Kernel k-means Algorithm

Kernel k-means:

Kernel k-means clustering method is a non-linear extension of the conventional k-means clustering method. Girolami (2002) first proposed the kernel k-means clustering method. It is an iterative method. It first maps the data points from the input space to a higher dimensional feature space through a nonlinear transformation and then minimizes the clustering error in that feature space.

Kernel k-means Algorithm:

This algorithm applies the same trick as k-means but with one difference here in the calculation of distance. The kernel method is used instead of the Euclidean distance.

Algorithm:
1. For each cluster C_j, find |C_j| and G(C_j).

2. Compute F(X_i, C_j) for each X_i and for each cluster C_j.

3. Find ||Φ(X_i) – μ_j||² using equation(4) and assign X_i to its nearest center.

4. Update μ_j, for j=1 to k, using equation(2).

5. Repeat step-1 through step-4 till convergence.