Importance attribution in neural networks by means of persistence landscapes of time series
This work addresses interpretability in neural networks for domain-specific applications like medical signal analysis, though it appears incremental as it builds on existing topological methods.
The authors tackled the problem of interpreting neural network decisions for time series classification by using topological data analysis to identify key features in electrocardiographic signals, achieving a method that reconstructs approximate shapes of time series to provide insight into classification decisions.
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.