Answer to Question #63993 in MatLAB | Mathematica | MathCAD | Maple for lolo

Question

K-Mean Algorithm
1. Initialize
• Select initial m cluster centers
2. Find associations
• For each xi, assign the cluster with nearest center
• Find A to minimize J(X; C, A) with fixed C
3. Find centers
• Compute each cluster center as the mean of data in
the cluster
• Find C to minimize J(X; C, A) with fixed A
4. Stopping criterion
• Stop if clusters stay the same. Otherwise go to step 2

prove that this algorithm is always convergent