In the field of statistical data mining, the Expectation Maximization (EM) algorithm is one of the most popular methods used for solving parameter estimation problems in the maximum likelihood (ML) framework. Compared to traditional methods such as steepest descent, conjugate gradient, or Newton-Raphson, which are often too complicated to use in solving these problems, EM has become a popular m...

P(X|θ) is the (observable) data likelihood. The parameter θ is omitted sometimes for simple notation. MLE is normally done by taking the derivative of the data likelihood P(X) with respect to the model parameter θ and solving the equation. However, in some cases where we have hidden (unobserved) variables in the model, the derivative w.r.t. the model parameter does not have a close form solutio...

The fluorescence lifetime technique offers an effective way to resolve fluorescent components with overlapping emission spectra. The presence of multiple fluorescent components in biological compounds can hamper their discrimination. The conventional method based on the nonlinear least-squares technique is unable to consistently determine the correct number of fluorescent components in a fluore...

Statistical language modeling (SLM) has been used in many different domains for decades and has also been applied to information retrieval (IR) recently. Documents retrieved using this approach are ranked according their probability of generating the given query. In this paper, we present a novel approach that employs the generalized Expectation Maximization (EM) algorithm to improve language m...

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geome...

Within the learning framework of maximum weighted likelihood (MWL) proposed by Cheung, 2004 and 2005, this paper will develop a batch Rival Penalized Expectation-Maximization (RPEM) algorithm for density mixture clustering provided that all observations are available before the learning process. Compared to the adaptive RPEM algorithm in Cheung, 2004 and 2005, this batch RPEM need not assign th...

Crime analysis and prevention is a systematic approach for identifying and analyzing patterns and trends in crime. Our system can predict regions which have high probability for crime occurrence and can visualize crime prone areas. With the increasing advent of computerized systems, crime data analysts can help the Law enforcement officers to speed up the process of solving crimes. About 10% of...

In SPECT/PET, the maximum-likelihood expectation-maximization (ML-EM) algorithm is getting more attention as the speed of computers increases. This is because it can incorporate various physical aspects into the reconstruction process leading to a more accurate reconstruction than other analytical methods such as filtered-backprojection algorithms. However, the convergence rate of the ML-EM alg...

The potential of the SAGE (Space Alternating Generalized Expectation Maximization) algorithm for navigation systems in order to distinguish the line-of-sight signal (LOSS) is to be considered. The SAGE algorithm is a low-complexity generalization of the EM (Expectation-Maximization) algorithm, which iteratively approximates the maximum likelihood estimator (MLE) and has been successfully applie...