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Efficient approximate Regularized Least Squares by Toeplitz matrix
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DOI：10.1016/j.patrec.2010.10.011.png)
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Machine Learning based on the Regularized Least Squares (RLS) model requires one to solve a system of linear equations. Direct-solution methods exhibit predictable complexity and storage, but often prove impractical for large-scale problems; iterative methods attain approximate solutions at lower complexities, but heavily depend on learning parameters. The paper shows that applying the properties of Toeplitz matrixes to RLS yields two benefits: first, both the computational cost and the memory space required to train an RLS-based machine reduce dramatically; secondly, timing and storage requirements are defined analytically. The paper proves this result formally for the one-dimensional case, and gives an analytical criterion for an effective approximation in multidimensional domains. The approach validity is demonstrated in several real-world problems involving huge data sets with highly dimensional data. (C) 2010 Elsevier B.V. All rights reserved.
Keyword:
Regularized Least Squares
Toeplitz matrix
Levinson-Trench-Zohar algorithm
Digital signal processor
Large-scale learning
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