http://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&feed=atom&action=historyrelevant Component Analysis - Revision history2024-03-28T12:42:28ZRevision history for this page on the wikiMediaWiki 1.41.0http://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=27448&oldid=prevConversion script: Conversion script moved page Relevant Component Analysis to relevant Component Analysis: Converting page titles to lowercase2017-08-30T13:45:17Z<p>Conversion script moved page <a href="/statwiki/index.php?title=Relevant_Component_Analysis" class="mw-redirect" title="Relevant Component Analysis">Relevant Component Analysis</a> to <a href="/statwiki/index.php?title=relevant_Component_Analysis" title="relevant Component Analysis">relevant Component Analysis</a>: Converting page titles to lowercase</p>
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</td></tr></table>Conversion scripthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3896&oldid=prevPkt: /* Experimental Results: Application to Clustering */2009-08-11T23:35:54Z<p><span dir="auto"><span class="autocomment">Experimental Results: Application to Clustering</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center>[[File:UC Irvive data results.JPG]]</center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center>[[File:UC Irvive data results.JPG]]</center></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">As it has been shown in this experiment, by introducing the constraints into am EM formulation, not only the negative constraints is handled, but also the RCA results has been improved dramatically in the case (f).</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similar to what (Xing et al., 2002) have done, we tested our method using two conditions:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similar to what (Xing et al., 2002) have done, we tested our method using two conditions:</div></td></tr>
</table>Pkthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3853&oldid=prevSttse: /* First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790. */2009-08-06T21:53:45Z<p><span dir="auto"><span class="autocomment">First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790.</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the adjustment learning paradigm, each data point is associated with a label ''but the label is unknown''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or ''chunklets'', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the adjustment learning paradigm, each data point is associated with a label ''but the label is unknown''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or ''chunklets'', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Adjustment learning aims to accomplish classification by exemplars, instead of by labels; meaning that an adjustment learning algorithm (e.g. RCA) has the capability to return data examples that "fall in the same class" with a given query datum. For example, the algorithm can return a set of Albert Einstein facial images when given an Albert Einstein facial image as the query datum. It is important to note that the above classification scheme does not involve explicitly labeling the data points (i.e. the algorithm does not label the images with "Albert Einstein").</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Adjustment learning aims to accomplish classification by exemplars, instead of by labels; meaning that an adjustment learning algorithm (e.g. RCA) has the capability to return data examples that "fall in the same class" with a given query datum. For example, the algorithm can return a set of Albert Einstein facial images when given an Albert Einstein facial image as the query datum. It is important to note that the above classification scheme does not involve explicitly labeling the data points (i.e. the algorithm does not <ins style="font-weight: bold; text-decoration: none;">(need to) </ins>label the images with "Albert Einstein").</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td></tr>
</table>Sttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3852&oldid=prevSttse: /* First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790. */2009-08-06T21:53:23Z<p><span dir="auto"><span class="autocomment">First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790.</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the adjustment learning paradigm, each data point is associated with a label ''but the label is unknown''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or ''chunklets'', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the adjustment learning paradigm, each data point is associated with a label ''but the label is unknown''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or ''chunklets'', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Adjustment learning aims to accomplish classification by exemplars, instead of by labels; meaning that an adjustment learning algorithm (RCA) has the capability to return data examples that "fall in the same class" with a given query datum. For example, the algorithm can return a set of Albert Einstein facial images when given an Albert Einstein facial image as the query datum. It is important to note that the above classification scheme does not involve explicitly labeling the data points.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Adjustment learning aims to accomplish classification by exemplars, instead of by labels; meaning that an adjustment learning algorithm (<ins style="font-weight: bold; text-decoration: none;">e.g. </ins>RCA) has the capability to return data examples that "fall in the same class" with a given query datum. For example, the algorithm can return a set of Albert Einstein facial images when given an Albert Einstein facial image as the query datum. It is important to note that the above classification scheme does not involve explicitly labeling the data points <ins style="font-weight: bold; text-decoration: none;">(i.e. the algorithm does not label the images with "Albert Einstein")</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td></tr>
