Canonical correlation analysis based on sparse penalty and through rank-1 matrix approximation

Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA and smooth or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper two new algorithms for sparse CCA and smooth CCA are proposed. These algorithms differ from the existing ones in their derivation which is based on penalized rank one matrix approximation and the orthogonal projectors onto the space spanned by the columns of the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithms are tested on simulated experiments. On these results it can be observed that they outperforms the state of the art sparse CCA algorithms

Adaptive kernel canonical correlation analysis algorithms for nonparametric identification of Wiener and Hammerstein systems

This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA) emerges as the logical solution to this problem.We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm

Online Kernel Canonical Correlation Analysis for Supervised Equalization of Wiener Systems

Abstract-We consider the application of kernel canonical correlation analysis (K-CCA) to the supervised equalization of Wiener systems. Although a considerable amount of research has been carried out on identification/equalization of Wiener models, in this paper we show that K-CCA is a particularly suitable technique for the inversion of these nonlinear dynamic systems. Another contribution of this paper is the development of an online K-CCA algorithm which combines a slidingwindow approach with a recently proposed reformulation of CCA as an iterative regression problem. This online algorithm permits fast equalization of time-varying Wiener systems. Simulation examples are added to illustrate the performance of the proposed method

Blind Identification via Lifting

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.Comment: Submitted to the IFAC World Congress 2014. arXiv admin note: text overlap with arXiv:1303.671

State–of–the–art report on nonlinear representation of sources and channels

This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels

Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system's requirements. Recently, a closed-form approximated expression was derived by the same author for the residual ISI obtained by nonblind adaptive equalizers for the single-input single-output (SISO) case. Up to now, there does not exist a closed-form expression for the residual ISI obtained by nonblind adaptive equalizers for the single-input multiple-output (SIMO) case. Furthermore, there does not exist a closed-form expression for the SER valid for the SISO or SIMO case that takes into account the residual ISI obtained by nonblind adaptive equalizers and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of 0.5 ≤ < 1. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO), valid for fGn input where the Hurst exponent is in the region of 0.5 ≤ < 1. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case

Adaptive noise cancellation using multichannel lattice structure.

This thesis presents a multichannel adaptive noise cancellation technique (MCLS) for cancelling the noise over nonlinear transmission channel. The technique applies to the situation in which the reference signal and noisy primary signal are collected simultaneously. The coefficients of the multichannel multiple regression transversal filter are modified adaptively according to the backward prediction error vector generated from the multichannel adaptive lattice predictor. This multichannel adaptive noise cancellation procedure involves the NLMS adaptive algorithm. The performance of the new technique using different types of transmission channels, different types of reference inputs and different types of noise-free primary inputs are examined analytically. The new approach is experimentally shown to have better noise cancellation performance than the existing single-channel adaptive lattice noise cancellation algorithm (SCLS) over nonlinear transmission channel case, especially in low input SNR situation.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .X54. Source: Masters Abstracts International, Volume: 43-01, page: 0288. Adviser: H. K. Kwan. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004