Time-series and persistence

Recently, I’ve been working on a project to apply persistent homology to neural spike train data, with the particular goal of seeing whether this technique can reveal “low frequency” relationships and co-firing patterns that standard dimensionality reduction methods like PCA have been throwing away. For example, some neurons fire at a very Hz, around ~75-100 Hz, while in fact most neurons fire at ~10-30 Hz in response to some stimulus. The loud, shouty neurons are drowning out the quiet, contemplative ones! What do the quiet neurons know? More to the point, how do I get it out of them? Continue reading