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

Abstract

This article describes a method to analyze time series with a neural network using a matrix of area-normalized persistence landscapes obtained with topological data analysis. The network’s architecture includes a gating layer that is able to identify the most relevant landscape levels for a classification task, thus working as an importance attribution system. Next, a matching is performed between the selected landscape levels and the corresponding critical points of the original time series. This matching enables reconstruction of a simplified shape of the time series that gives insight into the grounds of the classification decision. As a use case, this technique is tested in the article with input data from a dataset of electrocardiographic signals. The classification accuracy obtained using only a selection of landscape levels from data was 94.00%pm 0.13 averaged after five runs of a neural network, while the original signals achieved 98.41% pm 0.09 and landscape-reduced signals yielded 97.04% pm 0.14.