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<a href="." >聚类性能评估指标</a>
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<h1 id="&#x805A;&#x7C7B;&#x6A21;&#x578B;&#x6027;&#x80FD;&#x8BC4;&#x4F30;&#x6307;&#x6807;">&#x805A;&#x7C7B;&#x6A21;&#x578B;&#x6027;&#x80FD;&#x8BC4;&#x4F30;&#x6307;&#x6807;</h1>
<p>&#x805A;&#x7C7B;&#x7684;&#x6027;&#x80FD;&#x5EA6;&#x91CF;&#x5927;&#x81F4;&#x5206;&#x4E3A;&#x4E24;&#x7C7B;&#xFF1A;&#x4E00;&#x7C7B;&#x662F;&#x5C06;&#x805A;&#x7C7B;&#x7ED3;&#x679C;&#x4E0E;&#x67D0;&#x4E2A;&#x53C2;&#x8003;&#x6A21;&#x578B;&#x4F5C;&#x4E3A;&#x53C2;&#x7167;&#x8FDB;&#x884C;&#x6BD4;&#x8F83;&#xFF0C;&#x4E5F;&#x5C31;&#x662F;&#x6240;&#x8C13;&#x7684;<strong>&#x5916;&#x90E8;&#x6307;&#x6807;</strong>&#xFF1B;&#x53E6;&#x4E00;&#x7C7B;&#x662F;&#x5219;&#x662F;&#x76F4;&#x63A5;&#x5EA6;&#x91CF;&#x805A;&#x7C7B;&#x7684;&#x6027;&#x80FD;&#x800C;&#x4E0D;&#x4F7F;&#x7528;&#x53C2;&#x8003;&#x6A21;&#x578B;&#x8FDB;&#x884C;&#x6BD4;&#x8F83;&#xFF0C;&#x4E5F;&#x5C31;&#x662F;<strong>&#x5185;&#x90E8;&#x6307;&#x6807;</strong>&#x3002;</p>
<h2 id="&#x5916;&#x90E8;&#x6307;&#x6807;">&#x5916;&#x90E8;&#x6307;&#x6807;</h2>
<p><strong>&#x5916;&#x90E8;&#x6307;&#x6807;&#x901A;&#x5E38;&#x4F7F;&#x7528; Jaccard Coefficient(JC&#x7CFB;&#x6570;)&#x3001;Fowlkes and Mallows Index(FM&#x6307;&#x6570;)&#x4EE5;&#x53CA; Rand index&#xFF08;Rand&#x6307;&#x6570;&#xFF09;&#x3002;</strong></p>
<p>&#x60F3;&#x8981;&#x8BA1;&#x7B97;&#x4E0A;&#x8FF0;&#x6307;&#x6807;&#x6765;&#x5EA6;&#x91CF;&#x805A;&#x7C7B;&#x7684;&#x6027;&#x80FD;&#xFF0C;&#x9996;&#x5148;&#x9700;&#x8981;&#x8BA1;&#x7B97;&#x51FA;<script type="math/tex; ">a</script>&#xFF0C;<script type="math/tex; ">c</script>&#xFF0C;<script type="math/tex; ">d</script>&#xFF0C;<script type="math/tex; ">e</script>&#x3002;&#x5047;&#x8BBE;&#x6570;&#x636E;&#x96C6;<script type="math/tex; ">E=\{x_1,x_2,...,x_m\}</script>&#x3002;&#x901A;&#x8FC7;&#x805A;&#x7C7B;&#x6A21;&#x578B;&#x7ED9;&#x51FA;&#x7684;&#x7C07;&#x5212;&#x5206;&#x4E3A;<script type="math/tex; ">C=\{C_1,C_2,...C_k\}</script>&#xFF0C;&#x53C2;&#x8003;&#x6A21;&#x578B;&#x7ED9;&#x51FA;&#x7684;&#x7C07;&#x5212;&#x5206;&#x4E3A;<script type="math/tex; ">D=\{D_1,D_2,...D_s\}</script>&#x3002;<script type="math/tex; ">\lambda</script>&#x4E0E;<script type="math/tex; ">\lambda^*</script>&#x5206;&#x522B;&#x8868;&#x793A;<script type="math/tex; ">C</script>&#x4E0E;<script type="math/tex; ">D</script>&#x5BF9;&#x5E94;&#x7684;&#x7C07;&#x6807;&#x8BB0;&#xFF0C;&#x5219;&#x6709;:</p>
<p><script type="math/tex; ">
a=|\{(x_i, x_j)|\lambda_i=\lambda_j, \lambda^*_i=\lambda^*_j,i < j\}|
</script></p>
<p><script type="math/tex; ">
b=|\{(x_i, x_j)|\lambda_i=\lambda_j, \lambda^*_i\neq\lambda^*_j, i < j\}|
</script></p>
<p><script type="math/tex; ">
c=|\{(x_i, x_j)|\lambda_i\neq\lambda_j, \lambda^*_i=\lambda^*_j, i < j\}|
</script></p>
<p><script type="math/tex; ">
d=|\{(x_i, x_j)|\lambda_i\neq\lambda_j, \lambda^*_i\neq\lambda^*_j, i < j\}|
</script></p>
