Importance attribution in neural networks by means of persistence landscapes of time series

Abstract

We propose and implement a method to analyze time series with a neural network using a matrix of area-normalized persistence landscapes obtained through topological data analysis. We include a gating layer in the network's architecture that is able to identify the most relevant landscape levels for the classification task, thus working as an importance attribution system. Next, we perform a matching between the selected landscape functions and the corresponding critical points of the original time series. From this matching we are able to reconstruct an approximate shape of the time series that gives insight into the classification decision. We test this technique with input data from a dataset of electrocardiographic signals.