99 research outputs found

    Collaborative adaptive filtering for machine learning

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    Quantitative performance criteria for the analysis of machine learning architectures and algorithms have long been established. However, qualitative performance criteria, which identify fundamental signal properties and ensure any processing preserves the desired properties, are still emerging. In many cases, whilst offline statistical tests exist such as assessment of nonlinearity or stochasticity, online tests which not only characterise but also track changes in the nature of the signal are lacking. To that end, by employing recent developments in signal characterisation, criteria are derived for the assessment of the changes in the nature of the processed signal. Through the fusion of the outputs of adaptive filters a single collaborative hybrid filter is produced. By tracking the dynamics of the mixing parameter of this filter, rather than the actual filter performance, a clear indication as to the current nature of the signal is given. Implementations of the proposed method show that it is possible to quantify the degree of nonlinearity within both real- and complex-valued data. This is then extended (in the real domain) from dealing with nonlinearity in general, to a more specific example, namely sparsity. Extensions of adaptive filters from the real to the complex domain are non-trivial and the differences between the statistics in the real and complex domains need to be taken into account. In terms of signal characteristics, nonlinearity can be both split- and fully-complex and complex-valued data can be considered circular or noncircular. Furthermore, by combining the information obtained from hybrid filters of different natures it is possible to use this method to gain a more complete understanding of the nature of the nonlinearity within a signal. This also paves the way for building multidimensional feature spaces and their application in data/information fusion. To produce online tests for sparsity, adaptive filters for sparse environments are investigated and a unifying framework for the derivation of proportionate normalised least mean square (PNLMS) algorithms is presented. This is then extended to derive variants with an adaptive step-size. In order to create an online test for noncircularity, a study of widely linear autoregressive modelling is presented, from which a proof of the convergence of the test for noncircularity can be given. Applications of this method are illustrated on examples such as biomedical signals, speech and wind data

    Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

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    Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

    Study of L0-norm constraint normalized subband adaptive filtering algorithm

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    Limited by fixed step-size and sparsity penalty factor, the conventional sparsity-aware normalized subband adaptive filtering (NSAF) type algorithms suffer from trade-off requirements of high filtering accurateness and quicker convergence behavior. To deal with this problem, this paper proposes variable step-size L0-norm constraint NSAF algorithms (VSS-L0-NSAFs) for sparse system identification. We first analyze mean-square-deviation (MSD) statistics behavior of the L0-NSAF algorithm innovatively in according to a novel recursion form and arrive at corresponding expressions for the cases that background noise variance is available and unavailable, where correlation degree of system input is indicated by scaling parameter r. Based on derivations, we develop an effective variable step-size scheme through minimizing the upper bounds of the MSD under some reasonable assumptions and lemma. To realize performance improvement, an effective reset strategy is incorporated into presented algorithms to tackle with non-stationary situations. Finally, numerical simulations corroborate that the proposed algorithms achieve better performance in terms of estimation accurateness and tracking capability in comparison with existing related algorithms in sparse system identification and adaptive echo cancellation circumstances.Comment: 15 pages,15 figure
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