A persistent homology approach to heart rate variability analysis with
an application to sleep-wake classification
Persistent homology (PH) is a recently developed theory in the field of
algebraic topology. It is an effective and robust tool to study shapes of
datasets and has been widely applied. We demonstrate a general pipeline to
apply PH to study time series; particularly the heart rate variability (HRV).
First, we study the shapes of time series in two different ways -- sub-level
set and Taken's lag map. Second, we propose a systematic approach to
summarize/vectorize persistence diagrams, a companion tool of PH. To
demonstrate our proposed method, we apply these tools to the HRV analysis and
the sleep-wake, REM-NREM (rapid eyeball movement and non rapid eyeball
movement) and sleep-REM-NREM classification problems. The proposed algorithm is
evaluated on three different datasets via the cross-database validation scheme.
The performance of our approach is comparable with the state-of-the-art
algorithms, and are consistent throughout these different datasets.
Chung, Y-M; Hu, C-S; Lo, Y-L; Wu, H-T