</table>Sttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3851&oldid=prevSttse: /* First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790. */2009-08-06T21:51:36Z<p><span dir="auto"><span class="autocomment">First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790.</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the unsupervised learning paradigm, each data point is given without an associated label; the system aims to summarize how the data is organized and explain features of the data. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the unsupervised learning paradigm, each data point is given without an associated label; the system aims to summarize how the data is organized and explain features of the data. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the adjustment learning paradigm, each data point is associated with a label <del style="font-weight: bold; text-decoration: none;">'</del>''but the label is unknown<del style="font-weight: bold; text-decoration: none;">'</del>''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or <del style="font-weight: bold; text-decoration: none;">'</del>''chunklets<del style="font-weight: bold; text-decoration: none;">'</del>'', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the adjustment learning paradigm, each data point is associated with a label ''but the label is unknown''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or ''chunklets'', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given<ins style="font-weight: bold; text-decoration: none;">.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Adjustment learning aims to accomplish classification by exemplars, instead of by labels; meaning that an adjustment learning algorithm (RCA) has the capability to return data examples that "fall in the same class" with a given query datum. For example, the algorithm can return a set of Albert Einstein facial images when given an Albert Einstein facial image as the query datum. It is important to note that the above classification scheme does not involve explicitly labeling the data points</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td></tr>
</table>Sttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3850&oldid=prevSttse: /* First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790. */2009-08-06T21:45:28Z<p><span dir="auto"><span class="autocomment">First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790.</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Adjustment Learning'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Adjustment Learning'''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>a <del style="font-weight: bold; text-decoration: none;">term</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">''Adjusting learning'' is </ins>a <ins style="font-weight: bold; text-decoration: none;">learning paradigm the authors coined in their paper. As will be explained below, adjustment learning lies between supervised and unsupervised learning.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In the supervised learning paradigm, each data point is given with an associated label; the system learns the mapping from the set of data to the set of labels.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In the unsupervised learning paradigm, each data point is given without an associated label; the system aims to summarize how the data is organized and explain features of the data. </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In the adjustment learning paradigm, each data point is associated with a label '''but the label is unknown'''. Moreover, the adjustment learning paradigm assumes that input data is naturally partitioned into small subsets, or '''chunklets''', which are in turn subsets of equivalence classes that partition the input data. In other words, all data point in the same chunklet have the same (unknown) label; and different chunklets can be associated to the same label. The intuition behind adjust learning is that, by exploiting within-chunklet similarities, learning performance can be improved compared to unsupervised learning even when the labels are not given.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td></tr>
</table>Sttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3849&oldid=prevSttse: /* First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790. */2009-08-06T20:44:18Z<p><span dir="auto"><span class="autocomment">First paper: Shental et al., 2002 N. Shental, T. Hertz, D. Weinshall, and M. Pavel, "Adjustment Learning and Relevant Component Analysis," Proc. European Conference on Computer Vision (ECCV), 2002, pp. 776-790.</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In a second experiment, the authors used surveillance video footage divided into discrete clips in which a single person is featured. The same person can appear in multiple clips, and the task was to retrieve all clips in which a query person appears. A colour histogram is used to represent a person. Sources of irrelevant variation include reflections, occlusions, and illumination. In this experiment, the data does come naturally in chunklets: each clip features a single person, so frames in the same clip from a chunklet. Figure 7 in the paper shows the results of k-nearest neighbour classification (not reproduced here for copyright reasons).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In a second experiment, the authors used surveillance video footage divided into discrete clips in which a single person is featured. The same person can appear in multiple clips, and the task was to retrieve all clips in which a query person appears. A colour histogram is used to represent a person. Sources of irrelevant variation include reflections, occlusions, and illumination. In this experiment, the data does come naturally in chunklets: each clip features a single person, so frames in the same clip from a chunklet. Figure 7 in the paper shows the results of k-nearest neighbour classification (not reproduced here for copyright reasons).</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Adjustment Learning'''</ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">a term</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Second Paper: Bar-Hillel ''et al.'', 2003 <ref> A. Bar-Hillel, T. Hertz, N. Shental, and D. Weinshall, "Learning Distance Functions using Equivalence Relations," Proc. International Conference on Machine Learning (ICML), 2003, pp. 11-18. </ref> ==</div></td></tr>
