A geometric framework for sparse matrix problems
نویسندگان
چکیده
In this paper, we set up a geometric framework for solving sparse matrix problems. We introduce geometric sparseness, a notion which applies to several well-known families of sparse matrix. Two algorithms are presented for solving geometrically-sparse matrix problems. These algorithms are inspired by techniques in classical algebraic topology, and involve the construction of a simplicial complex from certain data on the matrix. In both cases, large parts of the computation can be parallelised. 2003 Elsevier Inc. All rights reserved.
منابع مشابه
Estimation in High Dimensions: a Geometric Perspective
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse ...
متن کاملThe Geometry of Multivariate Polynomial Division and Elimination
Multivariate polynomials are usually discussed in the framework of algebraic geometry. Solving problems in algebraic geometry usually involves the use of a Gröbner basis. This talk will show that linear algebra without any Gröbner basis computation suffices to solve basic problems from algebraic geometry. Three basic operations, multiplication, division and elimination, will be described using ...
متن کاملVoice-based Age and Gender Recognition using Training Generative Sparse Model
Abstract: Gender recognition and age detection are important problems in telephone speech processing to investigate the identity of an individual using voice characteristics. In this paper a new gender and age recognition system is introduced based on generative incoherent models learned using sparse non-negative matrix factorization and atom correction post-processing method. Similar to genera...
متن کاملA sparse algorithm for dense optimal transport
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of a new sparse algorithm to solve large dense problems by considering a sequenc...
متن کاملGeometric reconstruction from point-normal data
Creating virtual models of real spaces and objects is cumbersome and time consuming. This paper focuses on the problem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant and simple-to-state problems arise concerning when the geometry can be reconstructed. We describe results and counterexamples, and list open problems.
متن کامل