveniently recast in a material frame of reference fixed on the solid skeleton. By a proper choice of the characteristic magnitudes of the problem at hand, the equations are rewritten in non-dimensional form and the conditions which enable neglecting the inertial terms are discussed. The second part of the paper is devoted to the study of one-dimensional infiltration by the inertia-neglected model. It is shown that when the flow is driven through an elastic matrix by a constant rate liquid inflow at the border some exact results can be obtained.

Projection pursuit mixture density estimation

Abstract: In this paper we seek a Gaussian mixture model (GMM) of an n-variate probability density function. Usually the parameters of GMMs are determined in the original n-dimensional space by optimizing a maximum likelihood (ML) criterion. A practical deficiency of this method of fitting GMMs is its poor performance when dealing with high-dimensional data since a large sample size is needed to match the accuracy that is possible in low dimensions. We propose a method for fitting the GMM based on the projection pursuit strategy. This GMM is highly constrained and hence its ability to model structure in subspaces is enhanced, compared to a direct ML fitting of a GMM in high dimensions. Our method is closely related to recently developed independent factor analysis (IFA) mixture models. The comparisons with ML fitting of GMM in n-dimensions and IFA mixtures show that the proposed method is an attractive choice for fitting GMMs using small sizes of training sets.

Adjusting mixture weights of gaussian mixture model via regularized probabilistic latent semantic analysis

Abstract: Mixture models, such as Gaussian Mixture Model, have been widely used in many applications for modeling data. Gaussian mixture model (GMM) assumes that data points are generated from a set of Gaussian models with the same set of mixture weights. A natural extension of GMM is the probabilistic latent semantic analysis (PLSA) model, which assigns different mixture weights for each data point. Thus, PLSA is more flexible than the GMM method. However, as a tradeoff, PLSA usually suffers from the overfitting problem. In this paper, we propose a regularized probabilistic latent semantic analysis model (RPLSA), which can properly adjust the amount of model flexibility so that not only the training data can be fit well but also the model is robust to avoid the overfitting problem. We conduct empirical study for the application of speaker identification to show the effectiveness of the new model. The experiment results on the NIST speaker recognition dataset indicate that the RPLSA model outperforms both the GMM and PLSA models substantially. The principle of RPLSA of appropriately adjusting model flexibility can be naturally extended to other applications and other types of mixture models.