Detecting multifractality and exposing distributions of local fluctuations: Detrended fluctuation analysis with descriptive statistics pooling

2022 ◽  
Vol 155 ◽  
pp. 111678
Author(s):  
Şahin Telli ◽  
Hongzhuan Chen ◽  
Xufeng Zhao
Author(s):  
Javier Gómez-Gómez ◽  
Rafael Carmona-Cabezas ◽  
Ana B. Ariza-Villaverde ◽  
Eduardo Gutiérrez de Ravé ◽  
Francisco José Jiménez-Hornero

Author(s):  
NA LI ◽  
MARTIN CRANE ◽  
HEATHER J. RUSKIN

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.


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