Fig. 2: Pipeline to derive the measure circadian activity rhythm energy (CARE) from accelerometer data.
From: CARE as a wearable derived feature linking circadian amplitude to human cognitive functions
a Actogram to show 7 days of wrist accelerometer activity of a single participant. b A visual representation of the raw activity signal and the singular spectrum analysis (SSA) decomposed signals, including the base signal (i.e., the first sub-signal indicating the non-periodic trend with the largest energy among all sub-signals), the 24-h signal, and the behavioral noise signal (i.e., sum of the sub-signals with periods <24 h). We can obtain the raw activity signal by adding these three signals together. c The graphical display of SSA algorithm. Specifically, the activity time series \({{\rm{X}}}_{N}\) of length N could be decomposed using SSA as follows. First, we chose an appropriate window length L such that \(2\le L\le \frac{N}{2}\). Then, \({{\rm{X}}}_{N}\) was transferred into a trajectory matrix with K lagged vectors of \({{\rm{X}}}_{L}\) as given by T, where K = N – L + 1. The trajectory matrix T was decomposed by singular value decomposition. By grouping the eigentriples and averaging the elements of reconstructed trajectory matrix along anti diagonals, we could get filtered time series represented by \({{\rm{G}}}_{N}=\left\{{g}_{1},{g}_{2},\ldots ,{g}_{N}\right\}\).
