QSMP: finding representative time series subsequences through Quick Shift+Matrix Profile

Multivariate Time Series (MTS) clustering is an important tool in temporal data mining, aiming to discover latent group structures from complex observations without supervision. Although existing deep clustering methods can learn discriminative temporal representations, the resulting latent clusters are often difficult to relate back to waveform characteristics that practitioners can directly inspect and compare, limiting their ability to assess whether the discovered patterns reflect meaningful temporal behaviors. This paper, therefore, proposes WAVE (Waveform Aligned Visual-temporal Embedding), which treats time series and their deterministically rendered waveform plots as complementary views of the same observations. To produce discriminative representations whose cluster structures can be traced to observable waveform characteristics, WAVE aligns and integrates fine-grained temporal variations with holistic visual patterns, while associating each discovered cluster with its centroid-nearest authentic sample. Accordingly, interpretability in this work specifically refers to waveform-level traceability rather than a general explanation of model decisions. Extensive evaluations across 10 real-world public datasets show that WAVE achieves the highest macro-averaged clustering performance and the best average rank among the compared methods, while qualitative case studies illustrate how the discovered clusters can be inspected through authentic waveform records. The source code is available at https://github.com/Zheng-Zhu1/WAVE.

Time series data is very common in many real-world applications and in numerous domains, with increasing interest for automated information extraction using machine learning. One of these subfields is time series classification, which consists in assigning a label to each new, unseen time series. Many algorithms have been developed over the past decades, with the trade-off between predictive performance and computational cost being consistently discussed. Quant, an interval-based algorithm extracting quantiles from recursive, fixed, dyadic intervals, was shown to achieve high accuracy, while being very fast. We propose two changes to make this algorithm even faster. The first one is a better optimized implementation of the exact same algorithm. The second one is to derive approximate quantiles, using the Cornish-Fisher expansion, instead of exact quantiles. This change removes the necessity to sort the time series, leading to a smaller computational complexity. We call this novel algorithm MomentQuant. We provide evidence that our implementation of Quant is faster than the original one, and that MomentQuant is even faster than our implementation of Quant, at the cost of a tiny decrease in predictive performance. These improvements are especially relevant for real-life applications, where inference is performed much more often than training.

Time series data is very common in many real-world applications and in numerous domains, with increasing interest for automated information extraction using machine learning. One of these subfields is time series clustering, which consists in identifying clusters among a set of time series in an unsupervised fashion. Most time series clustering algorithms suffer from the same balancing act: they trade clustering performance for faster runtimes or vice versa. We present a novel time series clustering algorithm that we call CLUES-WEASEL, which stands for CLustering with the UnsupervisEd Second version of Word ExtrAction for time SEries cLassification. CLUES-WEASEL extracts features using the unsupervised version of the transformation step of WEASEL 2.0, which is a time series classification algorithm, then reduces these features using principal component analysis, and finally performs clustering with the $k$-means algorithm using these reduced extracted features. Through extensive experiments, we prove that CLUES-WEASEL is significantly better than any other existing time series clustering algorithm while being (much) faster than any state-of-the-art one. We also show that the architecture of CLUES-WEASEL can work well with other time series feature extraction algorithms. Our findings highlight the relevance of CLUES-WEASEL for time series clustering.