Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals
This is an incremental improvement for graph learning in applications like brain-network analysis.
The authors tackled the problem of learning sparse weighted graphs from smooth node signals by proposing a majorization-minimization algorithm that eliminates inactive variables without hyperparameter tuning. The result showed faster convergence in terms of average iterations compared to existing methods on synthetic and brain-network data.
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the principle of majorization-minimization (MM), wherein we first obtain a tight surrogate function for the graph learning objective and then solve the resultant surrogate problem which has a simple closed form solution. The proposed algorithm does not require tuning of any hyperparameter and it has the desirable feature of eliminating the inactive variables in the course of the iterations - which can help speeding up the algorithm. The numerical simulations conducted using both synthetic and real world (brain-network) data show that the proposed algorithm converges faster, in terms of the average number of iterations, than several existing methods in the literature.