jtmatterer
commented
9 years ago From the point of view of the clustering algorithm, it doesn't matter where your data came from (graph, etc), it takes a set of points in Euclidean space and finds good clusters for them. So, one answer to your question is none; there are no differences between clustering the vertices of a graph and Euclidean data.
However, I suspect this is not the answer you were looking for. Rather, you wanted to know why clustering the rows/columns of the adjacency matrix performed so poorly? This is an important distinction, because for the SBM, some embedding of vertices into R^d allow for very good theoretical guarantees of block recovery using clustering. So it's not that clustering graphs is necessarily bad, but the embedding into R^d provided by the adjacency matrix performs poorly for the clustering task at hand. (Furthermore, I contend that clustering the rows/columns of the adjacency matrix is a viable answer, but to a different question than the one we asked in class).
ajulian3
edunnwe1
When using a clustering algorithm, what differences occur between clustering a set of data (no edges, just sets of points in euclidean coordinate space) versus clustering a graph consisting of vertices and edges but no labels (vertices aren't assigned specific coordinate points and are only defined by an adjacency matrix).