Distortion Measure

#Computers

$\displaystyle J=\sum_{n = 1}^{N}\sum_{k = 1}^{K}r_{nk}\lVert x_{n}-\mu_{k}\rVert^{2}$

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