Expectation Maximization Step Research Articles

A resource selection model for analyzing pseudoreplicated data due to grouping behavior of animals

Quantifying resource selection is of primary interest in animal ecology. Many analyses of resource selection assume spatial and temporal independence of the sampling unit. Autocorrelation between observations, which is a general property of ecological variables, causes difficulties for most standard statistical procedures of resource selection because autocorrelated data violate the assumption of independence. To overcome this problem, we develop a mixed-effects model to estimate resource selection functions from data that are autocorrelated because of unobserved grouping behavior by animals. In the application of the expectation-maximization (EM) algorithm, the computation of the conditional expectation of the complete-data log-likelihood function does not have a closed-form solution requiring numerical integration. A Monte Carlo EM algorithm with Gibbs sampling can be used effectively in such situations to find exact maximum likelihood estimates. We propose a simple automated Monte Carlo EM algorithm with multiple sequences in which the Monte Carlo sample size is increased when the EM step is swamped by Monte Carlo errors.We demonstrate that the model can detect inherent autocorrelation and provide reasonable variance estimates when applied to nocturnal bird migration data. This approach could also be applied to ecological processes with various types of spatially and temporally autocorrelated data, circumventing serious problems caused by dangerous pseudoreplication.

Cluster ensemble Kalman filter

A modified ensemble Kalman filter (KF) is proposed which can enhance performance for highly non-linear prognostic models. The algorithm differs from the traditional ensemble KF by the addition of an expectation maximization step, which estimates the parameters of a Gaussian mixture model for the ensemble of forecast states. The algorithm is tested in twin experiments using a simple phytoplankton—zooplankton model.

Process Monitoring Using Bayesian Classification on PCA Subspace

A new approach to fault detection and isolation that combines principal component analysis (PCA) and Bayesian classification is proposed. For a given set of training data, a PCA subspace is constructed, and the score vectors are classified by solving the Bayesian classification problem with the deterministic annealing expectation maximization (DAEM) and robust mixture decomposition (RMD) algorithms. If data for new events do not belong to the existing subspace, the PCA subspace must be rebuilt to include the new events. Whereas new data form their own classes in the new subspace, existing classifications of the old data must also be updated in the newer subspace. This can be done using a simple translation and rotation if the dimensionality of the new subspace is the same as that of the old subspace. If the new subspace is of higher dimension, a good initial estimate is generated using translation and rotation. This estimate ensures convergence within a few expectation maximization steps. The proposed met...

Analysis of switching dynamics with competing support vector machines.

We present a framework for the unsupervised segmentation of switching dynamics using support vector machines. Following the architecture by Pawelzik et al., where annealed competing neural networks were used to segment a nonstationary time series, in this paper, we exploit the use of support vector machines, a well-known learning technique. First, a new formulation of support vector regression is proposed. Second, an expectation-maximization step is suggested to adaptively adjust the annealing parameter. Results indicate that the proposed approach is promising.

Video Object Segmentation: A Compressed Domain Approach

This paper addresses the problem of extracting video objects from MPEG compressed video. The only cues used for object segmentation are the motion vectors which are sparse in MPEG. A method for automatically estimating the number of objects and extracting independently moving video objects using motion vectors is presented here. First, the motion vectors are accumulated over a few frames to enhance the motion information, which are further spatially interpolated to get dense motion vectors. The final segmentation, using the dense motion vectors, is obtained by applying the expectation maximization (EM) algorithm. A block-based affine clustering method is proposed for determining the number of appropriate motion models to be used for the EM step and the segmented objects are temporally tracked to obtain the video objects. Finally, a strategy for edge refinement is proposed to extract the precise object boundaries. Illustrative examples are provided to demonstrate the efficacy of the approach. A prominent application of the proposed method is that of object-based coding, which is part of the MPEG-4 standard.

Iterative algorithm for reconstruction of entangled states

An iterative algorithm for the reconstruction of an unknown quantum state from the results of incompatible measurements is proposed. It consists of Expectation-Maximization step followed by a unitary transformation of the eigenbasis of the density matrix. The procedure has been applied to the reconstruction of the entangled pair of photons.