Evolving Systems

, Volume 10, Issue 3, pp 381–396 | Cite as

Dendrite ellipsoidal neurons based on k-means optimization

  • Fernando ArceEmail author
  • Erik Zamora
  • Carolina Fócil-Arias
  • Humberto Sossa
Original Paper


Dendrite morphological neurons are a type of artificial neural network that can be used to solve classification problems. The major difference with respect to classical perceptrons is that morphological neurons create hyperboxes to separate patterns from different classes, while perceptrons use hyperplanes. In this paper, we introduce an improved version of dendrite morphological neural networks, which we have called dendrite ellipsoidal neuron that employs hyperellipsoids instead of hyperboxes. This ellipsoidal neuron is presented with a new training algorithm, to set the covariance matrix and the centroid of each hyperellipsoid based on k-means++, by applying hill climbing to search for an optimum number of hyperellipsoids. The main advantage of this approach is that dendrite ellipsoidal neuron creates smoother decision boundaries. The proposed neural model was tested on synthetic and real datasets from the UCI machine learning repository (in a paired t-test) achieving an average accuracy of 80.7%, while multi-layer perceptrons gave 78.4%, support vector machines obtained 74.2%, and radial basis networks 72.7%. Lastly, to test the proposed method performance in solving real practical problems, our model was used to detect lane lines on an urban highway, for classifying figures with a Nao robot and for traffic detection.


Morphological neurons Dendrite morphological neural networks k-means++ Ellipsoidal neuron 



E. Zamora and H. Sossa would like to acknowledge the support provided by UPIITA-IPN and CIC-IPN in carrying out this research. This work was economically supported by SIP-IPN (grant numbers 20170836 and 20170693), and CONACYT grant number 65 (Frontiers of Science). F. Arce and C. Fócil-Arias acknowledge CONACYT for the scholarship granted towards pursuing their PhD studies. All the authors thank to the students exchange program Delfín and to the exchange students for implementing some DEN applications.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Fernando Arce
    • 1
    Email author
  • Erik Zamora
    • 2
  • Carolina Fócil-Arias
    • 1
  • Humberto Sossa
    • 1
    • 3
  1. 1.Instituto Politécnico Nacional, CICMexico CityMexico
  2. 2.Instituto Politécnico Nacional, UPIITAMexico CityMexico
  3. 3.Tecnológico de Monterrey Campus GuadalajaraZapopanMexico

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