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 its weighted adjacency matrix $W$. Let it have dimensionality $n imes n$. 3. Build the unnormalized Laplacian $L$ ($n imes n$). 4. If we wish to cluster the data into $k$ clusters (user-defined), then we consider the first $k$ eigenvectors of the matrix $L$. 5. Build an $n imes k$ matrix with each of the first $k$ eigenvectors as its 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-means clustering algorithm to put these distinct $a_i$ data points into clusters.