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FEMa: a finite element machine for fast learning

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Abstract

Machine learning has played an essential role in the past decades and has been in lockstep with the main advances in computer technology. Given the massive amount of data generated daily, there is a need for even faster and more effective machine learning algorithms that can provide updated models for real-time applications and on-demand tools. This paper presents FEMa—a finite element machine classifier—for supervised learning problems, where each training sample is the center of a basis function, and the whole training set is modeled as a probabilistic manifold for classification purposes. FEMa has its theoretical basis in the finite element method, which is widely used for numeral analysis in engineering problems. It is shown FEMa is parameterless and has a quadratic complexity for both training and classification phases when basis functions are used that satisfy certain properties. The proposed classifier yields very competitive results when compared to some state-of-the-art supervised pattern recognition techniques.

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Notes

  1. http://www.csie.ntu.edu.tw/ cjlin/libsvmtools/datasets.

  2. https://github.com/danillorp/libFemClassifier.

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Acknowledgements

The authors would like to thank FAPESP Grants #2013/07375-0, #2014/16250-9, #2014/12236-1, and #2016/19403-6, FAPESP/OSU Grant #2015/50319-9, and CNPq Grants #306166/2014-3 and #307066/2017-7.

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Authors and Affiliations

  1. UNOESTE - University of Western São Paulo, Presidente Prudente, Brazil

    Danilo R. Pereira

  2. UNESP - São Paulo State University, Bauru, Brazil

    Marco Antonio Piteri, André N. Souza & João Paulo Papa

  3. OSU - The Ohio State University, Columbus, USA

    Hojjat Adeli

Authors
  1. Danilo R. Pereira
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  2. Marco Antonio Piteri
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  3. André N. Souza
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  4. João Paulo Papa
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  5. Hojjat Adeli
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Correspondence to João Paulo Papa.

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Pereira, D.R., Piteri, M.A., Souza, A.N. et al. FEMa: a finite element machine for fast learning. Neural Comput & Applic 32, 6393–6404 (2020). https://doi.org/10.1007/s00521-019-04146-4

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