<p>&#x4E3E;&#x4E2A;&#x4F8B;&#x5B50;&#xFF0C;&#x53C2;&#x8003;&#x6A21;&#x578B;&#x7ED9;&#x51FA;&#x7684;&#x7C07;&#x4E0E;&#x805A;&#x7C7B;&#x6A21;&#x578B;&#x7ED9;&#x51FA;&#x7684;&#x7C07;&#x5212;&#x5206;&#x5982;&#x4E0B;&#xFF1A;</p>
<table>
<thead>
<tr>
<th>&#x7F16;&#x53F7;</th>
<th>&#x53C2;&#x8003;&#x7C07;</th>
<th>&#x805A;&#x7C7B;&#x7C07;</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>2</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>3</td>
<td>0</td>
<td>1</td>
</tr>
<tr>
<td>4</td>
<td>1</td>
<td>1</td>
</tr>
<tr>
<td>5</td>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>6</td>
<td>1</td>
<td>2</td>
</tr>
</tbody>
</table>
<p>&#x90A3;&#x4E48;&#x6EE1;&#x8DB3;<script type="math/tex; ">a</script>&#x7684;&#x6837;&#x672C;&#x5BF9;&#x4E3A;<script type="math/tex; ">(1, 2)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">1</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">2</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">0</script>&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">0</script></strong>)&#xFF0C;<script type="math/tex; ">(5, 6)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">5</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">6</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">1</script>&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">2</script></strong>)&#x3002;&#x603B;&#x5171;&#x6709;<script type="math/tex; ">2</script>&#x4E2A;&#x6837;&#x672C;&#x5BF9;&#x6EE1;&#x8DB3;<script type="math/tex; ">a</script>&#xFF0C;&#x56E0;&#x6B64;<script type="math/tex; ">a=2</script>&#x3002;</p>
<p>&#x6EE1;&#x8DB3;<script type="math/tex; ">b</script>&#x7684;&#x6837;&#x672C;&#x5BF9;&#x4E3A;<script type="math/tex; ">(3, 4)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">3</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">4</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x4F46;&#x805A;&#x7C7B;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">1</script></strong>)&#x3002;&#x603B;&#x5171;&#x6709;<script type="math/tex; ">1</script>&#x4E2A;&#x6837;&#x672C;&#x5BF9;&#x6EE1;&#x8DB3;<script type="math/tex; ">b</script>&#xFF0C;&#x56E0;&#x6B64;<script type="math/tex; ">b=1</script>&#x3002;</p>
<p>&#x90A3;&#x4E48;&#x6EE1;&#x8DB3;<script type="math/tex; ">c</script>&#x7684;&#x6837;&#x672C;&#x5BF9;&#x4E3A;<script type="math/tex; ">(1, 3)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">1</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">3</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x805A;&#x7C7B;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x4F46;&#x53C2;&#x8003;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">0</script></strong>)&#xFF0C;<script type="math/tex; ">(2, 3)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">2</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">3</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x805A;&#x7C7B;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x4F46;&#x53C2;&#x8003;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">0</script></strong>)&#xFF0C;<script