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Perturbation of matrices and non-negative rank with a view toward statistical models
Euclidean topology Jacobian matrix mixture models
2010/10/19
In this paper we study how perturbing a matrix changes its non-negative rank. We show that the non-negative rank is upper-semicontinuos and we describe some special families of perturbations. We apply...
Consider the matrix Δn = (( I(Xi + Xj > 0) ))i,j =1,2,...,n where Xi are i.i.d. and their distribution is continuous and symmetric around 0. We show that the rank rn of this matrix is equal in dist...
On asymptotic properties of the rank of a special random adjacency matrix
asymptotic property random matrix adjacency matrix
2009/3/23
Consider the matrix Δn = (( I(Xi + Xj > 0) ))i,j =1,2,...,n where Xi are i.i.d. and their distribution is continuous and symmetric around 0. We show that the rank rn of this matrix is equal in dist...