Matrix scaling and explicit doubly stochastic limits

Spatial stochastic network models: scaling limits and Monte-Carlo methods

Matrix Models, Argyres-Douglas singularities and double scaling limits

We construct an N = 1 theory with gauge group U(nN) and degree n + 1 tree level superpotential whose matrix model spectral curve develops an Argyres-Douglas singularity. The calculation of the tension of domain walls in the U(nN) theory shows that the standard large N expansion breaks down at the Argyres-Douglas points, with tension that scales as a fractional power of N . Nevertheless, it is p...

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...

Matrix Eigen-decomposition via Doubly Stochastic Riemannian Optimization

Matrix eigen-decomposition is a classic and long-standing problem that plays a fundamental role in scientific computing and machine learning. Despite some existing algorithms for this inherently non-convex problem, the study remains inadequate for the need of large data nowadays. To address this gap, we propose a Doubly Stochastic Riemannian Gradient EIGenSolver, DSRG-EIGS, where the double sto...

Computing the Nearest Doubly Stochastic Matrix with A Prescribed Entry

In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1, 1) entry to a given matrix. According to the well-established dual theory in optimization, the dual of the underlying problem is an unconstrained differentiable but not twice differentiable convex optimization problem. A Newton-type method is ...