An Improved Traffic Matrix Decomposition Method with Frequency-Domain Regularization

We propose a novel network traffic matrix decomposition method named Stable Principal Component Pursuit with Frequency-Domain Regularization (SPCP-FDR), which improves the Stable Principal Component Pursuit (SPCP) method by using a frequency-domain noise regularization function. An experiment demonstrates the feasibility of this new decomposition method.Comment: Accepted to IEICE Transactions on Information and System

On the semicircular law of large dimensional random quaternion matrices

It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a natural idea we want to get more universal results by removing the Gaussian condition. For the first step, in this paper we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.Comment: 20 page

On the limit of extreme eigenvalues of large dimensional random quaternion matrices

Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin (1988) obtained the necessary and sufficient conditions for the strong convergence of the extreme eigenvalues of a Wigner matrix. In this paper, we consider the case of quaternion self-dual Hermitian matrices. We prove the necessary and sufficient conditions for the strong convergence of extreme eigenvalues of quaternion self-dual Hermitian matrices corresponding to the Wigner case.Comment: 16 pages, 5 figure