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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"><HTML><HEAD> <TITLE>EM algorithm for Mixture models</TITLE></HEAD><BODY TEXT="#000000" BGCOLOR="#FFFFFF" LINK="#0000FF" VLINK="#000080" ALINK="#FF0000"><CENTER><TABLE BORDER=1 CELLSPACING=0 CELLPADDING=0 HEIGHT="20%" BGCOLOR="#FDF5E6" ><TR><TD><CENTER><P><B><FONT SIZE=+4> Gaussian Mixture Model<IMG SRC="../../../images/java_duke_small.gif" HEIGHT=38 WIDTH=49 ALIGN=ABSCENTER><BR>EM algorithm</FONT></B></P></CENTER></TD></TR></TABLE></CENTER><H3><B>Introduction</B></H3><P>The EM algorithm is short for Expectation-Maximization algorithm. Itis based on an iterative optimization of the centers and widths of thekernels. The aim is to optimize the likelihood that the given data pointsare generated by a mixture of Gaussians. The numbers next to the Gaussiansgive the relative importance (amplitude) of each component.</P><H3><B>Credits</B></H3><P>This applet was developed by <A HREF="http://www.etl.go.jp/etl/suri/akaho/welcome.html">S. Akaho</A> and adapted by <A HREF="http://diwww.epfl.ch/lami/team/michel">Olivier Michel</A>.</P><H3><B>Instructions</B></H3><OL><LI>You can select the Gaussian Mixture fitting by choosing <B>"GaussMix"</B>,or Multiple Line fitting by choosing <B>"LineMix"</B>. </LI><LI>Click in the image plane to add sample points. </LI><LI>You can add 10 uniformly distributed sample points by clicking on<B>"RandomPts"</B>. </LI><LI>You can also add 100 uniformly distributed sample points lying on a ring by clicking on <B>"RingPts"</B>. </LI><LI><B>"ClearPts"</B> allows to remove all sample points </LI><LI>You can choose the number of kernels by selecting <B>1</B> to <B>5</B>with the second rightmost button. </LI><LI>You can initialize the kernels by clicking on <B>"InitKernels"</B>.</LI><LI>You can start the EM algorithm by selecting <B>"EM Run"</B>or <B>"EM 1 Step" </B>(one step) </LI><LI>You can stop <B>"EM Run"</B> by selecting <B>"EM Stop"</B>.</LI></OL><H3>Applet</H3><CENTER><TABLE BORDER=2 CELLSPACING=0 CELLPADDING=0 ><TR ALIGN=CENTER VALIGN=CENTER><TD ALIGN=CENTER VALIGN=CENTER NOWRAP BGCOLOR="#C0C0C0"><APPLET codebase="../classes/" code="MixtureEM.class" width=600 height=630></APPLET></TD></TR></TABLE></CENTER><H3><B>Questions</B></H3><OL><LI>Define about 30 data points located in 3 separate clusters. One ofthe cluster may be a little bit larger than the others. Set the numberof kernels to 3. Switch the right-most button to 'EM 1 Step'. Click repeatedlyon this button and watch how the kernels converge to the clusters.</LI><LI>Keep the same data points and reinitialize the system. You can switchto 'EM Run', watch how it converges, and the reinitialize again. Repeatthis several times in order to find out how reliably the EM algorithm findsthe 3 clusters.</LI><LI>Use the same data points, but allow for 5 kernels. Does it still convergeto a reasonable solution? Repeat the experiment several times.</LI><LI>Add random data points by pressing the random points button once. Restartthe algorithm. Does it still find the original clusters? (Test it severaltimes). Add more random points by clicking again on the random points buttonand repeat the experiment.</LI><LI>Keep all data points and reduce the number of kernels back to 3. Doesthe algorithm still find the clusters?</LI><LI>Clear the data points and restart with two clusters (each 10 points)and two kernels. Add more and more points to one of the clusters and watchhow the importance of the respective Gaussian component increases. </LI></OL><H3><B>Bugs </B></H3><P>If Gaussians or Lines disappear by EM, initialize kernels by click <B>"InitKernels"</B>.<BR>EM algorithm sometimes stops by Applet exception error in Netscape Navigatorfor Windows95 and Solaris2.4 (netscape for SGI is rather stable).</P></BODY></HTML>⌨️ 快捷键说明
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