📄 demosimilaritygraphs.html
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<p align="left"><font face="Verdana" size="6">DemoSimilarityGraphs</font></p>
<p align="left"><font face="Verdana" size="4">a Matlab GUI to explore similarity graphs</font></p>
<p align="left"> </p>
<p align="left"><font face="Verdana">by <a href="http://www.ml.uni-saarland.de/index.html">Matthias Hein</a> and <a href="http://www.kyb.mpg.de/~ule">Ulrike von Luxburg</a></font></p>
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<p align="center"><a href="GraphDemo.html"><font face="Arial" size="5">[ Go to GraphDemo main page]</font></a></p>
<h3><font face="Verdana">Purpose</font></h3>
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<p><font face="Verdana">DemoSimilarityGraphs: Given a data set and a similarity function, there are many different ways how a similarity graph can be constructed: epsilon-neighborhood graphs,
k-nearest neighbor graphs in different flavors, completely connected graphs, weighted or unweighted graphs, and many more . Additionally, most of those graphs come with a parameter which has to
be chosen. The purpose of this demo is to show how different neighborhood graphs can behave on the same data set (see below for more details).</font></p>
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<h3><font face="Verdana">Tutorial</font></h3>
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<p><font face="Verdana">DemoSimilarityGraphs has been used for teaching purposes at the Machine Learning Summer School 2007, at the Max-Planck-Institute for Biological Cybernetics, Tuebingen,
Germany. The tutorial introduces the different neighborhood graphs and demonstrates properties and some surprising effects using the tool.</font></p>
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<p align="center"><a href="HeinLuxburg_SlidesSimilarityGraphs.pdf"><font face="Arial" size="5">Download the tutorial on similarity graphs.</font></a></p>
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<h3><font face="Verdana">Screenshot of DemoSimilarityGraphs</font></h3>
<p align="center"><img style="WIDTH: 52.26%; HEIGHT: 52.26%" height="948" src="fig_DemoSimilarityGraphs.png" width="100%" border="0"></p>
<h3><font face="Verdana">Panels in DemoSimilarityGraphs</font></h3>
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<li><font face="Verdana"><strong><em>Data set:</em></strong> here we plot the first two dimensions of the data set. All other dimensions are noise only.</font></li>
<li><font face="Verdana"><strong><em>Heat map of the similarity values:</em></strong> This is a plot of the similarity matrix on the given data points. Each pixel in the plot corresponds to one
entry in the similarity matrix. Red means "high value", blue means "low" value. This panel is meant to help the user to adjust a reasonable value sigma for the similarity function. Note that
the data points are ordered according to the clusters. Therefore one has a block structure in the similarity matrix.</font></li>
<li><font face="Verdana"><strong><em>Histogram of the similarity values:</em></strong> here we simply plot a histogram of all the entries in the similarity matrix. This panel is also meant to
help the user to adjust a reasonable value sigma for the similarity function.</font></li>
<li><font face="Verdana"><strong><em>Connectivity:</em></strong> In this panel we simply plot the edges of the graph. For speed reasons we refrained from color-coding the edge weights (all
edges are plotted in the same color, no matter what their edge weight is).</font></li>
<li><font face="Verdana"><strong><em>Degrees of the vertices:</em></strong> The degree of a vertex in the graph is the sum of the edge weights of the adjacent edges. In this plot we color code
the degree of all vertices (red = high, blue = low). Note that for all graph types, the degree can be interpreted as a density estimator of the underlying density at the given data
point.</font></li>
<li><font face="Verdana"><strong><em>Adjacency matrix:</em></strong> here we show a heat map of the adjacency matrix of the graph. In case the graph is weighted, of course also the adjacency
matrix is weighted. Note that the adjacency matrix encodes similarities <em>and</em> edges of the graph.</font></li>
<li><font face="Verdana"><strong><em>Points per connected component:</em></strong> It shows how many connected components the graph has, and how many points each of the connected components
contains. This plot is very important, as most graph-based learning algorithms treat different connected components individually.</font></li>
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