Predicting the future of Graph-supported Time Series (GTS) is a key challenge in many domains, such as climate monitoring, finance or neuroimaging. Yet it is a highly difficult problem as it requires to account jointly for time and graph (spatial) dependencies. To simplify this process, it is common to use a two-step procedure in which spatial and time dependencies are dealt with separately. In this paper, we are interested in comparing various linear spatial representations, namely structure-based ones and data-driven ones, in terms of how they help predict the future of GTS. To that end, we perform experiments with various datasets including spontaneous brain activity and raw videos.
Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8-12 Hz) are known to closely resemble short sinusoids, and thus are revealed by Fourier analysis or wavelet transforms, there is an evolving debate that electromagnetic neural signals are composed of more complex waveforms that cannot be analyzed by linear filters and traditional signal representations. In this paper, we propose to learn dedicated representations of such recordings using a multivariate convolutional sparse coding (CSC) algorithm. Applied to electroencephalography (EEG) or magnetoencephalography (MEG) data, this method is able to learn not only prototypical temporal waveforms, but also associated spatial patterns so their origin can be localized in the brain. Our algorithm is based on alternated minimization and a greedy coordinate descent solver that leads to state-of-the-art running time on long time series. To demonstrate the implications of this method, we apply it to MEG data and show that it is able to recover biological artifacts. More remarkably, our approach also reveals the presence of non-sinusoidal mu-shaped patterns, along with their topographic maps related to the somatosensory cortex. We introduce a novel recurrent neural network (RNN) approach to account for temporal dynamics and dependencies in brain networks observed via functional magnetic resonance imaging (fMRI). Our approach directly parameterizes temporal dynamics through recurrent connections, which can be used to formulate blind source separation with a conditional (rather than marginal) independence assumption, which we call RNN-ICA. This formulation enables us to visualize the temporal dynamics of both first order (activity) and second order (directed connectivity) information in brain networks that are widely studied in a static sense, but not well-characterized dynamically. RNN-ICA predicts dynamics directly from the recurrent states of the RNN in both task and resting state fMRI. Our results show both task-related and group-differentiating directed connectivity.