We propose the Deep Distance Measurement Method (DDMM) to improve retrieval accuracy in unsupervised multivariate time series similarity retrieval. DDMM enables learning of minute differences within states in the entire time series and thereby recognition of minute differences between states, which are of interest to users in industrial plants. To achieve this, DDMM uses a learning algorithm that assigns a weight to each pair of an anchor and a positive sample, arbitrarily sampled from the entire time series, based on the Euclidean distance within the pair and learns the differences within the pairs weighted by the weights. This algorithm allows both learning minute differences within states and sampling pairs from the entire time series. Our empirical studies showed that DDMM significantly outperformed state-of-the-art time series representation learning methods on the Pulp-and-paper mill dataset and demonstrated the effectiveness of DDMM in industrial plants. Furthermore, we showed that accuracy can be further improved by linking DDMM with existing feature extraction methods through experiments with the combined model.
Time series representation learning develops compact, transferable features that capture temporal patterns for forecasting, classification, retrieval, and anomaly detection.
In many realistic scenarios, large volumes of time series data are generated with limited or expensive annotations. This limitation makes supervised learning methods difficult to apply and leads to the use of unsupervised approaches capable of discovering meaningful structures directly from raw data. Clustering therefore plays a crucial role in organizing time series into groups that share similar temporal patterns, enabling exploratory analysis and downstream tasks without requiring manual labeling. However, existing deep clustering methods often struggle to capture long-range temporal dependencies or rely on architectures with high computational cost. This paper introduces FMMVCC, a Mamba-based deep clustering framework for time series that leverages state space sequence modeling to efficiently learn temporal representations with linear complexity. Additionally, it utilizes multi-view self-supervised learning with temporal masking and augmentations. Experimental evaluation in 15 benchmark datasets proves that FMMVCC consistently outperforms state-of-the-art baselines, achieving the best overall performance in 29 of 60 total metric evaluations and the highest average rank in all tested scenarios.
Elastic distances like dynamic time warping (DTW) are central to time series machine learning because they compare sequences under local temporal misalignment. Soft-DTW is an adaptation of DTW that can be used as a gradient-based loss by replacing the hard minimum in its dynamic-programming recursion with a smooth relaxation. However, this approach does not directly extend to elastic distances whose transition costs depend on the local alignment context. Move-Split-Merge (MSM) is one such distance: it uses context-aware split and merge penalties and has often outperformed DTW in supervised and unsupervised time series machine learning tasks such as classification and clustering. We introduce Soft-MSM, a smooth relaxation of MSM and an elastic alignment loss with context-aware transition costs. Central to the formulation is a smooth gated surrogate for MSM's piecewise split/merge cost, which enables gradients through both the dynamic-programming recursion and the local transition structure. We derive the forward recursion, backward recursion, soft alignment matrix, closed-form gradient, limiting behaviour, and divergence-corrected formulation. Experiments on 112 UCR datasets show that Soft-MSM gives lower MSM barycentre loss than existing MSM barycentre methods, and yields significantly better clustering and nearest-centroid classification performance than Soft-DTW-based alternatives. An implementation is available in the open-source aeon toolkit.
Christopher Holder, Anthony Bagnall
School of Electronics and Computer Science University of Southampton Southampton, SO17 1BJ, United Kingdom
A key operation for massive data series collection analysis is similarity search. According to recent studies, SAX-based indexes offer state-of-the-art performance for similarity search tasks. However, their performance lags under high-frequency, weakly correlated, excessively noisy, or other dataset-specific properties. In this work, we propose Deep Embedding Approximation (DEA), a novel family of data series summarization techniques based on deep neural networks. Moreover, we describe SEAnet, a novel architecture especially designed for learning DEA, that introduces the Sum of Squares preservation property into the deep network design. We further enhance SEAnet with SEAtrans encoder. Finally, we propose novel sampling strategies, SEAsam and SEAsamE, that allow SEAnet to effectively train on massive datasets. Comprehensive experiments on 7 diverse synthetic and real datasets verify the advantages of DEA learned using SEAnet in providing high-quality data series summarizations and similarity search results.