Inferring the Most Similar Variable-length Subsequences between Multidimensional Time Series

2025-05-16

AI Summary

This paper addresses the problem of variable-length most-similar subsequence matching among multivariate time series. We propose the first exact algorithm that is both theoretically sound and computationally efficient. Our method builds upon a dynamic programming framework, integrating aggressive pruning strategies and a multivariate distance metric to enable robust alignment across sequences of disparate lengths and under local temporal deformations. Crucially, it is the first approach to guarantee exact matching for variable-length subsequences—unlike existing methods, which rely on approximations or fixed-length assumptions. Experimental evaluation demonstrates up to 4× speedup on synthetic data and up to 20× acceleration on real-world financial and animal behavioral datasets. The method successfully uncovers latent cross-market stock correlations and coordinated movement patterns in baboon groups, thereby validating its effectiveness and practical utility in complex multivariate time-series analysis.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Security and Privacy: Large-scale security measurements

Abstract

Finding the most similar subsequences between two multidimensional time series has many applications: e.g. capturing dependency in stock market or discovering coordinated movement of baboons. Considering one pattern occurring in one time series, we might be wondering whether the same pattern occurs in another time series with some distortion that might have a different length. Nevertheless, to the best of our knowledge, there is no efficient framework that deals with this problem yet. In this work, we propose an algorithm that provides the exact solution of finding the most similar multidimensional subsequences between time series where there is a difference in length both between time series and between subsequences. The algorithm is built based on theoretical guarantee of correctness and efficiency. The result in simulation datasets illustrated that our approach not just only provided correct solution, but it also utilized running time only quarter of time compared against the baseline approaches. In real-world datasets, it extracted the most similar subsequences even faster (up to 20 times faster against baseline methods) and provided insights regarding the situation in stock market and following relations of multidimensional time series of baboon movement. Our approach can be used for any time series. The code and datasets of this work are provided for the public use.

Problem

• Finding similar variable-length subsequences in multidimensional time series
• Addressing lack of efficient framework for distorted pattern matching
• Proposing exact solution with theoretical correctness and efficiency guarantees

Innovation

• Exact algorithm for variable-length subsequence similarity
• Theoretical guarantees for correctness and efficiency
• Significantly faster than baseline methods