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zusammenfassung/zusammenfassung.md
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@ -331,7 +331,7 @@ Beispiel Silhouette Koeffizient für Punkt A1 berechnen:
1. Cohesion für Punk A1 berechnen 1. Cohesion für Punk A1 berechnen
* cohesion a(x): durchschnittlicher Abstand von x zu allen anderen Vektoren im selben Cluster * cohesion a(x): durchschnittlicher Abstand von x zu allen anderen Vektoren im selben Cluster
$$ $$
cohesion = \frac{\sum_{i=1}^k\sqrt{\sum_{i=1}^{n} (x_i-y_i)^2}}{k} cohesion=a(x)=\frac{\sum_{i=1}^k\sqrt{\sum_{i=1}^{n} (x_i-y_i)^2}}{k}
$$ $$
$$ $$
d(A1,A2)=\sqrt{(2-3)^2+(5-4)^2}=\sqrt{2} d(A1,A2)=\sqrt{(2-3)^2+(5-4)^2}=\sqrt{2}
@ -342,3 +342,33 @@ $$
$$ $$
cohesion(A1)=a(A1)=\frac{\sqrt{2}+\sqrt{5}}{2}=1.825 cohesion(A1)=a(A1)=\frac{\sqrt{2}+\sqrt{5}}{2}=1.825
$$ $$
2. Separation für Punk A1 berechnen
* separation b(x): durchschnittlicher Abstand von x zu Vektoren in den anderen Clustern. Finde das Minimum unter den Clustern
$$
separation=b(x)=\frac{\sum_{i=1}^k\sqrt{\sum_{i=1}^{n} (x_i-y_i)^2}}{k}
$$
$$
d(A1,B1)=\sqrt{(2-8)^2+(5-3)^2}=\sqrt{20}
$$
$$
d(A1,B2)=\sqrt{(2-9)^2+(5-2)^2}=\sqrt{58}
$$
$$
d(A1,B3)=\sqrt{(2-10)^2+(5-5)^2}=8
$$
$$
separation(A1)_B=b(A1)_B=\frac{\sqrt{20}+\sqrt{58}+8}{3}=6.696
$$
$$
d(A1,C1)=\sqrt{(2-6)^2+(5-10)^2}=\sqrt{26}
$$
$$
d(A1,C2)=\sqrt{(2-7)^2+(5-8)^2}=\sqrt{18}
$$
$$
d(A1,C3)=\sqrt{(2-8)^2+(5-9)^2}=\sqrt{32}
$$
$$
separation(A1)_B=b(A1)_C=\frac{\sqrt{26}+\sqrt{18}+\sqrt{32}}{3}=5.333
$$