Sampling and Reconstruction of Graph Signals via Weak Submodularity and Semidefinite Relaxation

We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end, we formulate the task at hand as the minimization of MSE subject to binary constraints, and approximate the resulting NP-hard problem via semidefinite programming (SDP) relaxation. Moreover, we provide an alternative formulation based on maximizing a monotone weak submodular function and propose a randomized-greedy algorithm to find a sub-optimal subset. We then derive a worst-case performance guarantee on the MSE returned by the randomized greedy algorithm for general non-stationary graph signals. The efficacy of the proposed methods is illustrated through numerical simulations on synthetic and real-world graphs. Notably, the randomized greedy algorithm yields an order-of-magnitude speedup over state-of-the-art greedy sampling schemes, while incurring only a marginal MSE performance loss

Distributed Adaptive Learning of Graph Signals

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. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201

Enhancement of a structural optimization simulation tool using machine learning

openLa produzione additiva ha aperto possibilità inesplorate nella fabbricazione di strutture elastiche non realizzabili tramite processi tradizionali di stampaggio e lavorazione. L'obiettivo di questo progetto è esplorare i vantaggi dell'introduzione di tecniche di machine learning (ML) nelle pipeline di ottimizzazione topologica esistenti per migliorarne l'efficienza e la precisione. Particolare enfasi sarà dedicata alla valutazione della capacità degli algoritmi ML di ridurre il carico computazionale dovuto alle fasi di generazione e adattamento della mesh nell'ottimizzazione della topologia.Additive manufacturing has opened unexplored possibilities in the fabrication of elastic structures not manufacturable via traditional moulding and machining processes. The goal of this project is to explore the benefits of introducing machine learning (ML) techniques into existing topology optimisation pipelines to improve their efficiency and accuracy. Special emphasis will be devoted to assess the capability of ML algorithms to reduce the computational burden due to the mesh generation and adaptation steps in topology optimisation