Localized Iterative Methods for Interpolation in Graph Structured Data
This work addresses interpolation in graph-structured data, which is incremental as it builds on existing methods for graph signal processing.
The paper tackles the problem of interpolating graph signals from partial samples by proposing two localized graph filtering methods, one extending prior bandlimited reconstruction with improved computational efficiency and another using a regularization framework with closed-form and iterative solutions, showing effectiveness on recommendation system datasets.
In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on reconstructing bandlimited graph signals from partially observed samples. The iterative graph filtering approach very closely approximates the solution proposed in the that work, while being computationally more efficient. As an alternative, we propose a regularization based framework in which we define the cost of reconstruction to be a combination of smoothness of the graph signal and the reconstruction error with respect to the known samples, and find solutions that minimize this cost. We provide both a closed form solution and a computationally efficient iterative solution of the optimization problem. The experimental results on the recommendation system datasets demonstrate effectiveness of the proposed methods.