Fig. 1
From: Coupling spectral analysis and hidden Markov models for the segmentation of behavioural patterns
Sketch of the methodological procedure applied to raw depth time series: 1. the depth time series are analysed in the time-frequency domain using a Short Term Fourier Transform analysis in order to identify cyclic patterns and activity levels across time from periodograms; 2. The periodograms were divided into two parts: (i) between 6 and 72 h (S6-72 h); (ii) between half an hour and 6 h (S0.5-6 h); 3. For each STFT time window (i.e. one day) (a) the information contained in the 26 frequency bandwidths of S6-72 h was summarized by nine factors using a Non Negative Matrix Factorization (NNMF, see Additional file 3: Figure S3); (b) for the higher-frequency range S0.5-6 h, we computed an index of fine scale movement randomness by calculating the slope of the linear relationship between the log transformed variance densities and frequencies (see Additional file 3: Figure S1b); 4. We fitted HMMs to the time series of metrics formed by the nine-dimensional NNMF decomposition of each periodogram and the value of SLPLog-Log. Given a fitted HMM, we derive from each depth time series a time series of behavioural states (see Figs. 5 and 6)