  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.
