Sparse representation of electrodermal activity with knowledge-driven dictionaries

Abstract

Biometric sensors and portable devices are being increasingly embedded into our everyday life, creating the need for robust physiological models that efficiently represent, analyze, and interpret the acquired signals. We propose a knowledge-driven method to represent electrodermal activity (EDA), a psychophysiological signal linked to stress, affect, and cognitive processing. We build EDA-specific dictionaries that accurately model both the slow varying tonic part and the signal fluctuations, called skin conductance responses (SCR), and use greedy sparse representation techniques to decompose the signal into a small number of atoms from the dictionary. Quantitative evaluation of our method considers signal reconstruction, compression rate, and information retrieval measures, that capture the ability of the model to incorporate the main signal characteristics, such as SCR occurrences. Compared to previous studies fitting a predetermined structure to the signal, results indicate that our approach provides benefits across all aforementioned criteria. This paper demonstrates the ability of appropriate dictionaries along with sparse decomposition methods to reliably represent EDA signals and provides a foundation for automatic measurement of SCR characteristics and the extraction of meaningful EDA features.

Trial registration: ClinicalTrials.gov NCT02077985.

Figures

Fig. 1

Example of an electrodermal activity (EDA) signal of skin conductance responses (SCR), marked with red “o,” and an indicative notation of SCR amplitude measure.

Fig. 2

Examples of normalized phasic atoms represented with sigmoid-exponential, Bateman and chi-square functions for different time scale parameters s = 0.06, 0.1, 0.14 and time offset t0 = 20. For each time-scale value, plots were created using all combinations of corresponding atom-specific parameters.

Fig. 3

EDA representation scheme and SCR detection for an example signal frame. (a) Input and reconstructed signal with solid blue and dashed red lines. The location of expert hand-annotated SCRs is marked (red “×”), along with the signal peaks (magenta “*”) and the SCRs estimated based on the phasic atoms of the sparse decomposition algorithm (green “•”). The final SCRs (black “○”) are located by combining the SCRs from the phasic atoms according to their location and mapping them to the signal peaks. (b) The normalized dictionary atoms selected by the first four iterations of OMP. The first tonic atom (solid cyan line) captures the signal level, the first and third phasic atoms (dashed magenta and dash-dotted green lines) the first SCR, while the second phasic atom (black dotted line) the second SCR. (c) The normalized phasic atoms multiplied by the corresponding OMP coefficients (dashed magenta, dotted black, and dash-dotted green lines). The energy of each atom is indicative of the order they have been selected by OMP with higher energy atoms selected first.

Fig. 4

Logarithmic ratio between the second-order norms of the residual Rnf and original signal f, r = 2 · log10 (‖Rnf ‖2/‖f‖2), computed for 1–50 orthogonal matching pursuit (OMP) iterations based on a dictionary of tonic and Bateman phasic atoms. Red-dashed line denotes a decay of approximately constant rate between 15–30 iterations. Green dashed-dotted line denotes a steeper constant decay between 30–50 OMP iterations.

Fig. 5

Signal reconstruction and SCR detection results. (a) Root mean square (RMS) error between original and reconstructed signal with respect to (w.r.t.) the number of (orthogonal) matching pursuit ((O)MP) iterations. (b) Absolute number of relative difference between real and estimated SCRs w.r.t. the number of (O)MP iterations. (c) Mean distance of estimated SCRs from their closest real SCR w.r.t. (O)MP iterations. (d), (e), (f) Precision, recall, and Fscore of SCR detection with 6 (O)MP iterations w.r.t maximum distance threshold dmax between real and detected SCRs, the latter ranging between 10–100 samples, or 0.3125–3.125 s. Results on Fig. (b)– (f) are reported based on a tenfold cross validation, during which SCR detection on the test set is performed using the parameter combination (dthr, Nb) that gave the best results on the training data, where dthr is the distance threshold for mapping estimated SCRs to the nearest signal peaks and Nb is the number of histograms bins for grouping the selected phasic atoms of each analysis frame. Same legend applies to all plots.

Fig. 6

Percentage of selected tonic atoms with respect to the number of iterations for (orthogonal) matching pursuit ((O)MP) and the various dictionaries (with sigmoid-exponential, Bateman and chi-square phasic atoms).

Fig. 7

Compression rate of the original EDA signal and the EDA representation with the proposed sparse decomposition and the least-squares fit methods. (Y-axis break between 100 and 900 bits/s).

Fig. 8

Effect of the analysis frame length L (in seconds) to signal reconstruction and SCR detection. (a) Root mean square (RMS) error between original and reconstructed signal for 1–15 orthogonal matching pursuit (OMP) iterations. (b) and (c) Fscore of SCR detection with 4 and 10 OMP iterations. Same legend applies to both plots.

Fig. 9

SCR detection metrics with respect to the distance threshold dthr for mapping estimated SCRs to signal peaks and the number of histogram bins Nb for grouping the selected phasic atoms from sparse decomposition. (a) Absolute relative difference RDiff of real and detected SCRs. (b) Mean distance MinDist of detected SCRs to the closest real one.