Bayesian feature and model selection for Gaussian mixture models

We present a Bayesian method for mixture model training that simultaneously treats the feature selection and the model selection problem. The method is based on the integration of a mixture model formulation that takes into account the saliency of the features and a Bayesian approach to mixture learning that can be used to estimate the number of mixture components. The proposed learning algorithm follows the variational framework and can simultaneously optimize over the number of components, the saliency of the features, and the parameters of the mixture model. Experimental results using high-dimensional artificial and real data illustrate the effectiveness of the method.     

A divide-and-conquer method for multi-net classifiers

Several researchers have shown that substantial improvements can be achieved in difficult pattern recognition problems by combining the outputs of multiple neural networks. In this work, we present and test a pattern classification multi-net system based on both supervised and unsupervised learning. Following the ‘divide-and-conquer’ framework, the input space is partitioned into overlapping subspaces and neural networks are subsequently used to solve the respective classification subtasks. Finally, the outputs of individual classifiers are appropriately combined to obtain the final classification decision. Two clustering methods have been applied for input space partitioning and two schemes have been considered for combining the outputs of the multiple classifiers. Experiments on well-known data sets indicate that the multi-net classification system exhibits promising performance compared with the case of single network training, both in terms of error rates and in terms of training speed (especially if the training of the classifiers is done in parallel). ID="A1"Correspondance and offprint requests to: D. Frosyniotis, National Technical University of Athens, Department of Electrical and Computer Engineering, Zographou 157 73, Athens, Greece. E-mail: andreas@cs.ntua.gr     

A kurtosis-based dynamic approach to Gaussian mixture modeling

We address the problem of probability density function estimation using a Gaussian mixture model updated with the expectation-maximization (EM) algorithm. To deal with the case of an unknown number of mixing kernels, we define a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kurtoses of the kernels. This measure provides an indication of how well the Gaussian mixture fits the data. Then we propose a new dynamic algorithm for Gaussian mixture density estimation which monitors the total kurtosis at each step of the EM algorithm in order to decide dynamically on the correct number of kernels and possibly escape from local maxima. We show the potential of our technique in approximating unknown densities through a series of examples with several density estimation problems     

Visual tracking using the Earth Mover's Distance between Gaussian mixtures and Kalman filtering

In this paper, we demonstrate how the differential Earth Mover's Distance (EMD) may be used for visual tracking in synergy with Gaussian mixtures models (GMM). According to our model, motion between adjacent frames results in variations of the mixing proportions of the Gaussian components representing the object to be tracked. These variations are computed in closed form by minimizing the differential EMD between Gaussian mixtures, yielding a very fast algorithm with high accuracy, without recurring to the EM algorithm in each frame. Moreover, we also propose a framework to handle occlusions, where the prediction for the object's location is forwarded to an adaptive Kalman filter whose parameters are estimated on line by the motion model already observed. Experimental results show significant improvement in tracking performance in the presence of occlusion.     

Neural-network methods for boundary value problems with irregularboundaries

Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. The article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the exact satisfaction of the boundary conditions. The method has been successfully tested on two-dimensional and three-dimensional PDEs and has yielded accurate results.     

Shared kernel models for class conditional density estimation

We present probabilistic models which are suitable for class conditional density estimation and can be regarded as shared kernel models where sharing means that each kernel may contribute to the estimation of the conditional densities of an classes. We first propose a model that constitutes an adaptation of the classical radial basis function (RBF) network (with full sharing of kernels among classes) where the outputs represent class conditional densities. In the opposite direction is the approach of separate mixtures model where the density of each class is estimated using a separate mixture density (no sharing of kernels among classes). We present a general model that allows for the expression of intermediate cases where the degree of kernel sharing can be specified through an extra model parameter. This general model encompasses both the above mentioned models as special cases. In all proposed models the training process is treated as a maximum likelihood problem and expectation-maximization algorithms have been derived for adjusting the model parameters.     

Reinforcement Learning Using the Stochastic Fuzzy Min–Max Neural Network

The fuzzy min–max neural network constitutes a neural architecture that is based on hyperbox fuzzy sets and can be incrementally trained by appropriately adjusting the number of hyperboxes and their corresponding volumes. An extension to this network has been proposed recently, that is based on the notion of random hyperboxes and is suitable for reinforcement learning problems with discrete action space. In this work, we elaborate further on the random hyperbox idea and propose the stochastic fuzzy min–max neural network, where each hyperbox is associated with a stochastic learning automaton. Experimental results using the pole balancing problem indicate that the employment of this model as an action selection network in reinforcement learning schemes leads to superior learning performance compared with the traditional approach where the multilayer perceptron is employed.     

A class-adaptive spatially variant mixture model for image segmentation.

We propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model. According to this model, the pixel labels are random variables and a smoothness prior is imposed on them. The main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models. These Gauss-Markov random field-based priors allow all their parameters to be estimated in closed form via the maximum a posteriori (MAP) estimation using the expectation-maximization methodology. Thus, it is possible to introduce priors with multiple parameters that adapt to different aspects of the data. Numerical experiments are presented where the proposed MAP algorithms were tested in various image segmentation scenarios. These experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model-based segmentation.     

Bayesian kernel methods for analysis of functional neuroimages

We propose an approach to analyzing functional neuroimages in which 1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data and 2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). Kernel methods have become a staple of modern machine learning. Herein, we show that these techniques show promise for neuroimage analysis. In an on-off design, we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude, and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a Reversible-Jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting). In each method, after estimating the activation pattern, we test for local activation using a GLRT. We evaluate the results using receiver operating characteristic (ROC) curves for simulated neuroimaging data and example results for real fMRI data. We find that, while RVM and RJMCMC both produce good results, RVM requires far less computation time, and thus appears to be the more promising of the two approaches.     

A reinforcement learning approach based on the fuzzy min-max neural network

The fuzzy min-max neural network constitutes a neural architecture that is based on hyperbox fuzzy sets and can be incrementally trained by appropriately adjusting the number of hyperboxes and their corresponding volumes. Two versions have been proposed: for supervised and unsupervised learning. In this paper a modified approach is presented that is appropriate for reinforcement learning problems with discrete action space and is applied to the difficult task of autonomous vehicle navigation when no a priori knowledge of the enivronment is available. Experimental results indicate that the proposed reinforcement learning network exhibits superior learning behavior compared to conventional reinforcement schemes.