One of the current puzzles is why knowledge discovery techniques for graph data do not perform as well, in practice, as they should in theory. The Netflix prize competition, which asks teams to predict user ratings of new movies based on several years of data about previous ratings, has turned out to be surprisingly difficult.

Ronald Coifman’s invited talk at the SIAM Data Mining Conference had something to add to this approach. He showed that the spectral approach to graph analysis, which works with eigenvectors of some matrix derived from the adjacency matrix of the graph, is really the same underneath as a wavelet approach, in which the structure in the graph is analyzed at varying scales. He has applied these ideas to graphs in which the edge affinities are derived from the thresholded pairwise affinities of data records, which makes it straightforward to turn attributed data into graph data without having to commit to a particular set of attributes in advance. This makes the approach easy to apply to data such as images and audio where there are a very large number of attributes.

The abstract of the talk is here, and slides may eventually be posted on this site as well.

Maggioni’s web site is a good place to read more.

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