Intrinsic dimensionality analysis of neuronal population activity

The manifold hypothesis in application to neural data states that brain activity patterns are confined to a low-dimensional manifold that spans a small fraction of the theoretically available state space. We test this hypothesis using in vivo calcium imaging data from hippocampal neurons in mice during novel arena exploration. We compute the intrinsic dimensionality of neural activity and compare it with other dimensionality estimates. Due to the inevitable scarcity of in vivo recordings, both in terms of neurons recorded and duration, we follow the dimensionality patterns as the amount of available data increases. We find a nontrivial power-law scaling of intrinsic dimension with the number of recorded neurons, and discuss its potential biological significance.