  In present paper we discuss several approaches to reconstructing the topology
of the physical space from neural activity data of CA1 fields in mice
hippocampus, in particular, having Cognitome theory of brain function in mind.
In our experiments, animals were placed in different new environments and
discovered these moving freely while their physical and neural activity was
recorded. We test possible approaches to identifying place cell groups out of
the observed CA1 neurons. We also test and discuss various methods of dimension
reduction and topology reconstruction. In particular, two main strategies we
focus on are the Nerve theorem and point cloud-based methods. Conclusions on
the results of reconstruction are supported with illustrations and mathematical
background which is also briefly discussed.
