Performance of the clustering.

<p>(a) shows the silhouette value at different scales. (b) and (c) show the size of clusters at different scales. We use the radius of gyration [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147216#pone.0147216.ref026" target="_blank">26</a>] to measure the size of the cluster. It is defined as <math><mrow><msub><mi>r</mi><mi>g</mi></msub><mo>=</mo><msqrt><mrow><mn>1</mn><mrow><msub><mi>n</mi><mi>c</mi></msub></mrow><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mi>c</mi></msub></mrow><mrow><mrow><mrow><mo>(</mo><mrow><msub><mi>r</mi><mo>→</mo><mi>i</mi></msub><mo>−</mo><msub><mi>r</mi><mo>→</mo><mi>c</mi></msub></mrow><mo>)</mo></mrow></mrow><mn>2</mn></mrow></mrow></msqrt></mrow></math>, where <math><mrow><msub><mi>r</mi><mo>→</mo><mi>c</mi></msub></mrow></math> is the center of the cluster, <math><mrow><msub><mi>r</mi><mo>→</mo><mi>i</mi></msub></mrow></math> is the position of the <i>i</i>-th service point, and <i>n</i>_<i>c</i> is the number of service points in the cluster. We plot the semi-quartile and median of <i>r</i>_<i>g</i> in the <i>y</i>-axis to study the change in the cluster's spatial dispersion.