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.

翻译：在持续学习（CL）环境中，概念漂移通常指数据分布变化的分析。输入数据的漂移可能对学习预测器及系统稳定性产生负面影响。大多数概念漂移方法侧重于分析非平稳数据随时间推移的统计变化。在此背景下，我们提出另一种视角：概念漂移还应包含数据流拓扑特征的实质性变化。本文提出一种用于监测多维数据流变化的新框架。我们通过探究数据拓扑结构的变化，为标准概念漂移问题提供新的分析维度。所开发的方法基于持续熵与拓扑保持投影技术，适用于持续学习场景。该框架可在无监督与有监督环境中运行。为验证框架的有效性，我们使用MNIST样本生成的数据流，在三种场景下对模型进行分析。实验结果表明拓扑数据分析在偏移检测中具有应用潜力，为该领域的进一步研究提供了支持。