An attraction-repulsion expectation-maximization (AREM) algorithm for density estimation is proposed in this
paper. We introduce a Gibbs distribution function for attraction and inverse Gibbs distribution for repulsion
as an augmented penalty function in order to determine equilibrium between over-smoothing and over-fitting.
The logarithm of the likelihood function augmented the Gibbs density mixture is solved under expectation-maximization
(EM) method. We demonstrate the application of the proposed attraction-repulsion expectation-maximization
algorithm to image reconstruction and sensor field estimation problem using computer simulation.
We show that the proposed algorithm improves the performance considerably.
In this paper, we propose a maximum-entropy expectation-maximization algorithm. We use the proposed algorithm
for density estimation. The maximum-entropy constraint is imposed in order to ensure smoothness of
the estimated density function. The exact derivation of the maximum-entropy expectation-maximization algorithm
requires determination of the covariance matrix combined with the maximum entropy likelihood function,
which is difficult to solve directly. We therefore introduce a new lower-bound for the EM algorithm derived
by using the Cauchy-Schwartz inequality to obtain a suboptimal solution. We use the proposed algorithm for
function interpolation and image segmentation. We propose the use of the EM algorithm for image recovery from
randomly sampled data and signal reconstruction from randomly scattered sensors. We further propose to use
our approach to maximum-entropy expectation-maximization (MEEM) in all of these applications. Computer
simulation experiments are used to demonstrate the performance of our algorithm in comparison to existing
methods.
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