type="math/tex; ">(4, 5)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">4</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">5</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x805A;&#x7C7B;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x4F46;&#x53C2;&#x8003;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">1</script></strong>)&#xFF0C;<script type="math/tex; ">(4, 6)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">4</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">6</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x805A;&#x7C7B;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x4F46;&#x53C2;&#x8003;&#x7C07;&#x90FD;&#x4E3A;<script type="math/tex; ">1</script></strong>)&#x3002;&#x603B;&#x5171;&#x6709;<script type="math/tex; ">4</script>&#x4E2A;&#x6837;&#x672C;&#x5BF9;&#x6EE1;&#x8DB3;<script type="math/tex; ">c</script>&#xFF0C;&#x56E0;&#x6B64;<script type="math/tex; ">c=4</script>&#x3002;</p>
<p>&#x6EE1;&#x8DB3;<script type="math/tex; ">d</script>&#x7684;&#x6837;&#x672C;&#x5BF9;&#x4E3A;<script type="math/tex; ">(1, 4)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">1</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">4</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(1, 5)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">1</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">5</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(1, 6)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">1</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">6</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(2, 4)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">2</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">4</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(2, 5)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">2</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">5</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(2, 6)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">2</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">6</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(3, 5)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">3</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">5</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#xFF0C;<script type="math/tex; ">(3, 6)</script>(<strong>&#x56E0;&#x4E3A;<script type="math/tex; ">3</script>&#x53F7;&#x6837;&#x672C;&#x4E0E;<script type="math/tex; ">6</script>&#x53F7;&#x6837;&#x672C;&#x7684;&#x53C2;&#x8003;&#x7C07;&#x4E0D;&#x540C;&#xFF0C;&#x805A;&#x7C7B;&#x7C07;&#x4E5F;&#x4E0D;&#x540C;</strong>)&#x3002;&#x603B;&#x5171;&#x6709;<script type="math/tex; ">8</script>&#x4E2A;&#x6837;&#x672C;&#x5BF9;&#x6EE1;&#x8DB3;<script type="math/tex; ">d</script>&#xFF0C;&#x56E0;&#x6B64;<script type="math/tex; ">d=8</script>&#x3002;</p>
<h3 id="jc&#x7CFB;&#x6570;">JC&#x7CFB;&#x6570;</h3>
