Time-series similarity problems and well-separated geometric sets
Given a pair of nonidentical complex objects, defining (and determining) how similar they are to each other is a nontrivial problem. In data mining applications, one frequently needs to determine the similarity between two time series. We analyze a model of time-series similarity that allows outliers, and different scaling functions. We present deterministic and randomized algorithms for computing this notion of similarity. The algorithms are based on nontrivial tools and methods from computational geometry. In particular, we use properties of families of well-separated geometric sets. The randomized algorithm has provably good performance and also works extremely efficiently in practice.
Proceedings of the Annual Symposium on Computational Geometry
Bollobas, B., Das, G., & Gunopulos, D. (1997). Time-series similarity problems and well-separated geometric sets. Proceedings of the Annual Symposium on Computational Geometry, 454-456. https://doi.org/10.1145/262839.263080