Matteo Ceccarello

Matteo Ceccarello, Francesco Pio Monaco, Francesco Silvestri

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least $1-δ$, where $δ$ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Martin Aumüller, Matteo Ceccarello

This paper reconsiders common benchmarking approaches to nearest neighbor search. It is shown that the concept of local intrinsic dimensionality (LID) allows to choose query sets of a wide range of difficulty for real-world datasets. Moreover, the effect of different LID distributions on the running time performance of implementations is empirically studied. To this end, different visualization concepts are introduced that allow to get a more fine-grained overview of the inner workings of nearest neighbor search principles. The paper closes with remarks about the diversity of datasets commonly used for nearest neighbor search benchmarking. It is shown that such real-world datasets are not diverse: results on a single dataset predict results on all other datasets well.