Efficient Filtering of Graph Based Data Using Graph Partitioning

An algebraic framework for processing graph signals
axiomatically designates the graph adjacency matrix as the shift
operator. In this setup, we often encounter a problem wherein we
know the filtered output and the filter coefficients, and need to
find out the input graph signal. Solution to this problem using
direct approach requires O(N3) operations, where N is the number
of vertices in graph. In this paper, we adapt the spectral graph
partitioning method for partitioning of graphs and use it to reduce
the computational cost of the filtering problem. We use the example
of denoising of the temperature data to illustrate the efficacy of the
approach.