In this paper some sufficient conditions are given for when two bounded rank-one transformations non-isomorphic and they disjoint. We also obtain a transformation to have minimal self-joinings. For c

In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. many cases, the challenge to discover low-dimensional structure in data, often concealed by existence of nuisance parameters and noise. Motivated such challenges, we consider problem estimating signal its scaled, cyclically shifted noisy observations. We focus on particula...

We provide the first positive result on nonsmooth optimization landscape of robust principal component analysis, to best our knowledge. It is object several conjectures and remains mostly uncharted territory. identify a necessary sufficient condition for absence spurious local minima in rank-one case. Our proof exploits subdifferential regularity objective function order eliminate existence qua...

let h be a finite dimensional complex hilbert space, b(h)+ be the set of all positive semi-definite operators on h and phi is a (not necessarily linear) unital map of b(h) + preserving the entropy-gibbs transformation. then there exists either a unitary or an anti-unitary operator u on h such that phi(a) = uau* for any b(h) +. thermodynamics, a branch of physics that is concerned with the study...

Finding the symmetric and orthogonal decomposition (SOD) of a tensor is a recurring problem in signal processing, machine learning and statistics. In this paper, we review, establish and compare the perturbation bounds for two natural types of incremental rank-one approximation approaches. Numerical experiments and open questions are also presented and discussed.

We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n ? 1 real parameters. This representation, which we refer to as the Schur parameterization of H; facilitates the development of eecient algorithms for this class of matrices. We...

Abstract We show how the spectrum of a graph Laplacian changes with respect to certain type rank-one perturbation. apply our finding give new short proofs spectral version Kirchhoff’s Matrix Tree Theorem and known derivations for characteristic polynomials Laplacians several well-known families graphs, including complete, complete multipartite, crown threshold graphs.

Today, we will shift gears and begin to discuss RandNLA algorithms for low-rank matrix approximation. We will start with additive-error low-rank matrix approximation with sampling and projections. These are of interest historically and since they illustrate several techniques (normsquared sampling, simple linear algebraic manipulations, the use of matrix perturbation theory, etc.), but they are...