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

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