The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide structure information for a model f(X). However, with the recent popularity of neural networks (GNNs), directly encoding A into model, i.e., f(A, X), has become more common approach. While we show that brings little-to-no benefit existing GNNs, and propose simple but non-trivial variant...

Transfer learning proves to be effective for leveraging labeled data in the source domain build an accurate classifier target domain. The basic assumption behind transfer is that involved domains share some common latent factors. Previous methods usually explore these factors by optimizing two separate objective functions, i.e., either maximizing empirical likelihood, or preserving geometric st...

Let G be a finite simple graph of order n, maximum degree ∆, and minimum degree δ. A compact regularization of G is a ∆-regular graph H of which G is an induced subgraph: H is symmetric if every automorphism of G can be extended to an automorphism of H. The index |H : G| of a regularization H of G is the ratio |V (H)|/|V (G)|. Let mcr(G) denote the index of a minimum compact regularization of G...

In this article, we improve extreme learning machines for regression tasks using a graph signal processing based regularization. We assume that the target signal for prediction or regression is a graph signal. With this assumption, we use the regularization to enforce that the output of an extreme learning machine is smooth over a given graph. Simulation results with real data confirm that such...

When discrete ill-posed problems are analyzed and solved by various numerical regularization techniques, a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector. In particular, the graph associated with Tikhonov regularization plays a central role. The main purpose of this paper is to advo...

A critical task in graph signal processing is to estimate the true from noisy observations over a subset of nodes, also known as reconstruction problem. In this paper, we propose node-adaptive regularization for reconstruction, which surmounts conventional Tikhonov regularization, giving rise more degrees freedom; hence, an improved performance. We formulate denoising problem, study its bias-va...