FEMa: a finite element machine for fast learning

  • Danilo R. Pereira
  • Marco Antonio Piteri
  • André N. Souza
  • João Paulo PapaEmail author
  • Hojjat Adeli
Original Article


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.


Finite element method Pattern classification Pattern recognition 



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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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.UNOESTE - University of Western São PauloPresidente PrudenteBrazil
  2. 2.UNESP - São Paulo State UniversityBauruBrazil
  3. 3.OSU - The Ohio State UniversityColumbusUSA

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