Graph-Based Classification with Multiple Shift Matrices

Due to their effectiveness in capturing similarities between different entities, graphical models are widely used to represent datasets that reside on irregular and complex manifolds. Graph signal processing offers support to handle such complex datasets. In this paper, we propose a novel graph filter design method for semi-supervised data classification. The proposed design uses multiple graph shift matrices, one for each feature, and is shown to provide improved performance when the feature qualities are uneven. We introduce three methods to optimize for the graph filter coefficients and the graph combining coefficients. The first method uses the alternating minimization approach. In the second method, we optimize our objective function by convex relaxation that provides a performance benchmark. The third method adopts a genetic algorithm, which is computationally efficient and better at controlling overfitting. In our simulation experiments, we use both synthetic and real datasets with informative and non-informative features. Monte Carlo simulations demonstrate the effectiveness of multiple graph shift operators in the graph filters. Significant improvements in comparison to conventional graph filters are shown, in terms of average error rate and confidence scores. Furthermore, we perform cross validation to show how our approach can control overfitting and improve generalization performance.