Learning along a Channel: the Expectation part of Expectation-Maximisation

Expectation Maximisation

The Expectation Maximisation (EM) algorithm is a procedure that iteratively optimises parameters of a given model, to maximise the likelihood of observing a given (training) dataset. Assuming that our framework has unobserved data, X, observed data, Y , parameters Θ, and a likelihood function L(X,Y,Θ) = P(X,Y |Θ), we can derive the steps of the algorithm as follows: 1. Choose initial parameters...

Online Expectation-Maximisation

Expectation Maximisation for Sensor Data Fusion

The expectation maximisation algorithm (EM) was introduced by Dempster, Laird and Rubin in 1977 [DLR77]. The basic of expextation maximisation is maximum likelihood estimation (MLE). In modern sensor data fusion expectation maximisation becomes a substantial part in several applications, e.g. multi target tracking with probabilistic multi hypothesis tracking (PMHT), target extraction within pro...

Diffused Expectation Maximisation for image segmentation

Diffused Expectation Maximisation (DEM) is a novel algorithm for image segmentation. The method models an image as a finite mixture, where each mixture component corresponds to a region class and uses a maximum likelihood approach to estimate the parameters of each class, via the expectation maximisation (EM) algorithm, coupled with anisotropic diffusion on classes, in order to account for the ...

Expectation-Maximisation Algorithm Derivation and a cookbook for further recepies

To simplify the treatment, we consider here only how to derive and apply the expectation-maximisation algorithm in the context of soft clustering. The treatment of other applications is analogous. The soft-clustering is based on a probabilistic model, which combines k different data sources. More precisely, we assume that individual observations x1, . . . ,xn are generated by k different data s...