Time series distance measures are fundamental in numerous domains, including finance, healthcare, and signal processing, enabling crucial tasks such as pattern recognition, anomaly detection, and predictive modeling. However, many applications require computing distances between all pairs of time series in large datasets, a computationally intensive task that can become a significant bottleneck in analysis pipelines. The tsdistances library is a high-performance Python package designed for computing distances between time series, with GPU support for accelerated processing. This article introduces tsdistances and its key features, focusing on the implementation of elastic distance algorithms and their optimizations. We present both CPU and GPU implementations, highlighting the use of dynamic programming techniques and GPU-specific optimizations such as warp-based parallelization. The performance of tsdistances is compared with existing alternatives in the literature, demonstrating significant speed improvements, especially for large-scale time series analysis tasks.

Abstract This paper presents , a novel distance between time series based on Random Forests (RFs). We extend to the time-series domain concepts and tools of RF distances, a recent class of robust data-dependent distances defined for vectorial representations, thus proposing the first RF distance for time series. The distance is determined by (i) creating an RF to model a set of time series, and (ii) exploiting the trained RF to quantify the similarity between time series. As for the first step, we introduce in this paper the Extremely Randomized Canonical Interval Forest (ERCIF), a novel extension of Canonical Interval Forests that can model time series and can be trained without labels. We then exploit three different schemes, following ideas already employed in the vectorial case. The proposed distance, in different variants, has been thoroughly evaluated with 128 datasets from the archive, showing promising results compared with literature alternatives.