2019/08/09 by Yu-Min Chung, Chung, Yu-Min, Chuan-Shen Hu +7 · 9 citations
Computer Science · Engineering · Medicine · Neuroscience · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #Algorithm #Artificial intelligence #Computer science #Data Analysis #Data mining #Eye movement #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Physical sciences #Heart rate #Heart rate variability #Machine Learning (cs.LG) #Machine learning #Non-rapid eye movement sleep #Persistent homology #Series (stratigraphy) #Signal Processing (eess.SP) #Statistics and Probability (physics.data-an) #Time series #Topological and Geometric Data Analysis #Topological data analysis #Tryptophan and brain disorders #cs.LG #eess.SP #electronic engineering #information engineering #physics.data-an
paper · pdf · doi:10.48550/arxiv.1908.06856
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/08/09 · openalex created_date 2019/08/22 · arxiv created 2020/05/02 · arxiv updated 2020/05/05 · openalex updated_date 2026/07/28
Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general pipeline to apply PH to study time series; particularly the instantaneous heart rate time series for the heart rate variability (HRV) analysis. The first step is capturing the shapes of time series from two different aspects -- the PH's and hence persistence diagrams of its sub-level set and Taken's lag map. Second, we propose a systematic and computationally efficient approach to summarize persistence diagrams, which we coined \em persistence statistics. 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 better than the state-of-the-art algorithms, and the result is consistent throughout different datasets.