Related papers: Matrices with prescribed row and column sums
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…
This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith…
The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose…
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…
The theory of the column-row determinants has been considered for matrices over a non-split quaternion algebra. In this paper the concepts of column-row determinants are extending to a split quaternion algebra. New definitions of the column…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
We investigate eigenvector statistics of the Truncated Unitary ensemble $\mathrm{TUE}(N,M)$ in the weakly non-unitary case $M=1$, that is when only one row and column are removed. We provide an explicit description of generalized overlaps…
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…
It is well known that any positive matrix can be scaled to have prescribed row and column sums by multiplying its rows and columns by certain positive scaling factors (which are unique up to a positive scalar). This procedure is known as…
We show that the {\em column sum optimization problem}, of finding a $(0,1)$-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all…
The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see…
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
A binary contingency table is an m x n array of binary entries with prescribed row sums r=(r_1,...,r_m) and column sums c=(c_1,...,c_n). The configuration model for uniformly sampling binary contingency tables proceeds as follows. First,…
The CP 2002 paper entitled "Breaking Row and Column Symmetries in Matrix Models" by Flener et al. (https://link.springer.com/chapter/10.1007%2F3-540-46135-3_31) describes some of the first work for identifying and analyzing row and column…
Biclustering is a method for detecting homogeneous submatrices in a given observed matrix, and it is an effective tool for relational data analysis. Although there are many studies that estimate the underlying bicluster structure of a…