<p><strong>JC&#x7CFB;&#x6570;</strong>&#x6839;&#x636E;&#x4E0A;&#x9762;&#x6240;&#x63D0;&#x5230;&#x7684;<script type="math/tex; ">a</script>&#xFF0C;<script type="math/tex; ">b</script>&#xFF0C;<script type="math/tex; ">c</script>&#x6765;&#x8BA1;&#x7B97;&#xFF0C;&#x5E76;&#x4E14;&#x503C;&#x57DF;&#x4E3A;<script type="math/tex; ">[0, 1]</script>&#xFF0C;&#x503C;&#x8D8A;&#x5927;&#x8BF4;&#x660E;&#x805A;&#x7C7B;&#x6027;&#x80FD;&#x8D8A;&#x597D;&#xFF0C;&#x516C;&#x5F0F;&#x5982;&#x4E0B;&#xFF1A;</p>
<p><script type="math/tex; ">
JC=\frac{a}{a+b+c}
</script></p>
<p>&#x56E0;&#x6B64;&#x521A;&#x521A;&#x7684;&#x4F8B;&#x5B50;&#x4E2D;&#xFF0C;<script type="math/tex; ">JC=\frac{2}{2+1+4}=\frac{2}{7}</script></p>
<h3 id="fm&#x6307;&#x6570;">FM&#x6307;&#x6570;</h3>
<p><strong>FM&#x6307;&#x6570;</strong>&#x6839;&#x636E;&#x4E0A;&#x9762;&#x6240;&#x63D0;&#x5230;&#x7684;<script type="math/tex; ">a</script>&#xFF0C;<script type="math/tex; ">b</script>&#xFF0C;<script type="math/tex; ">c</script>&#x6765;&#x8BA1;&#x7B97;&#xFF0C;&#x5E76;&#x4E14;&#x503C;&#x57DF;&#x4E3A;<script type="math/tex; ">[0, 1]</script>&#xFF0C;&#x503C;&#x8D8A;&#x5927;&#x8BF4;&#x660E;&#x805A;&#x7C7B;&#x6027;&#x80FD;&#x8D8A;&#x597D;&#xFF0C;&#x516C;&#x5F0F;&#x5982;&#x4E0B;&#xFF1A;</p>
<p><script type="math/tex; ">
FMI=\sqrt{\frac{a}{a+b}*\frac{a}{a+c}}
</script></p>
<p>&#x56E0;&#x6B64;&#x521A;&#x521A;&#x7684;&#x4F8B;&#x5B50;&#x4E2D;&#xFF0C;<script type="math/tex; ">FMI=\sqrt{\frac{2}{2+1}*\frac{2}{2+4}}=\sqrt{\frac{4}{18}}</script></p>
<h3 id="rand&#x6307;&#x6570;">Rand&#x6307;&#x6570;</h3>
<p><strong>Rand&#x6307;&#x6570;</strong>&#x6839;&#x636E;&#x4E0A;&#x9762;&#x6240;&#x63D0;&#x5230;&#x7684;<script type="math/tex; ">a</script>&#x548C;<script type="math/tex; ">d</script>&#x6765;&#x8BA1;&#x7B97;&#xFF0C;&#x5E76;&#x4E14;&#x503C;&#x57DF;&#x4E3A;<script type="math/tex; ">[0, 1]</script>&#xFF0C;&#x503C;&#x8D8A;&#x5927;&#x8BF4;&#x660E;&#x805A;&#x7C7B;&#x6027;&#x80FD;&#x8D8A;&#x597D;&#xFF0C;&#x5047;&#x8BBE;<script type="math/tex; ">m</script>&#x4E3A;&#x6837;&#x672C;&#x6570;&#x91CF;&#xFF0C;&#x516C;&#x5F0F;&#x5982;&#x4E0B;&#xFF1A;</p>
<p><script type="math/tex; ">
RandI=\frac{2(a+d)}{m(m-1)}
</script></p>
<p>&#x56E0;&#x6B64;&#x521A;&#x521A;&#x7684;&#x4F8B;&#x5B50;&#x4E2D;&#xFF0C;<script type="math/tex; ">RandI=\frac{2*(2+8)}{6*(6-1)}=\frac{2}{3}</script>&#x3002;</p>
<h2 id="&#x5185;&#x90E8;&#x6307;&#x6807;">&#x5185;&#x90E8;&#x6307;&#x6807;</h2>
<p><strong>&#x5185;&#x90E8;&#x6307;&#x6807;&#x901A;&#x5E38;&#x4F7F;&#x7528; Davies-Bouldin Index (DB&#x6307;&#x6570;)&#x4EE5;&#x53CA; Dunn Index&#xFF08;Dunn&#x6307;&#x6570;&#xFF09;&#x3002;</strong></p>
<h5 id="db&#x6307;&#x6570;">DB&#x6307;&#x6570;</h5>
<p><strong>DB&#x6307;&#x6570;</strong>&#x53C8;&#x79F0; DBI &#xFF0C;&#x8BA1;&#x7B97;&#x516C;&#x5F0F;&#x5982;&#x4E0B;&#xFF1A;</p>
<p><script type="math/tex; ">
DBI=\frac{1}{k}\sum_{i=1}^kmax(\frac{avg(C_i)+avg(C_j)}{d_c(\mu_i,\mu_j)}), i \neq j
</script></p>
