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📄 clustering - hierarchical.htm

📁 数据挖掘Apriori算法的java源码
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<P align=justify><FONT face="Times New Roman, Times, serif">After merging MI 
with TO we obtain the following matrix:</FONT></P>
<P align=justify></P>
<TABLE width="35%" align=center border=1>
  <TBODY>
  <TR>
    <TD>&nbsp;</TD>
    <TD>
      <DIV align=center><STRONG>BA</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>FI</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>NA</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>RM</STRONG></DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>BA</STRONG></DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>662</DIV></TD>
    <TD>
      <DIV align=center>877</DIV></TD>
    <TD>
      <DIV align=center>255</DIV></TD>
    <TD>
      <DIV align=center>412</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>FI</STRONG></DIV></TD>
    <TD>
      <DIV align=center>662</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD>
    <TD>
      <DIV align=center>468</DIV></TD>
    <TD>
      <DIV align=center>268</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD>
    <TD>
      <DIV align=center>877</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>754</DIV></TD>
    <TD>
      <DIV align=center>564</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>NA</STRONG></DIV></TD>
    <TD>
      <DIV align=center>255</DIV></TD>
    <TD>
      <DIV align=center>468</DIV></TD>
    <TD>
      <DIV align=center>754</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>219</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>RM</STRONG></DIV></TD>
    <TD>
      <DIV align=center>412</DIV></TD>
    <TD>
      <DIV align=center>268</DIV></TD>
    <TD>
      <DIV align=center>564</DIV></TD>
    <TD>
      <DIV align=center>219</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD></TR></TBODY></TABLE>
<P align=center><IMG src="Clustering - Hierarchical.files/italia02.gif"> </P>
<P align=justify><FONT face="Times New Roman, Times, serif">min d(i,j) = 
d(NA,RM) = 219 =&gt; merge NA and RM into a new cluster called NA/RM<BR>L(NA/RM) 
= 219<BR>m = 2</FONT></P>
<P></P>
<TABLE width="35%" align=center border=1>
  <TBODY>
  <TR>
    <TD>&nbsp;</TD>
    <TD>
      <DIV align=center><STRONG>BA</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>FI</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>NA/RM</STRONG></DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>BA</STRONG></DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>662</DIV></TD>
    <TD>
      <DIV align=center>877</DIV></TD>
    <TD>
      <DIV align=center>255</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>FI</STRONG></DIV></TD>
    <TD>
      <DIV align=center>662</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD>
    <TD>
      <DIV align=center>268</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD>
    <TD>
      <DIV align=center>877</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>564</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>NA/RM</STRONG></DIV></TD>
    <TD>
      <DIV align=center>255</DIV></TD>
    <TD>
      <DIV align=center>268</DIV></TD>
    <TD>
      <DIV align=center>564</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD></TR></TBODY></TABLE>
<P align=center><IMG src="Clustering - Hierarchical.files/italia03.gif"> </P>
<P><FONT face="Times New Roman, Times, serif">min d(i,j) = d(BA,NA/RM) = 255 
=&gt; merge BA and NA/RM into a new cluster called BA/NA/RM<BR>L(BA/NA/RM) = 
255<BR>m = 3</FONT></P>
<P></P>
<TABLE width="35%" align=center border=1>
  <TBODY>
  <TR>
    <TD>&nbsp;</TD>
    <TD>
      <DIV align=center><STRONG>BA/NA/RM</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>FI</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>BA/NA/RM</STRONG></DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>268</DIV></TD>
    <TD>
      <DIV align=center>564</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>FI</STRONG></DIV></TD>
    <TD>
      <DIV align=center>268</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD>
    <TD>
      <DIV align=center>564</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD></TR></TBODY></TABLE>
<P align=center><IMG src="Clustering - Hierarchical.files/italia04.gif"> </P>
<P><FONT face="Times New Roman, Times, serif">min d(i,j) = d(BA/NA/RM,FI) = 268 
=&gt; merge BA/NA/RM and FI into a new cluster called 
BA/FI/NA/RM<BR>L(BA/FI/NA/RM) = 268<BR>m = 4</FONT></P>
<P></P>
<TABLE width="35%" align=center border=1>
  <TBODY>
  <TR>
    <TD>&nbsp;</TD>
    <TD>
      <DIV align=center><STRONG>BA/FI/NA/RM</STRONG></DIV></TD>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>BA/FI/NA/RM</STRONG></DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD></TR>
  <TR>
    <TD>
      <DIV align=center><STRONG>MI/TO</STRONG></DIV></TD>
    <TD>
      <DIV align=center>295</DIV></TD>
    <TD>
      <DIV align=center>0</DIV></TD></TR></TBODY></TABLE>
<P align=center><IMG src="Clustering - Hierarchical.files/italia05.gif"></P>
<P align=justify><FONT face="Times New Roman, Times, serif">Finally, we merge 
the last two clusters at level 295.</FONT></P>
<P align=justify><FONT face="Times New Roman, Times, serif">The process is 
summarized by the following hierarchical tree:</FONT></P>
<P align=center><IMG src="Clustering - Hierarchical.files/image057.gif"></P>
<P></P>
<P align=justify><EM><FONT face="Arial, Helvetica, sans-serif" 
size=+1>Problems</FONT></EM><FONT face="Times New Roman, Times, serif"><BR>The 
main weaknesses of agglomerative clustering methods are:</FONT></P>
<UL>
  <LI><FONT face="Times New Roman, Times, serif" align="justify">they do not 
  scale well: time complexity of at least <EM>O(n<SUP>2</SUP>)</EM>, where n is 
  the number of total objects;</FONT> 
  <LI><FONT face="Times New Roman, Times, serif" align="justify">they can never 
  undo what was done previously.</FONT> </LI></UL>
<P></P>
<P align=justify><FONT face="Arial, Helvetica, sans-serif" 
size=+1><EM>Bibliography</EM></FONT></P>
<DIV align=justify>
<UL>
  <LI><FONT face="Times New Roman, Times, serif"><A name=johnson></A>S. C. 
  Johnson (1967): "Hierarchical Clustering Schemes" <EM>Psychometrika</EM>, 
  2:241-254</FONT> 
  <LI><FONT face="Times New Roman, Times, serif"><A name=dandrade></A>R. 
  D'andrade (1978): "U-Statistic Hierarchical Clustering" 
  <EM>Psychometrika</EM>, 4:58-67</FONT> 
  <LI><FONT face="Times New Roman, Times, serif">Andrew Moore: 揔-means and 
  Hierarchical Clustering - Tutorial Slides
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