Algorithm : Input : Similarity Matrix and number of clusters k.

1. Represent all data points as nodes in a graph.
2. Build the similarity graph given a similarity matrix. Calculate it's weighted adjacency matrix W. Let these have the dimentionality n x n.
3. Build the unnormalized Laplacian L (n x n)
4. If we wish to cluster the data into k points (user defined), then we consider the first k eigenvectors of the matrix L.
5. Build an n x k matrix with each of the first k eigenvectors as it's columns. Let us call this matrix M.
6. Interpret each ROW of the matrix M as a separate data point $a_i$ .
7. Run the k-mean clustering algorithm to put these distinct $a_i$ data points into clusters.