<p>&#x516C;&#x5F0F;&#x4E2D;&#x7684;&#x8868;&#x8FBE;&#x5F0F;&#x5176;&#x5B9E;&#x5F88;&#x597D;&#x7406;&#x89E3;&#xFF0C;&#x5176;&#x4E2D;<script type="math/tex; ">k</script>&#x4EE3;&#x8868;&#x805A;&#x7C7B;&#x6709;&#x591A;&#x5C11;&#x4E2A;&#x7C07;&#xFF0C;<script type="math/tex; ">\mu_i</script>&#x4EE3;&#x8868;&#x7B2C;<script type="math/tex; ">i</script>&#x4E2A;&#x7C07;&#x7684;&#x4E2D;&#x5FC3;&#x70B9;&#xFF0C;<script type="math/tex; ">avg(C_i)</script>&#x4EE3;&#x8868;<script type="math/tex; ">C_i</script>&#x7B2C;<script type="math/tex; ">i</script>&#x4E2A;&#x7C07;&#x4E2D;&#x6240;&#x6709;&#x6570;&#x636E;&#x4E0E;&#x7B2C;<script type="math/tex; ">i</script>&#x4E2A;&#x7C07;&#x7684;&#x4E2D;&#x5FC3;&#x70B9;&#x7684;&#x5E73;&#x5747;&#x8DDD;&#x79BB;&#x3002;<script type="math/tex; ">d_c(\mu_i, \mu_j)</script>&#x4EE3;&#x8868;&#x7B2C;<script type="math/tex; ">i</script>&#x4E2A;&#x7C07;&#x7684;&#x4E2D;&#x5FC3;&#x70B9;&#x4E0E;&#x7B2C;<script type="math/tex; ">j</script>&#x4E2A;&#x7C07;&#x7684;&#x4E2D;&#x5FC3;&#x70B9;&#x7684;&#x8DDD;&#x79BB;&#x3002;</p>
<p>&#x4E3E;&#x4E2A;&#x4F8B;&#x5B50;&#xFF0C;&#x73B0;&#x5728;&#x6709;<script type="math/tex; ">6</script>&#x6761;&#x897F;&#x74DC;&#x6570;&#x636E;<script type="math/tex; ">\{x_1,x_2,...,x_6\}</script>&#xFF0C;&#x8FD9;&#x4E9B;&#x6570;&#x636E;&#x5DF2;&#x7ECF;&#x805A;&#x7C7B;&#x6210;&#x4E86;<script type="math/tex; ">2</script>&#x4E2A;&#x7C07;&#x3002;</p>
<table>
<thead>
<tr>
<th>&#x7F16;&#x53F7;</th>
<th>&#x4F53;&#x79EF;</th>
<th>&#x91CD;&#x91CF;</th>
<th>&#x7C07;</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>3</td>
<td>4</td>
<td>1</td>
</tr>
<tr>
<td>2</td>
<td>6</td>
<td>9</td>
<td>2</td>
</tr>
<tr>
<td>3</td>
<td>2</td>
<td>3</td>
<td>1</td>
</tr>
<tr>
<td>4</td>
<td>3</td>
<td>4</td>
<td>1</td>
</tr>
<tr>
<td>5</td>
<td>7</td>
<td>10</td>
<td>2</td>
</tr>
<tr>
<td>6</td>
<td>8</td>
<td>11</td>
<td>2</td>
</tr>
</tbody>
</table>
<p>&#x4ECE;&#x8868;&#x683C;&#x53EF;&#x4EE5;&#x770B;&#x51FA;&#xFF1A;</p>
<p><script type="math/tex; ">
k=2
</script></p>
<p><script type="math/tex; ">
\mu_1=(\frac{(3+2+3)}{3}, \frac{(4+3+4)}{3})=(2.67,3.67)
</script></p>
<p><script type="math/tex; ">
\mu_2=(\frac{(6+7+8)}{3}, \frac{(9+10+11)}{3})=(7,10)
</script></p>
<p><script type="math/tex; ">
d_c(\mu_1, \mu_2)=\sqrt{(2.67-7)^2+(3.67-10)^2}=7.67391
</script></p>
<p><script type="math/tex; ">
avg(C_1)=(\sqrt{(3-2.67)^2+(4-3.67)^2}+\sqrt{(2-2.67)^2+(3-3.67)^2}+\sqrt{(3-2.67)^2+(4-3.67)^2})/3=0.628539
</script></p>
<p><script type="math/tex; ">
avg(C_2)=(\sqrt{(6-7)^2+(9-10)^2}+\sqrt{(7-7)^2+(10-10)^2}+\sqrt{(8-7)^2+(11-10)^2})/3=0.94281
</script></p>
<p>&#x56E0;&#x6B64;&#x6709;&#xFF1A;</p>
<p><script type="math/tex; ">
DBI=\frac{1}{k}\sum_{i=1}^kmax(\frac{avg(C_i)+avg(C_j)}{d_c(\mu_i,\mu_j)})=0.204765
</script></p>
<p><strong>DB&#x6307;&#x6570;&#x8D8A;&#x5C0F;&#x5C31;&#x8D8A;&#x5C31;&#x610F;&#x5473;&#x7740;&#x7C07;&#x5185;&#x8DDD;&#x79BB;&#x8D8A;&#x5C0F;&#x540C;&#x65F6;&#x7C07;&#x95F4;&#x8DDD;&#x79BB;&#x8D8A;&#x5927;&#xFF0C;&#x4E5F;&#x5C31;&#x662F;&#x8BF4;DB&#x6307;&#x6570;&#x8D8A;&#x5C0F;&#x8D8A;&#x597D;&#x3002;</strong></p>
