Ricerc@Sapienza

This work merges tools from graph signal processing and linear systems theory to propose sampling strategies for observing the initial state of a process evolving over a graph. The proposed method is ratified by a mathematical analysis that provides insights on the role played by the different actors, such as the graph topology, the process bandwidth, and the sampling strategy. Moreover, conditions when the graph process is observable from a few samples and (sub)optimal sampling strategies that jointly exploit the nature of the graph structure and graph process are proposed.

A key tool to analyze signals defined over a graph is the so called Graph Fourier Transform (GFT). Alternative definitions of GFT have been proposed, based on the eigen-decomposition of either the graph Laplacian or adjacency matrix. In this paper, we introduce an alternative approach, valid for the general case of directed graphs, that builds the graph Fourier basis as the set of orthonormal vectors that minimize a well-defined continuous extension of the graph cut size, known as Lovász extension.

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean-square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided.

The analysis of signals defined over a graph is relevant in many applications, such as social and economic networks, big data or biological networks, and so on. A key tool for analyzing these signals is the so-called graph Fourier transform (GFT). Alternative definitions of GFT have been suggested in the literature, based on the eigen-decomposition of either the graph Laplacian or adjacency matrix.

This work proposes distributed recursive least squares (RLS) strategies for adaptive reconstruction and learning of signals defined over graphs. First, we introduce a centralized RLS estimation strategy with probabilistic sampling, and we propose a sparse sensing method that selects the sampling probability at each node in the graph in order to guarantee adaptive signal reconstruction and a target steady-state performance. Then, a distributed RLS strategy is derived and is shown to be convergent to its centralized counterpart.

The aim of this paper is to propose optimal sampling strategies for adaptive learning of signals defined over graphs. Introducing a novel least mean square (LMS) estimation strategy with probabilistic sampling, we propose two different methods to select the sampling probability at each node, with the aim of optimizing the sampling rate, or the mean-square performance, while at the same time guaranteeing a prescribed learning rate.

Real-world networks are typically described in terms of nodes, links, and communities, having signal values often associated with them. The aim of this letter is to introduce a novel Compound Markov random field model (Compound MRF, or CMRF) for signals defined over graphs, encompassing jointly signal values at nodes, edge weights, and community labels. The proposed CMRF generalizes Markovian models previously proposed in the literature, since it accounts for different kinds of interactions between communities and signal smoothness constraints.

In this paper, we introduce a novel adaptive method for distributed recovery of graph processes, which are observed over a dynamic set of vertices. The proposed algorithm hinges on proximal gradient optimization techniques, while leveraging in-network projections as a mechanism to enforce graph bandwidth constraints in a cooperative and distributed fashion, and thresholding operators to identify anomalous sparse components hidden in the signals. The theoretical analysis illustrates the mean-square stability of the proposed adaptive method.

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 finds a block sparse representation of the data by associating a graph, whose Laplacian matrix admits the sparsifying dictionary as its eigenvectors. The main idea is to associate a graph topology to the data in order to make the observed signals band-limited over the inferred graph.

The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and then it is especially useful to deal with signals defined over non-metric spaces. We focus on signals defined over simplicial complexes. Graph Signal Processing (GSP) represents a special case of Topological Signal Processing (TSP), referring to the situation where the signals are associated only with the vertices of a graph.