Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data
This work addresses the challenge of modeling multivariate data for applications like brain-computer interfaces, though it appears incremental as it builds on existing graph-based methods.
The paper tackles the problem of representing multivariate signals by proposing a Graph-Dictionary signal model that uses a weighted sum of graph Laplacians to capture complex relationships, and it shows improved graph reconstruction in synthetic settings and better classification of imagined motion in brain activity data compared to baselines.
Representing and exploiting multivariate signals require capturing complex relations between variables. We define a novel Graph-Dictionary signal model, where a finite set of graphs characterizes relationships in data distribution through a weighted sum of their Laplacians. We propose a framework to infer the graph dictionary representation from observed data, along with a bilinear generalization of the primal-dual splitting algorithm to solve the learning problem. Our new formulation allows to include a priori knowledge on signal properties, as well as on underlying graphs and their coefficients. We show the capability of our method to reconstruct graphs from signals in multiple synthetic settings, where our model outperforms previous baselines. Then, we exploit graph-dictionary representations in a motor imagery decoding task on brain activity data, where we classify imagined motion better than standard methods relying on many more features.