q EM Algorithm Examples

EM Algorithm Examples

(Note: videos below are given in both quicktime and mpeg formats; however, the quicktime videos tend to be higher quality and are therefore recommended. If you do not have quicktime installed, you can download the free player (Mac/Windows) from Apple.)
Below, we illustrate the convergence behavior of the Expectation-Maximization (EM) algorithm on some 2d synthetic data examples. For each animation, the pink region indicates the distribution of the underlying data (uniformly distributed in the pink region), except for the "anti-annular" examples, where the white region indicates the data distribution.
Annular region, five scalar covariances
(400 x 400)
(high-quality, quicktime, 848 kb)
(lower-quality, mpeg, 700 kb)
Annular region, seven scalar covariances
(400 x 400)
(high-quality, quicktime, 724 kb)
(lower-quality, mpeg, 584 kb)
Annular region, five full covariance matrices
(400 x 400)
(high-quality, quicktime, 464 kb)
(lower-quality, mpeg, 360 kb)
Anti-annular region, nine scalar covariances
(400 x 400)
(high-quality, quicktime, 644 kb)
(lower-quality, mpeg, 540 kb)
Anti-annular region, 11 scalar covariances
(400 x 400)
(high-quality, quicktime, 756 kb)
(lower-quality, mpeg, 604 kb)
Anti-annular region, seven full covariance matrices
(400 x 400)
(high-quality, quicktime, 572 kb)
(lower-quality, mpeg, 492 kb)
Anti-annular region, nine full covariance matrices
(400 x 400)
(high-quality, quicktime, 808 kb)
(lower-quality, mpeg, 684 kb)
E-shaped polygonal region, nine scalar covariances (example #1)
(400 x 400)
(high-quality, quicktime, 532 kb)
(lower-quality, mpeg, 440 kb)
E-shaped polygonal region, nine scalar covariances (example #2)
(400 x 400)
(high-quality, quicktime, 1020 kb)
(lower-quality, mpeg, 836 kb)
E-shaped polygonal region, four full covariance matrices
(400 x 400)
(high-quality, quicktime, 668 kb)
(lower-quality, mpeg, 556 kb)
Anti-E-shaped polygonal region, eight scalar covariances (example #1)
(400 x 400)
(high-quality, quicktime, 608 kb)
(lower-quality, mpeg, 492 kb)
Anti-E-shaped polygonal region, eight scalar covariances (example #2)
(400 x 400)
(high-quality, quicktime, 480 kb)
(lower-quality, mpeg, 396 kb)
Anti-E-shaped polygonal region, three full covariance matrices (example #2)
(400 x 400)
(high-quality, quicktime, 1168 kb)
(lower-quality, mpeg, 1052 kb)
Last updated September 8, 2003 by Michael C. Nechyba