Related papers: Sparse Graph Learning from Sparse Data via Fiedler…
Partition problems in graphs are extremely important in applications, as shown in the Data science and Machine learning literature. One approach is spectral partitioning based on a Fiedler vector, i.e., an eigenvector corresponding to the…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
In this paper, we are interested in learning the underlying graph structure behind training data. Solving this basic problem is essential to carry out any graph signal processing or machine learning task. To realize this, we assume that the…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. Existing regularization methods often focus on dropping/penalizing weights in a global…
Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
We propose a supervised learning approach for predicting an underlying graph from a set of graph signals. Our approach is based on linear regression. In the linear regression model, we predict edge-weights of a graph as the output, given a…
The Fiedler value $\lambda_2$, also known as algebraic connectivity, is the second smallest Laplacian eigenvalue of a graph. We study the maximum Fiedler value among all planar graphs $G$ with $n$ vertices, denoted by $\lambda_{2\max}$, and…
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…
Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…
In agronomics, predicting crop yield at a per field/county granularity is important for farmers to minimize uncertainty and plan seeding for the next crop cycle. While state-of-the-art prediction techniques employ graph convolutional nets…