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New perspectives on optimal transforms of random vectors

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Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 32))

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Abstract

We present a new transform which is optimal over the class of transforms generated by second-degree polynomial operators. The transform is based on the solution of the best constrained approximation problem with the approximant formed by a polynomial operator. It is shown that the new transform has advantages over the Karhunen–Loève transform, arguably the most popular transform, which is optimal over the class of linear transforms of fixed rank. We provide a strict justification of the technique, demonstrate its advantages and describe useful extensions and applications.

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Authors and Affiliations

  1. Centre for Industrial and Applicable Mathematics, The University of South Australia, Mawson Lakes, SA 5095, Australia

    P. G. Howlett

  2. School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia

    C. E. M. Pearce

  3. Centre for Industrial and Applicable Mathematics, The University of South Australia, Mawson Lakes, SA 5095, Australia

    A. P. Torokhti

Authors
  1. P. G. Howlett
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  2. C. E. M. Pearce
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  3. A. P. Torokhti
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Correspondence to P. G. Howlett .

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    © 2009 Springer-Verlag New York

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    Howlett, P.G., Pearce, C.E.M., Torokhti, A.P. (2009). New perspectives on optimal transforms of random vectors. In: Pearce, C., Hunt, E. (eds) Optimization. Springer Optimization and Its Applications, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-0-387-98096-6_13

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