Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph signal processing tools cannot be used anymore. Researchers have proposed approaches to infer a graph topology from observations of signals on its vertices. Since the problem is ill-posed, these approaches make assumptions, such as smoothness of the signals on the graph, or sparsity priors. In this paper, we propose a characterization of the space of valid graphs, in the sense that they can explain stationary signals. To simplify the exposition in this paper, we focus here on the case where signals were i.i.d. at some point back in time and were observed after diffusion on a graph. We show that the set of graphs verifying this assumption has a strong connection with the eigenvectors of the covariance matrix, and forms a convex set. Along with a theoretical study in which these eigenvectors are assumed to be known, we consider the practical case when the observations are noisy, and experimentally observe how fast the set of valid graphs converges to the set obtained when the exact eigenvectors are known, as the number of observations grows. To illustrate how this characterization can be used for graph recovery, we present two methods for selecting a particular point in this set under chosen criteria, namely graph simplicity and sparsity. Additionally, we introduce a measure to evaluate how much a graph is adapted to signals under a stationarity assumption. Finally, we evaluate how state-of-the-art methods relate to this framework through experiments on a dataset of temperatures.

Few-shot classification aims at leveraging knowledge learned in a deep learning model, in order to obtain good classification performance on new problems, where only a few labeled samples per class are available. Recent years have seen a fair number of works in the field, each one introducing their own methodology. A frequent problem, though, is the use of suboptimally trained models as a first building block, leading to doubts about whether proposed approaches bring gains if applied to more sophisticated pretrained models. In this work, we propose a simple way to train such models, with the aim of reaching top performance on multiple standardized benchmarks in the field. This methodology offers a new baseline on which to propose (and fairly compare) new techniques or adapt existing ones.

We propose EEG-SimpleConv, a straightforward 1D convolutional neural network for Motor Imagery decoding in BCI. Our main motivation is to propose a simple and performing baseline that achieves high classification accuracy, using only standard ingredients from the literature, to serve as a standard for comparison. The proposed architecture is composed of standard layers, including 1D convolutions, batch normalisations, ReLU activation functions and pooling functions. EEG-SimpleConv architecture is accompanied by a straightforward and tailored training routine, which is subjected to an extensive ablation study to quantify the influence of its components. We evaluate its performance on four EEG Motor Imagery datasets, including simulated online setups, and compare it to recent Deep Learning and Machine Learning approaches. EEG-SimpleConv is at least as good or far more efficient than other approaches, showing strong knowledge-transfer capabilities across subjects, at the cost of a low inference time. We believe that using standard components and ingredients can significantly help the adoption of Deep Learning approaches for BCI. We make the code of the models and the experiments accessible.