Laplacian Related Constraint

Laplacian-related constraints are used in various fields to learn graph structures from data, focusing on efficiently estimating sparse precision matrices that represent conditional dependencies. Current research emphasizes developing algorithms, such as proximal Newton methods and ADMM, to solve optimization problems incorporating these constraints, often alongside sparsity-inducing penalties like the $\ell_0$ or MCP norms, to improve accuracy and efficiency. These techniques find applications in diverse areas including network topology inference, crystal structure prediction, and subspace clustering, enabling improved modeling of complex relationships within data.