Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Very fast EM-based mixture model clustering using multiresolution kd-trees
Proceedings of the 1998 conference on Advances in neural information processing systems II
Efficient clustering of high-dimensional data sets with application to reference matching
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Accelerating EM for Large Databases
Machine Learning
On-Line Unsupervised Outlier Detection Using Finite Mixtures with Discounting Learning Algorithms
Data Mining and Knowledge Discovery
An incremental EM-based learning approach for on-line prediction of hospital resource utilization
Artificial Intelligence in Medicine
Semi-supervised Bayesian ARTMAP
Applied Intelligence
Convergence of a Particle-Based Approximation of the Block Online Expectation Maximization Algorithm
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special Issue on Monte Carlo Methods in Statistics
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The EM algorithm is a popular method for parameter estimation in situations where the data can be viewed as being incomplete. As each E-step visits each data point on a given iteration, the EM algorithm requires considerable computation time in its application to large data sets. Two versions, the incremental EM (IEM) algorithm and a sparse version of the EM algorithm, were proposed recently by Neal R.M. and Hinton G.E. in Jordan M.I. (Ed.), Learning in Graphical Models, Kluwer, Dordrecht, 1998, pp. 355–368 to reduce the computational cost of applying the EM algorithm. With the IEM algorithm, the available n observations are divided into B (B ≤ n) blocks and the E-step is implemented for only a block of observations at a time before the next M-step is performed. With the sparse version of the EM algorithm for the fitting of mixture models, only those posterior probabilities of component membership of the mixture that are above a specified threshold are updated; the remaining component-posterior probabilities are held fixed. In this paper, simulations are performed to assess the relative performances of the IEM algorithm with various number of blocks and the standard EM algorithm. In particular, we propose a simple rule for choosing the number of blocks with the IEM algorithm. For the IEM algorithm in the extreme case of one observation per block, we provide efficient updating formulas, which avoid the direct calculation of the inverses and determinants of the component-covariance matrices. Moreover, a sparse version of the IEM algorithm (SPIEM) is formulated by combining the sparse E-step of the EM algorithm and the partial E-step of the IEM algorithm. This SPIEM algorithm can further reduce the computation time of the IEM algorithm.