Structured BFGS Method for Optimal Doubly Stochastic Matrix Approximation

Stochastic algorithms for solving structured low-rank matrix approximation problems

In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. We demonstrate that finding optimal s...

An asymptotic approximation for the permanent of a doubly stochastic matrix

A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order O(n−1). keywords: Doubly stochastic Dirichlet distribution; Maximum-likelihood projection; Sinkhorn projection

A Parallel BFGS-SQP Method for Stochastic Linear Programs

Matrix Conditioning and Adaptive Simultaneous Perturbation Stochastic Approximation Method

This paper proposes a modification to the simultaneous per tu rba t ion stochastic approximation (SPSA) methods based on the comparisons made between the first o rder and the second order SPSA (1SPSA and 2SPSA) algori thms f rom the perspective of loss function Hessian. At finite iterations, the convergence rate depends on the matr ix conditioning of the loss function Hessian. It is shown that ...

Low-Rank Doubly Stochastic Matrix Decomposition for Cluster Analysis

Cluster analysis by nonnegative low-rank approximations has experienced a remarkable progress in the past decade. However, the majority of such approximation approaches are still restricted to nonnegative matrix factorization (NMF) and suffer from the following two drawbacks: 1) they are unable to produce balanced partitions for large-scale manifold data which are common in real-world clusterin...