相关论文: On the linear equation method for the subduction p…

An important problem in the field of graph signal processing is developing appropriate overcomplete dictionaries for signals defined on different families of graphs. The Cayley graph of the symmetric group has natural applications in ranked…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately,…

We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary $R$-matrix and to a simple object in a unitary braided fusion category. Unitary $R$-matrices, namely unitary solutions to the…

We consider a group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose…

We investigate a principled approach for symbolic operation completion (SOC), a minimal task for studying symbolic reasoning. While conceptually similar to matrix completion, SOC poses a unique challenge in modeling abstract relationships…

Calculations of the number of equivalence classes of Sudoku boards has to this point been done only with the aid of a computer, in part because of the unnecessarily large symmetry group used to form the classes. In particular, the…

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this…

Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

For solving the continuous Sylvester equation, a class of the multiplicative splitting iteration method is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations…

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label…

Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with undirected graphs have been defined and studied in several seemingly independent areas including number theory, discrete geometry, and dynamical systems. In particular,…

The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…

The set $X$ of $k$-subsets of an $n$-set has a natural graph structure where two $k$-subsets are connected if and only if the size of their intersection is $k-1$. This is known as the Johnson graph. The symmetric group $S_n$ acts on the…

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…

We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive…

In the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations…