Classification via regularization on graphs

We present a novel data classifier that is based on the regularization of graph signals. Our approach is based on the theory of discrete signal processing on graphs where the graph represents similarities between data and we interpret labels for the dataset elements as a signal indexed by the nodes of the graph. We postulate that true labels form a low-frequency graph signal and the classifier finds the smoothest graph signal that satisfies constraints given by known data labels. Our experiments demonstrate that our approach achieves high accuracy in multiclass classification and outperforms other classification approaches.