Graph learning under spectral sparsity constraints

Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a case for inferring graphs on which the observed data has high variation. We propose a signal processing based inference model that allows for wideband frequency variation in the data and propose an algorithm for graph inference. The proposed inference algorithm consists of two steps: 1) learning orthogonal eigenvectors of a graph from the data; 2) recovering the adjacency matrix of the graph topology from the given graph eigenvectors. The first step is solved by an iterative algorithm with a closed-form solution. In the second step, the adjacency matrix is inferred from the eigenvectors by solving a convex optimization problem. Numerical results on synthetic data show the proposed inference algorithm can effectively capture the meaningful graph topology from observed data under the wideband assumption

Fast Graph Convolutional Recurrent Neural Networks

This paper proposes a Fast Graph Convolutional Neural Network (FGRNN) architecture to predict sequences with an underlying graph structure. The proposed architecture addresses the limitations of the standard recurrent neural network (RNN), namely, vanishing and exploding gradients, causing numerical instabilities during training. State-of-the-art architectures that combine gated RNN architectures, such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) with graph convolutions are known to improve the numerical stability during the training phase, but at the expense of the model size involving a large number of training parameters. FGRNN addresses this problem by adding a weighted residual connection with only two extra training parameters as compared to the standard RNN. Numerical experiments on the real 3D point cloud dataset corroborates the proposed architecture.Comment: 5 pages.Submitted to Asilomar Conference on Signals, Systems, and Computer