Fast Optimization Algorithm on Riemannian Manifolds and Its Application in Low-Rank Representation
This addresses optimization bottlenecks in machine learning applications like matrix completion and low-rank representation, though it appears incremental as an improvement over existing manifold optimization methods.
The paper tackles optimization of composite functions on Riemannian manifolds by proposing a new first-order algorithm (FOA) with quadratic convergence, showing in matrix completion experiments that it outperforms other first-order methods on manifolds and achieves faster convergence and higher accuracy in low-rank representation tasks.
The paper addresses the problem of optimizing a class of composite functions on Riemannian manifolds and a new first order optimization algorithm (FOA) with a fast convergence rate is proposed. Through the theoretical analysis for FOA, it has been proved that the algorithm has quadratic convergence. The experiments in the matrix completion task show that FOA has better performance than other first order optimization methods on Riemannian manifolds. A fast subspace pursuit method based on FOA is proposed to solve the low-rank representation model based on augmented Lagrange method on the low rank matrix variety. Experimental results on synthetic and real data sets are presented to demonstrate that both FOA and SP-RPRG(ALM) can achieve superior performance in terms of faster convergence and higher accuracy.