Learning Evolvable Time-series Shapelets

Shapelets are subsequences that are effective for classifying time-series instances. In this study, we consider when each time-series instance is obtained as progress, and formulate the problem of learning shapelet evolution over progress. For example, shapelets can change their shapes according to progress with human habituation, seasonal effects, and system degradation. When given time-series instances, progress values, and binary class labels, the proposed optimization formulation can jointly learn not only the shapelets and a classifier but also regression models for predicting shapelet evolution. The derived optimization solution method allows regression models to be learned by using off-the-shelf regression solvers, and scales linearly with time-series length. We demonstrate its effectiveness in industrial case studies.