pystop.solver.SLPG_l21

X, output_dict = SLPG_l21( obj_fun, manifold, Xinit = None, maxit= 100, gamma = 0, gtol = 1e-5, post_process = True, verbosity = 2, **kwargs)

Description

Minimize fun over the Stiefel manifold by starting from Xinit and applying penalty-free infeasible first-order method. Here the fun can be expressed as f(X)+r(X), where f is smooth and r(X) is 2,1-norm regularizer, i.e. r(X)=i=1nγ||Xi||2. For more details, we suggest the interested reader refer to a related paper.

 

Input arguments

 

Output results

 

Examples

In these examples, we solve the following 2,1-norm regularized PCA problem

minXSn,p 12tr(XAAX)+γ1inXi2,

where Xi refers to the i-th row vector of X and ARn×m is the data matrix. The following examples introduces how to apply SLPG_l21 to solve this problem.