Extracting Fundamental Periods to Segment Biomedical Signals

We address the problem of segmenting nearly periodic time series into period-like segments. We introduce a definition of nearly periodic time series via triplets 〈 basic shape, shape transformation, time scaling 〉 that covers a wide range of time series. To split the time series into periods, we select a pair of principal components of the Hankel matrix. We then cut the trajectory of the selected principal components by its symmetry axis and, thus, obtaining half-periods that are merged into segments. We describe a method of automatic selection of periodic pairs of principal components, corresponding to the fundamental periodicity. We demonstrate the application of the proposed method to the problem of period extraction for accelerometric time series of human gait. We see the automatic segmentation into periods as a problem of major importance for human activity recognition problem, since it allows to obtain interpretable segments: each extracted period can be seen as an ultimate entity of gait. The method we propose is more general compared to the application specific methods and can be used for any nearly periodical time series. We compare its performance to classical mathematical methods of period extraction and find that it is not only comparable to the alternatives, but in some cases performs better.