Efficient approximate Regularized Least Squares by Toeplitz matrix

Authors:
Sergio Decherchi;Paolo Gastaldo;Rodolfo Zunino
Affiliations:
DIBE - Dept. Biophysical and Electronic Eng., University of Genova, V. Opera Pia 11a, 16145 Genova, Italy;DIBE - Dept. Biophysical and Electronic Eng., University of Genova, V. Opera Pia 11a, 16145 Genova, Italy;DIBE - Dept. Biophysical and Electronic Eng., University of Genova, V. Opera Pia 11a, 16145 Genova, Italy
Venue:
Pattern Recognition Letters
Year:
2011

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Abstract

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.