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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 perturbations. As a result, any method relying on the graph topology may yield suboptimal results if those imperfections are ignored. Motivated by this, we propose a novel approach for handling perturbations on the links of the graph and apply it to the problem of robust graph filter (GF) identification from input-output observations. Different from existing works, we formulate a non-convex optimization problem that operates in the vertex domain and jointly performs GF identification and graph denoising. As a result, on top of learning the desired GF, an estimate of the graph is obtained as a byproduct. To handle the resulting bi-convex problem, we design an algorithm that blends techniques from alternating optimization and majorization minimization, showing its convergence to a stationary point. The second part of the paper i) generalizes the design to a robust setup where several GFs are jointly estimated, and ii) introduces an alternative algorithmic implementation that reduces the computational complexity. Finally, the detrimental influence of the perturbations and the benefits resulting from the robust approach are numerically analyzed over synthetic and real-world datasets, comparing them with other state-of-the-art alternatives.

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As data quality and quantity increase, the prediction of future events using machine learning (ML) techniques across engineering disciplines grows by the day. Air transportation cannot be an exception. Delay prediction is paramount in the aerospace industry, since air traffic delays are responsible for millions of dollars in losses to airlines and passengers, along with negative impacts on the environment. In this contribution, we leverage recent signal processing and ML advances to put forth a processing-and-learning pipeline for the prediction of air traffic delays. The proposed approach is executed in several steps. Firstly, we apply signal processing and data science techniques to filter and denoise the original information. Secondly, we run a descriptive analysis of the data and design new features tailored to the prediction problem. Thirdly, we implement a scheme to select the most informative of those features, contributing to a better generalization performance, and offering useful insights. Two algorithms are used to that end: one based on random forests and one employing a sparse logistic regression approach. Finally, once the features are selected, we implement, analyse, and compare several ML architectures (from classical classifiers to deep learning) to predict the delay. While the focus of the comparison is prediction accuracy, metrics such as sample and computational complexity are also discussed. Numerical experiments are drawn from the US domestic market for the year 2018, when more than 7 million flights between 358 airports were flown. The designed processing/learning pipeline reveals interesting insights and achieves better prediction results than the state of the art. The results confirm that air traffic delay prediction is a challenging problem, mainly because the delay is extremely airport-dependent and the data is highly unbalanced (i.e., only a small percentage of flights are noticeable delayed), and identify worth-pursuing future lines of work.