Kernel Adaptive Filtering Algorithms with Improved Tracking Ability

Released on by Jad Kabbara
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  • Kernel Adaptive Filtering Algorithms with Improved Tracking Ability Book Detail

  • Author : Jad Kabbara
  • Release Date : 2014
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  • File Size : 6,6 MB
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Kernel Adaptive Filtering Algorithms with Improved Tracking Ability by Jad Kabbara PDF Summary

Book Description: "In recent years, there has been an increasing interest in kernel methods in areas such as machine learning and signal processing as these methods show strong performance in classification and regression problems. Interesting "kernelized" extensions of many well-known algorithms in artificial intelligence and signal processing have been presented, particularly, kernel versions of the popular online recursive least squares (RLS) adaptive algorithm, namely kernel RLS (KRLS). These algorithms have been receiving significant attention over the past decade in statistical estimation problems, among which those problems involving tracking time-varying systems. KRLS algorithms obtain a non-linear least squares (LS) regressor as a linear combination of kernel functions evaluated at the elements of a carefully chosen subset, called a dictionary, of the received input vectors. As such, the number of coefficients in that linear combination, i.e., the weights, is equal to the size of the dictionary. This coupling between the number of weights and the dictionary size introduces a trade-off. On one hand, a large dictionary would accurately capture the dynamics of the input-output relationship over time. On the other, it has a detrimental effect on the algorithm's ability to track changes in that relationship because having to adjust a large number of weights can significantly slow down adaptation. In this thesis, we present a new KRLS algorithm designed specifically for the tracking of time-varying systems. The key idea behind the proposed algorithm is to break the dependency of the number of weights on the dictionary size. In the proposed method, the number of weights K is fixed and is independent from the dictionary size.Particularly, we use a novel hybrid approach for the construction of the dictionary that employs the so-called surprise criterion for admitting data samples along with a simple pruning method ("remove-the-oldest") that imposes a hard limit on the dictionary size. Then, we propose to construct a K-sparse LS regressor tracking the relationship of the most recent training input-output pairs using the K dictionary elements that provide the best approximation of the output values. Identifying those dictionary elements is a combinatorial optimization problem with a prohibitive computational complexity. To overcome this, we extend the Subspace Pursuit algorithm (SP) which, in essence, is a low complexity method to obtain LS solutions with a pre-specified sparsity level, to non-linear regression problems and introduce a kernel version of SP, which we call Kernel SP (KSP). The standard KRLS is used to recursively update the weights until a new dictionary element selection is triggered by the admission of a new input vector to the dictionary. Simulations show that that the proposed algorithm outperforms existing KRLS-type algorithms in tracking time-varying systems and highly chaotic time series." --

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