Reconstructing the topologies of hippocampal cognitive maps.

D.S. Touretzky1,2, A. Gupta3,2, M.C.Fuhs1,2, P. Dollar4, A.P. Maurer5, B.L.McNaughton5

1Computer Science Dept., Carnegie Mellon; Pittsburgh, PA
2Center for the Neural Basis of Cognition, Carnegie Mellon; Pittsburgh, PA
3Robotics Institute, Carnegie Mellon; Pittsburgh, PA
4Computer Science Dept., UCSD, San Diego, CA
5Div. of Neural Systems, Memory, and Aging, Univ. of Arizona, Tucson, AZ

The population activity of place cells in the rodent hippocampus was suggested by O'Keefe and Nadel to implement Tolman's notion of a "cognitive map." Such maps need not be simple 2D surfaces with points in 1-1 correspondence with physical locations. Rodents can exhibit different place codes in the same location, depending on behavioral variables such as direction of travel or phase of task. They can also show the same place code at distinct locations, e.g., two visually identical boxes connected by a corridor (Fuhs et. al, 2005). The true shape of the hippocampal cognitive map must be reconstructed from the population activity data.

We used techniques from machine learning to reconstruct maps from several datasets: a circular track with barrier (82 cells), a rectangular arena (45-50 cells), and two connected boxes (43 real cells plus 45 synthetic cells created by horizontally or vertically flipping real place fields). In some cases we used the actual spike trains; in others we generated synthetic spike trains from spatially smoothed place fields plus the actual rat trajectory. Noise was reduced by temporal (and optionally spatial) smoothing. Three dimensionality reduction algorithms were tried: ISOMAP (Tenenbaum et al., 2000), MVU (Weinberger and Saul, 2006), and our own procedure that uses a combination of EM, a node-linking heuristic, and a spring force layout algorithm. The figure shows the results of our algorithm on real spike train data from a circular track (left), and on synthetic spike train data from two connected boxes (right). Since place cells were directional on the circular track, the map exhibited a double ring topology which differs from the physical environment. In the two connected boxes environment, the distinction between the boxes is clear; the rat made too few journeys between them for our algorithm to recover the passageway.

Studying the topologies of reconstructed cognitive maps is a promising approach to understanding how the integration of spatial and other contextual information (e.g., behavior) leads to complex hippocampal representation of the animal's world.

Keyword (Complete): hippocampus; place cells; cognitive map; dimensionality reduction