# Unsupervised Assessment of Landscape Shifts Based on Persistent Entropy and Topological Preservation

arXiv: https://arxiv.org/abs/2410.04183 · HTML: https://mlsanity.com/paper/2410.04183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 52 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Challenges in Benchmarking Stream Learning Algorithms with Real-world Data](https://mlsanity.com/paper/2005.00113/) (2020)
- [Model Based Explanations of Concept Drift](https://mlsanity.com/paper/2303.09331/) (2023)
- [Data Representativity for Machine Learning and AI Systems](https://mlsanity.com/paper/2203.04706/) (2022)
- [Persistent Homology of Complex Networks for Dynamic State Detection](https://mlsanity.com/paper/1904.07403/) (2019)
- [WATCH: Wasserstein Change Point Detection for High-Dimensional Time Series Data](https://mlsanity.com/paper/2201.07125/) (2022)
- [stream-learn -- open-source Python library for difficult data stream batch analysis](https://mlsanity.com/paper/2001.11077/) (2020)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [Active Weighted Aging Ensemble for Drifted Data Stream Classification](https://mlsanity.com/paper/2112.10150/) (2021)
- [Suitability of Different Metric Choices for Concept Drift Detection](https://mlsanity.com/paper/2202.09486/) (2022)
- [Tracking changes using Kullback-Leibler divergence for the continual learning](https://mlsanity.com/paper/2210.04865/) (2022)
- [Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss](https://mlsanity.com/paper/2205.12307/) (2022)
- [A Natural Gas Consumption Forecasting System for Continual Learning Scenarios based on Hoeffding Trees with Change Point Detection Mechanism](https://mlsanity.com/paper/2309.03720/) (2023)
- [A Self-Organizing Clustering System for Unsupervised Distribution Shift Detection](https://mlsanity.com/paper/2404.16656/) (2024)

## Abstract (arXiv)

In Continual Learning (CL) contexts, concept drift typically refers to the analysis of changes in data distribution. A drift in the input data can have negative consequences on a learning predictor and the system's stability. The majority of concept drift methods emphasize the analysis of statistical changes in non-stationary data over time. In this context, we consider another perspective, where the concept drift also integrates substantial changes in the topological characteristics of the data stream. In this article, we introduce a novel framework for monitoring changes in multi-dimensional data streams. We explore variations in the topological structures of the data, presenting another angle on the standard concept drift. Our developed approach is based on persistent entropy and topology-preserving projections in a continual learning scenario. The framework operates in both unsupervised and supervised environments. To show the utility of the proposed framework, we analyze the model across three scenarios using data streams generated with MNIST samples. The obtained results reveal the potential of applying topological data analysis for shift detection and encourage further research in this area.