K-means algorithms

Input {$x_1$, $x_2$, ..., $x_m$}

1. Initialize cluster centriods: $c_1$, $c_2$, ..., $c_k$

2. Repeat

   2.1 assign $x_i$ to $c_j$

   2.2 update $c_j$ according to group sample

   2.3 break when center distance is less than a threshold

As the distortion function $J$ is a non-convex function, the alogrithm will …