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Hyperconic Multilayer Perceptron

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Abstract

This paper introduces the design of the hyperconic multilayer perceptron (HC-MLP). Complex non-linear decision regions for classification purposes are generated by quadratic hyper-surfaces spawned by the hyperconic neurons in the hidden layer (for instance, spheres, ellipsoids, paraboloids, hyperboloids and degenerate conics). In order to generate quadratic hyper-surfaces, the hyperconic neurons’ transfer function includes the estimation of a quadratic polynomial. The proper assignment of decision regions to classes is achieved in the output layer by using spheres to determine whether a point is inside or outside the spherical region. The particle swarm optimization algorithm is used for training the HC-MLP. The learning of the HC-MLP selects the best conic surface that separates the data set vectors. For illustration purposes, two experiments are conducted using two distributions of synthetic data in order to show the advantages of HC-MLP when the patterns between classes are contiguous. Furthermore a comparison to the traditional multilayer perceptron is carried out to evaluate the complexity (in terms of the number of estimated patterns) and classification accuracy. HC-MLP is the principal component to implement a diagnosis system to detect faults in an induction motor and to implement an image segmentation system. The performance of HC-MLP is compared to other leading algorithms by using 4 databases commonly used in related literature.

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Acknowledgments

The first author would like to thank to Antonio Zamarron for technical advice in induction motors. The third author would like to thank the International Centre for Theoretical Physics (ICTP) and the Institut Des Hautes Etudes Scientifiques (IHES) for its hospitality and support.

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Authors and Affiliations

  1. Information Technologies Laboratory, Technological Institute of Irapuato (ITESI), Irapuato, Guanajuato, Mexico

    Juan Pablo Serrano-Rubio

  2. Computer Science Department, Center for Research in Mathematics (CIMAT), Guanajuato, Mexico

    Arturo Hernández-Aguirre

  3. Mathematics Department, Center for Research in Mathematics (CIMAT), Guanajuato, Mexico

    Rafael Herrera-Guzmán

Authors
  1. Juan Pablo Serrano-Rubio
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  2. Arturo Hernández-Aguirre
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  3. Rafael Herrera-Guzmán
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Correspondence to Juan Pablo Serrano-Rubio.

Additional information

Juan Pablo Serrano-Rubio is partially supported by a PRODEP grant and Rafael Herrera-Guzmán is partially supported by a CONACYT grant.

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Serrano-Rubio, J.P., Hernández-Aguirre, A. & Herrera-Guzmán, R. Hyperconic Multilayer Perceptron. Neural Process Lett 45, 29–58 (2017). https://doi.org/10.1007/s11063-016-9505-2

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