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

Question #63993

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

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

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