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

arXiv: https://arxiv.org/abs/2302.03132 · HTML: https://mlsanity.com/paper/2302.03132/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Computing the Testing Error without a Testing Set](https://mlsanity.com/paper/2005.00450/) (2020)
- [Activation Landscapes as a Topological Summary of Neural Network Performance](https://mlsanity.com/paper/2110.10136/) (2021)
- [Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks](https://mlsanity.com/paper/1906.05795/) (2019)
- [Predicting the generalization gap in neural networks using topological data analysis](https://mlsanity.com/paper/2203.12330/) (2022)
- [Topology-based Representative Datasets to Reduce Neural Network Training Resources](https://mlsanity.com/paper/1903.08519/) (2019)
- [Reconstructing Embedded Graphs from Persistence Diagrams](https://mlsanity.com/paper/1912.08913/) (2019)
- [Understanding Deep Neural Networks Using Topological Data Analysis](https://mlsanity.com/paper/1811.00852/) (2018)
- [Reconstruction of univariate functions from directional persistence diagrams](https://mlsanity.com/paper/2203.01894/) (2022)

## Built on by (most cited first, 1 of 1)

- [Topology of Out-of-Distribution Examples in Deep Neural Networks](https://mlsanity.com/paper/2501.12522/) (2025)

## Abstract (arXiv)

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.