Geometric Fusion via Joint Delay Embeddings
This work addresses the challenge of integrating data from multiple sensors for improved analysis, representing an incremental advancement in fusion techniques.
The paper tackles the problem of fusing multi-sensor time series by introducing a new framework using geometric and topological methods, which outperforms traditional metric fusion methods in synthetic and real-world experiments.
We introduce geometric and topological methods to develop a new framework for fusing multi-sensor time series. This framework consists of two steps: (1) a joint delay embedding, which reconstructs a high-dimensional state space in which our sensors correspond to observation functions, and (2) a simple orthogonalization scheme, which accounts for tangencies between such observation functions, and produces a more diversified geometry on the embedding space. We conclude with some synthetic and real-world experiments demonstrating that our framework outperforms traditional metric fusion methods.