Given two strings S and R , the matching statistics of S with respect to R is an array of length | S | whose i th entry encodes the longest prefix of the i th suffix of S that occurs in R . Introduced by Chang and Lawler in 1990 for approximate string matching, matching statistics have since found a variety of applications in computational biology, data compression, and string processing. In this article, we survey these applications, as well as the main ideas underlying the different algorithms for efficient construction of the matching statistics that have appeared in the last 30 years.

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.

We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem can be solved in optimal time $\mathcal{O}(\log N)$ whp for the updates and $\mathcal{O}(1)$ worst-case time for the queries, where $N$ is the total collection size [Gawrychowski et al., SODA 2018]. We present here a much simpler solution based on a forest of enhanced splay trees (FeST), where both the updates and the substring comparison take $\mathcal{O}(\log n)$ amortized time, $n$ being the lengths of the strings involved. The longest common prefix of length $\ell$ is computed in $\mathcal{O}(\log n + \log^2\ell)$ amortized time. Our query results are correct whp. Our simpler solution enables other more general updates in $\mathcal{O}(\log n)$ amortized time, such as reversing a substring and/or mapping its symbols. We can also regard substrings as circular or as their omega extension.

In this work, we concentrate on the detection of anomalous behaviors in systems operating in the physical world and for which it is usually not possible to have a complete set of all possible anomalies in advance. We present a data augmentation and retraining approach based on adversarial learning for improving anomaly detection. In particular, we first define a method for generating adversarial examples for anomaly detectors based on Hidden Markov Models (HMMs). Then, we present a data augmentation and retraining technique that uses these adversarial examples to improve anomaly detection performance. Finally, we evaluate our adversarial data augmentation and retraining approach on four datasets showing that it achieves a statistically significant performance improvement and enhances the robustness to adversarial attacks. Key differences from the state-of-the-art on adversarial data augmentation are the focus on multivariate time series (as opposed to images), the context of one-class classification (in contrast to standard multi-class classification), and the use of HMMs (in contrast to neural networks).

We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a reference string. We then use this data structure to distribute suffixes into a partial order, and subsequently to speed up suffix comparisons to complete the generalized suffix array. Our experimental evidence with a prototype implementation (a tool we call sacamats) shows that on string collections with highly similar strings we can construct the suffix array in time competitive with or faster than the fastest available methods. Along the way, we describe a heuristic for fast computation of the matching statistics of two strings, which may be of independent interest.

In this paper, we propose the use of subspace clustering to detect the states of dynamical systems from sequences of observations. In particular, we generate sparse and interpretable models that relate the states of aquatic drones involved in autonomous water monitoring to the properties (e.g., statistical distribution) of data collected by drone sensors. The subspace clustering algorithm used is called SubCMedians. A quantitative experimental analysis is performed to investigate the connections between i) learning parameters and performance, ii) noise in the data and performance. The clustering obtained with this analysis outperforms those generated by previous approaches.