Time-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistence
This work addresses the challenge of poor learning performance and frequent model updates in time-dependent data analysis, particularly for applications like traffic flow, blockchain, and medical signals, though it appears incremental as it builds on existing topological representation learning directions.
The paper tackles the problem of learning time-evolving objects like multivariate time series and dynamic networks by proposing a time-aware knowledge representation mechanism that captures implicit time-dependent topological information. The result is the Temporal MultiPersistence (TMP) method, which shows competitive performance on benchmark datasets and improves computational efficiency by up to 59.5 times compared to state-of-the-art multipersistence summaries.
Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent information contained in the data. Such information is typically not directly observed but plays a key role in the learning task performance. In turn, lack of time dimension in knowledge encoding mechanisms for time-dependent data leads to frequent model updates, poor learning performance, and, as a result, subpar decision-making. Here we propose a new approach to a time-aware knowledge representation mechanism that notably focuses on implicit time-dependent topological information along multiple geometric dimensions. In particular, we propose a new approach, named \textit{Temporal MultiPersistence} (TMP), which produces multidimensional topological fingerprints of the data by using the existing single parameter topological summaries. The main idea behind TMP is to merge the two newest directions in topological representation learning, that is, multi-persistence which simultaneously describes data shape evolution along multiple key parameters, and zigzag persistence to enable us to extract the most salient data shape information over time. We derive theoretical guarantees of TMP vectorizations and show its utility, in application to forecasting on benchmark traffic flow, Ethereum blockchain, and electrocardiogram datasets, demonstrating the competitive performance, especially, in scenarios of limited data records. In addition, our TMP method improves the computational efficiency of the state-of-the-art multipersistence summaries up to 59.5 times.