</table>Sttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3784&oldid=prevAmir: /* Experimental Results: Application to Clustering */2009-08-02T18:46:29Z<p><span dir="auto"><span class="autocomment">Experimental Results: Application to Clustering</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center>[[File:UC Irvive data results.JPG]]</center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center>[[File:UC Irvive data results.JPG]]</center></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Similar to what (Xing et al., 2002) have done, we tested our method using two conditions:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">I) Using "little" side-information <math> \mathbf{S} </math> </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">II) Using "much" side-information.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In all of four experiments we sued K-means with multiple restarts. We have showed the results of all algorithms described above when we use the two conditions of "little" and "much" side-information.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">As it can be seen clearly in results, using RCA as a distance measure has a significant impact on improving the results over the original K-means algorithm. Our results compared to (Xing et al., 2002) indicate that RCA achieves similar results. In this respect it should be noted that the RCA metric computation is a single step efficient computation, whereas the method presented in (Xing et al., 2002) requires gradient descent and iterative projections.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references/></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references/></div></td></tr>
</table>Amirhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3783&oldid=prevAmir: /* Experimental Results: Application to Clustering */2009-08-02T18:33:03Z<p><span dir="auto"><span class="autocomment">Experimental Results: Application to Clustering</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:33, 2 August 2009</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where <math>\mathbf{1\{.\}}</math> is the indicator function, <math>\mathbf{\{\hat{c_i}\}_{i=1}^m}</math> is the cluster to which point <math> \mathbf{x_i} </math> is assigned by the clustering algorithm, and <math> \mathbf{c_i} </math> is the "correct" or desired assignment. The above score can be regarded as computing the probability that the algorithm's assignment <math> \mathbf{\hat{c}} </math> of two randomly drawn points <math> \mathbf{x_i} </math> and <math> \mathbf{x_j} </math> agrees with the "true" asignment <math> \mathbf{c} </math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where <math>\mathbf{1\{.\}}</math> is the indicator function, <math>\mathbf{\{\hat{c_i}\}_{i=1}^m}</math> is the cluster to which point <math> \mathbf{x_i} </math> is assigned by the clustering algorithm, and <math> \mathbf{c_i} </math> is the "correct" or desired assignment. The above score can be regarded as computing the probability that the algorithm's assignment <math> \mathbf{\hat{c}} </math> of two randomly drawn points <math> \mathbf{x_i} </math> and <math> \mathbf{x_j} </math> agrees with the "true" asignment <math> \mathbf{c} </math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:UC Irvive data results.JPG]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center></ins>[[File:UC Irvive data results.JPG]]<ins style="font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references/></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references/></div></td></tr>
</table>Amirhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=relevant_Component_Analysis&diff=3782&oldid=prevAmir: /* Experimental Results: Application to Clustering */2009-08-02T18:31:40Z<p><span dir="auto"><span class="autocomment">Experimental Results: Application to Clustering</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:31, 2 August 2009</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where <math>\mathbf{1\{.\}}</math> is the indicator function, <math>\mathbf{\{\hat{c_i}\}_{i=1}^m}</math> is the cluster to which point <math> \mathbf{x_i} </math> is assigned by the clustering algorithm, and <math> \mathbf{c_i} </math> is the "correct" or desired assignment. The above score can be regarded as computing the probability that the algorithm's assignment <math> \mathbf{\hat{c}} </math> of two randomly drawn points <math> \mathbf{x_i} </math> and <math> \mathbf{x_j} </math> agrees with the "true" asignment <math> \mathbf{c} </math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where <math>\mathbf{1\{.\}}</math> is the indicator function, <math>\mathbf{\{\hat{c_i}\}_{i=1}^m}</math> is the cluster to which point <math> \mathbf{x_i} </math> is assigned by the clustering algorithm, and <math> \mathbf{c_i} </math> is the "correct" or desired assignment. The above score can be regarded as computing the probability that the algorithm's assignment <math> \mathbf{\hat{c}} </math> of two randomly drawn points <math> \mathbf{x_i} </math> and <math> \mathbf{x_j} </math> agrees with the "true" asignment <math> \mathbf{c} </math>.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references/></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references/></div></td></tr>
</table>Amir