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We study graph-based Laplacian semi-supervised learning at low labeling rates. Laplacian learning uses harmonic extension on a graph to propagate labels. At very low label rates, Laplacian learning becomes degenerate and the solution is…
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis…
Graph sampling theory extends the traditional sampling theory to graphs with topological structures. As a key part of the graph sampling theory, subset selection chooses nodes on graphs as samples to reconstruct the original signal. Due to…
The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…
This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
In this paper, we focus on learning the underlying product graph structure from multidomain training data. We assume that the product graph is formed from a Cartesian graph product of two smaller factor graphs. We then pose the product…
Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first…
A statistician designing an experiment wants to get as much information as possible from the data gathered. Often this means the most precise estimate possible (that is, an estimate with minimum possible variance) of the unknown parameters.…
Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel…
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive…
We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we…
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to…
For a given graph $\mathcal{G}$ of order $n$ with $m$ edges, and a real symmetric matrix associated to the graph, $M\left(\mathcal{G}\right)\in\mathbb{R}^{n\times n}$, the interlacing graph reduction problem is to find a graph…
Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…
Graph-based semi-supervised learning has been shown to be one of the most effective approaches for classification tasks from a wide range of domains, such as image classification and text classification, as they can exploit the connectivity…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…
We consider the general problem of utilizing both labeled and unlabeled data to improve data representation performance. A new semi-supervised learning framework is proposed by combing manifold regularization and data representation methods…