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Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

  1. Yedidyah Dordek
  2. Daniel Soudry
  3. Ron Meir
  4. Dori Derdikman Is a corresponding author
  1. Technion - Israel Institute of Technology, Israel
  2. Columbia University, United States
  3. Technion - Israel Institute Of technology, Israel
Research Article
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Cite as: eLife 2016;5:e10094 doi: 10.7554/eLife.10094

Abstract

Many recent models study the downstream projection from grid cells to place cells, while recent data has pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells.We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights were learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network were non-negative, the output converged to a hexagonal lattice. Without the non-negativity constraint the output converged to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules was ~1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

Article and author information

Author details

  1. Yedidyah Dordek

    Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel
    Competing interests
    The authors declare that no competing interests exist.
  2. Daniel Soudry

    Department of Statistics, Columbia University, New York, United States
    Competing interests
    The authors declare that no competing interests exist.
  3. Ron Meir

    Faculty of Electrical Engineering, Technion - Israel Institute Of technology, Haifa, Israel
    Competing interests
    The authors declare that no competing interests exist.
  4. Dori Derdikman

    Rappaport Faculty of Medicine and Research Institute, Technion - Israel Institute of Technology, Haifa, Israel
    For correspondence
    derdik@technion.ac.il
    Competing interests
    The authors declare that no competing interests exist.

Reviewing Editor

  1. Michael J Frank, Reviewing Editor, Brown University, United States

Publication history

  1. Received: July 15, 2015
  2. Accepted: March 8, 2016
  3. Accepted Manuscript published: March 8, 2016 (version 1)
  4. Version of Record published: April 13, 2016 (version 2)

Copyright

© 2016, Dordek et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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