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Fixed-size Least Squares Support Vector Machines: A Large Scale Application in Electrical Load Forecasting

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Abstract

Based on the Nyström approximation and the primal-dual formulation of the least squares support vector machines, it becomes possible to apply a nonlinear model to a large scale regression problem. This is done by using a sparse approximation of the nonlinear mapping induced by the kernel matrix, with an active selection of support vectors based on quadratic Renyi entropy criteria. The methodology is applied to the case of load forecasting as an example of a real-life large scale problem in industry. The forecasting performance, over ten different load series, shows satisfactory results when the sparse representation is built with less than 3% of the available sample.

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Authors and Affiliations

  1. ESAT/SISTA, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, 3000, Leuven, Belgium

    Marcelo Espinoza, Johan A. K. Suykens & Bart De Moor

Authors
  1. Marcelo Espinoza
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  2. Johan A. K. Suykens
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  3. Bart De Moor
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Corresponding author

Correspondence to Marcelo Espinoza.

Additional information

This work is supported by grants and projects for the Research Council K.U.Leuven (GOA-Mefisto 666, GOA-Ambiorics, several PhD/ Postdocs & fellow grants), the Flemish Government (FWO: PhD/ Postdocs grants, projects G.0211.05, G.0240.99, G.0407.02, G.0197.02, G.0141.03, G.0491.03, G.0120.03, G.0452.04, G.0499.04, ICCoS, ANMMM; AWI; IWT: PhD grants, GBOU (McKnow) Soft4s), the Belgian Federal Government (Belgian Federal Science Policy Office: IUAP V-22; PODO-II (CP/ 01/40), the EU (FP5- Quprodis; ERNSI, Eureka 2063- Impact; Eureka 2419- FLiTE) and Contracts Research / Agreements (ISMC /IPCOS, Data4s, TML, Elia, LMS, IPCOS, Mastercard). J. Suykens and B. De Moor are an associate professor and a full professor with K.U.Leuven, Belgium, respectively. The scientific responsibility is assumed by its authors.

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Espinoza, M., Suykens, J.A.K. & Moor, B.D. Fixed-size Least Squares Support Vector Machines: A Large Scale Application in Electrical Load Forecasting. CMS 3, 113–129 (2006). https://doi.org/10.1007/s10287-005-0003-7

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