Abstract: This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.
Abstract: In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.
Abstract: This paper introduces a novel approach to estimate the
clique potentials of Gibbs Markov random field (GMRF) models
using the Support Vector Machines (SVM) algorithm and the Mean
Field (MF) theory. The proposed approach is based on modeling the
potential function associated with each clique shape of the GMRF
model as a Gaussian-shaped kernel. In turn, the energy function of
the GMRF will be in the form of a weighted sum of Gaussian
kernels. This formulation of the GMRF model urges the use of the
SVM with the Mean Field theory applied for its learning for
estimating the energy function. The approach has been tested on
synthetic texture images and is shown to provide satisfactory results
in retrieving the synthesizing parameters.