Distortion Measure

$J=\sum _{n=1}^N\sum _{k=1}^K{r}_{nk}\Vert x_n-{\mu }_k{\Vert }^2$

• How much the data points vary/are distorted from the clusters they’ve been assigned to
• $N$ is the number of data points
• $K$ is the number of clusters
• $r_{nk}$ is an indicator function with value $1$ if data point $x_n$ is assigned to class/cluster $k$ and 0 otherwise
• ${\mu }_k$ is the cluster prototype