<h3 id="dunn&#x6307;&#x6570;">Dunn&#x6307;&#x6570;</h3>
<p><strong>Dunn&#x6307;&#x6570;</strong>&#x53C8;&#x79F0;DI&#xFF0C;&#x8BA1;&#x7B97;&#x516C;&#x5F0F;&#x5982;&#x4E0B;&#xFF1A;</p>
<p><script type="math/tex; ">
DI=min_{1\leq i\leq k}\{min_{i\neq j}(\frac{d_min(C_i,C_j)}{max_{1\leq l\leq k}diam(C_l)})\}
</script></p>
<p>&#x516C;&#x5F0F;&#x4E2D;&#x7684;&#x8868;&#x8FBE;&#x5F0F;&#x5176;&#x5B9E;&#x5F88;&#x597D;&#x7406;&#x89E3;&#xFF0C;&#x5176;&#x4E2D;<script type="math/tex; ">k</script>&#x4EE3;&#x8868;&#x805A;&#x7C7B;&#x6709;&#x591A;&#x5C11;&#x4E2A;&#x7C07;&#xFF0C;<script type="math/tex; ">d_{min}(C_i,C_j)</script>&#x4EE3;&#x8868;&#x7B2C;<script type="math/tex; ">i</script>&#x4E2A;&#x7C07;&#x4E2D;&#x7684;&#x6837;&#x672C;&#x4E0E;&#x7B2C;<script type="math/tex; ">j</script>&#x4E2A;&#x7C07;&#x4E2D;&#x7684;&#x6837;&#x672C;&#x4E4B;&#x95F4;&#x7684;&#x6700;&#x77ED;&#x8DDD;&#x79BB;&#xFF0C;<script type="math/tex; ">diam(C_l)</script>&#x4EE3;&#x8868;&#x7B2C;<script type="math/tex; ">l</script>&#x4E2A;&#x7C07;&#x4E2D;&#x76F8;&#x8DDD;&#x6700;&#x8FDC;&#x7684;&#x6837;&#x672C;&#x4E4B;&#x95F4;&#x7684;&#x8DDD;&#x79BB;&#x3002;</p>
<p>&#x8FD8;&#x662F;&#x8FD9;&#x4E2A;&#x4F8B;&#x5B50;&#xFF0C;&#x73B0;&#x5728;&#x6709; 6 &#x6761;&#x897F;&#x74DC;&#x6570;&#x636E;<script type="math/tex; ">\{x_1,x_2,...,x_6\}</script>&#xFF0C;&#x8FD9;&#x4E9B;&#x6570;&#x636E;&#x5DF2;&#x7ECF;&#x805A;&#x7C7B;&#x6210;&#x4E86; 2 &#x4E2A;&#x7C07;&#x3002;</p>
<table>
<thead>
<tr>
<th>&#x7F16;&#x53F7;</th>
<th>&#x4F53;&#x79EF;</th>
<th>&#x91CD;&#x91CF;</th>
<th>&#x7C07;</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>3</td>
<td>4</td>
<td>1</td>
</tr>
<tr>
<td>2</td>
<td>6</td>
<td>9</td>
<td>2</td>
</tr>
<tr>
<td>3</td>
<td>2</td>
<td>3</td>
<td>1</td>
</tr>
<tr>
<td>4</td>
<td>3</td>
<td>4</td>
<td>1</td>
</tr>
<tr>
<td>5</td>
<td>7</td>
<td>10</td>
<td>2</td>
</tr>
<tr>
<td>6</td>
<td>8</td>
<td>11</td>
<td>2</td>
</tr>
</tbody>
</table>
<p>&#x4ECE;&#x8868;&#x683C;&#x53EF;&#x4EE5;&#x770B;&#x51FA;&#xFF1A;</p>
<p><script type="math/tex; ">
k=2
</script></p>
<p><script type="math/tex; ">
d_{min}(C_1,C_2)=\sqrt{(3-6)^2+(4-9)^2}=5.831
</script></p>
<p><script type="math/tex; ">
diam(C_1)=\sqrt{(3-2)^2+(4-2)^2}=1.414
</script></p>
<p><script type="math/tex; ">
diam(C_2)=\sqrt{(6-8)^2+(9-11)^2}=2.828
</script></p>
<p>&#x56E0;&#x6B64;&#x6709;&#xFF1A;</p>
<p><script type="math/tex; ">
DI=min_{1\leq i\leq k}\{min_{i\neq j}(\frac{d_min(C_i,C_j)}{max_{1\leq l\leq k}diam(C_l)})\}=2.061553
</script></p>
<p><strong>Dunn&#x6307;&#x6570;&#x8D8A;&#x5927;&#x610F;&#x5473;&#x7740;&#x7C07;&#x5185;&#x8DDD;&#x79BB;&#x8D8A;&#x5C0F;&#x540C;&#x65F6;&#x7C07;&#x95F4;&#x8DDD;&#x79BB;&#x8D8A;&#x5927;&#xFF0C;&#x4E5F;&#x5C31;&#x662F;&#x8BF4;Dunn&#x6307;&#x6570;&#x8D8A;&#x5927;&#x8D8A;&#x597D;&#x3002;</strong></p>
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