49,536 research outputs found
The Rank of the Covariance Matrix of an Evanescent Field
Evanescent random fields arise as a component of the 2-D Wold decomposition
of homogenous random fields. Besides their theoretical importance, evanescent
random fields have a number of practical applications, such as in modeling the
observed signal in the space time adaptive processing (STAP) of airborne radar
data. In this paper we derive an expression for the rank of the low-rank
covariance matrix of a finite dimension sample from an evanescent random field.
It is shown that the rank of this covariance matrix is completely determined by
the evanescent field spectral support parameters, alone. Thus, the problem of
estimating the rank lends itself to a solution that avoids the need to estimate
the rank from the sample covariance matrix. We show that this result can be
immediately applied to considerably simplify the estimation of the rank of the
interference covariance matrix in the STAP problem
Structural Analysis of Network Traffic Matrix via Relaxed Principal Component Pursuit
The network traffic matrix is widely used in network operation and
management. It is therefore of crucial importance to analyze the components and
the structure of the network traffic matrix, for which several mathematical
approaches such as Principal Component Analysis (PCA) were proposed. In this
paper, we first argue that PCA performs poorly for analyzing traffic matrix
that is polluted by large volume anomalies, and then propose a new
decomposition model for the network traffic matrix. According to this model, we
carry out the structural analysis by decomposing the network traffic matrix
into three sub-matrices, namely, the deterministic traffic, the anomaly traffic
and the noise traffic matrix, which is similar to the Robust Principal
Component Analysis (RPCA) problem previously studied in [13]. Based on the
Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated
Proximal Gradient (APG) algorithm, we present an iterative approach for
decomposing a traffic matrix, and demonstrate its efficiency and flexibility by
experimental results. Finally, we further discuss several features of the
deterministic and noise traffic. Our study develops a novel method for the
problem of structural analysis of the traffic matrix, which is robust against
pollution of large volume anomalies.Comment: Accepted to Elsevier Computer Network
Optimal CUR Matrix Decompositions
The CUR decomposition of an matrix finds an
matrix with a subset of columns of together with an matrix with a subset of rows of as well as a
low-rank matrix such that the matrix approximates the matrix
that is, , where
denotes the Frobenius norm and is the best matrix
of rank constructed via the SVD. We present input-sparsity-time and
deterministic algorithms for constructing such a CUR decomposition where
and and rank. Up to constant
factors, our algorithms are simultaneously optimal in and rank.Comment: small revision in lemma 4.
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