Mining Time Series for Maximal Coverage with Matrix Profiles and Constraint Optimization

Abstract

Time Series Data (TSD) is essential in many areas of modern data analysis because they reflect how different processes change over time. Understanding these data can still be challenging. One of the main challenges is that the underlying states of a system are often hidden, making it harder to interpret patterns and draw reliable conclusions. This thesis addresses the critical task of mining recurrent patterns from systems whose internal states are neither directly observable nor controllable. It introduces a novel unsupervised approach explicitly designed to maximize coverage in TSD.

The research proposes a structured approach comprising three key steps: firstly, generating candidate patterns and their occurrences using an advanced Matrix Profile (MP) algorithm known for its efficiency and accuracy in detecting subtle recurrent patterns; secondly, translating these candidate patterns into a constraint-based model incorporating group constraints to enforce selection of all instances of the same pattern and exclusion constraints to prevent overlapping occurrences; and thirdly, selecting an optimal subset of core patterns using either a constraint solver to ensure optimal selection on shorter Time Series (TS), or scalable greedy heuristic methods that offer practical efficiency for larger or more complex datasets, thereby effectively balancing optimality with computational feasibility.

The effectiveness of the proposed approach is demonstrated through rigorous evaluations on real-world power consumption TSDs representing computer activities, alongside controlled synthetic datasets, using metrics such as coverage efficiency, computational time, and pattern compactness—striving to maximize data representation with minimal redundancy. Our experimental results show that the proposed method improves how efficiently data is covered, striking a practical balance between capturing key patterns and avoiding unnecessary repetition. This work contributes to the advancement in unsupervised pattern mining and has useful applications in areas such as forecasting, system health monitoring, anomaly detection, and policy verification.