用拓扑分析检测数据流变化，无需标签也能发现分布漂移。
Unsupervised Assessment of Landscape Shifts Based on Persistent Entropy and Topological Preservation
- 基于持久熵与拓扑保持投影，捕捉数据流的拓扑结构变化。
- 在MNIST生成的数据流上验证，能有效识别多维数据漂移。
- 适合持续学习中无监督异常检测，尤其关注数据结构演变。
在持续学习（CL）场景中，概念漂移通常指数据分布随时间的变化。输入数据的漂移可能对学习预测器和系统稳定性产生负面影响。现有方法主要关注非平稳数据中统计特性的变化。本文提出新视角，将概念漂移扩展至数据流拓扑特征的显著变化。我们构建了一种新型框架，用于监测多维数据流中的变化，通过分析数据的拓扑结构，为传统概念漂移提供新角度。该方法基于持久熵与拓扑保持投影，在无监督和有监督环境中均可运行。通过三个使用MNIST样本生成的数据流场景验证，结果表明拓扑数据分析在漂移检测中具有潜力，鼓励进一步研究。
原文摘要 · Abstract (English)
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.
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