EM experiment #1: good initialization (full covariances)

Number of Gaussians, assumes scalar covariances

Choose number of Gaussians in mixture model

k = 5 ;

Assumes full covariance matrices

initFull = EMInitializationFull[data1, k] ;

Compute EM algorithm

RowBox[{Timing, [, RowBox[{RowBox[{em, , =, , RowBox[{EM, [, RowBox[{data1, ,, initFull, ,, 0.001}], ]}]}], ;}], ]}]

RowBox[{{, RowBox[{RowBox[{0.13, , Second}], ,, Null}], }}]

Visualization

Initial model

AnnularAllPlot[c1, rr1, rr2, em//First] ;

[Graphics:../HTMLFiles/index_25.gif]

Final model

AnnularAllPlot[c1, rr1, rr2, em//Last] ;

[Graphics:../HTMLFiles/index_27.gif]

Plot log-likelihood of data given the model as a function of EM iteration

PlotLogLikelihood[em, data1] ;

[Graphics:../HTMLFiles/index_29.gif]

Save solution

goodInitialization = em ;

Animation

AnnularAllPlot[c1, rr1, rr2, #] & /@ goodInitialization ;

Created by Mathematica  (September 8, 2003)