Reviews: Structured Graph Learning Via Laplacian Spectral Constraints

Learning graphs from data is an important problem finding many practical applications. This paper contributes by a new regularization strategy that employs spectral constraints of graph Laplacian. The resulting algorithm appears to be novel and technically sound. However, I think this paper will benefit significantly from major revision making the practical relevance of the proposed approach clearer: 1) The authors originally suggested four different spectral constraints but only one of them (k-component graph) was actually evaluated. Implementing and evaluating more than one constraints in this framework could help understand the nature of this strategy.