相关论文: On near and the nearest correlation matrix
In this paper, we discuss the adjacency matrices of finite undirected simple graphs over a finite prime field $\mathbb{F}_p$. We apply symmetric (row and column) elementary transformations to the adjacency matrix over $\mathbb{F}_p$ in…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
We show how some Hamiltonians may be approximated using rotating wave approximation methods. In order to achieve this we use the algebra of boson ladder operators, and transformation formulas between normal and symmetric ordering of the…
In this paper, we study correlation clustering under fairness constraints. Fair variants of $k$-median and $k$-center clustering have been studied recently, and approximation algorithms using a notion called fairlet decomposition have been…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
We propose a simple decoding algorithm for CSS codes taking into account the correlations between the X part and the Z part of the error. Applying this idea to surface codes, we derive an improved version of the perfect matching decoding…
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for…
An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed…
We introduce a graph decomposition which exists for all simple, connected graphs $G=(V,E)$. The decomposition $V = A \cup B \cup C$ is such that each vertex in $A$ has more neighbors in $B$ than in $A$ and vice versa. $C$ is `balanced':…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
The graphical representation of the correlation matrix by means of different multivariate statistical methods is reviewed, a comparison of the different procedures is presented with the use of an example data set, and an improved…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
From fundamental sciences to economics and industry, discrete optimization problems are ubiquitous. Yet, their complexity often renders exact solutions intractable, necessitating the use of approximate methods. Heuristics inspired by…