# Wearables and the Quantified Self: Systematic Benchmarking of Physiological Sensors

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## Abstract

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## 1. Introduction

## 2. Sensor Benchmark Methods—Related Work

#### 2.1. Similarity Measures

#### 2.2. Correlation Statistics

## 3. Physiological Parameter of Interest and Sensors used for Benchmarking

- HR: heart rate, i.e., heartbeat frequency, unit: beats per minute
- IBI: inter beat interval, also known as the RR interval, i.e., the time between two R-peaks in the ECG’s QRS complex, unit: milliseconds
- ECG: electrocardiogram, i.e., electrical activity of the heart, unit: millivolt
- GSR: galvanic skin response, i.e., the level of electric conductance of the skin, unit: microSiemens [μS]

#### 3.1. VarioPort

#### 3.2. Zephyr BioHarness 3

#### 3.3. Empatica E4

## 4. Benchmark Method

#### 4.1. Study Setup and Participants

- Resting phase: 5 min of rested seating on the ergometer, not performing any physical activity; used as a calibration phase for the measurements
- Cycling phase: 10 min of cycling at a constant 50 rpm; stepwise increase of physical load (5 steps of 2 min each, during which the resistance/power of the ergometer was increased from 35–65–100–133–165 W)
- Cool down phase: 5 min cool down, rested seating like in the resting phase

#### 4.2. Data Acquisition

#### 4.3. Data Pre-Processing

#### 4.4. Statistical Signal Analysis—Time Series Correlation and Similarity Analysis

- Very low frequency VLF (0.025–0.07 Hz)
- Low frequency LF (0.07–0.14 Hz)
- High frequency HF (0.14–0.5 Hz)

## 5. Results

#### 5.1. Visualisation: Exploratory Plots

^{2}of 0.971 for raw data and 0.997 for the moving averaged data. This means that 97.1% and 99.7%, respectively, of the data’s total variance can be explained by a linear model. This plot also confirms what is seen in the time plot, namely that in the low range the residuals are higher than in the high range. Note that the higher residuals in red in the upper right quarter of the plot refer to the time plot at ~750 s, where the blue curve drops below the red curve (indicated by a black arrow in Figure 4a,b). The HR cross-correlation plots show the highest cross-correlation for the as-is version (Figure 4c) at a lag of 1 s, and the highest cross-correlation for the moving averaged version (Figure 4d) at a lag of 2 s. In other words, the local trend of the BH is lagging 1 and 2 s, respectively, “behind” the local trend of the VP on average.

^{2}of 0.882 for raw data and 0.896 for the moving averaged data. This means that 88.2% and 89.6%, respectively, of the data’s total variance can be explained by a linear model. The cross-correlation plots (Figure 5c) show the highest cross-correlation for the as-is version at lag of 2 s, and the highest cross-correlation for the moving averaged version at a lag of 1 s. In other words, the local trend of the E4 sensor is lagging 2 and 1 s, respectively, “behind” the local trend of the VP sensor on average.

#### 5.2. Quantitative Analysis

#### 5.2.1. Linear Regression and Coefficient of Determination R^{2}

^{2}, which quantifies the percentage of the variance of the two given parameters that can be explained by a linear regression model. In addition to the R

^{2}of individual pairs of parameters, as shown in the scatter-plots (refer to Section 5.1, Figure 4b and Figure 5b), we now investigate all pairs among all participants and explore the corresponding R

^{2}pattern. This pattern can be derived from the R

^{2}matrix shown in Figure 6. Furthermore, for each group of parameters, e.g., all IBI related parameter, we calculate the total average per participant in order to get an impression of the impact of each participant’s individual overall measured activity (GSR base level, skin contact of electrodes, etc.).

^{2}matrix, the pairs of equal-type parameters, measured by different sensors (or derived from another signal of the same sensor) show a high linear relationship across the majority of the participants. This relationship also indicates that these parameters are rather robust from a measuring point of view. However, the matrix also shows some cases with no relationship at all, see for instance IBI derived from ECG BH (moving averaged version), and IBI derived from ECG VP (moving averaged version) at row three for participant RP 8-20 and RP 1-2. This may indicate that one of the sensors did not have proper contact between the electrodes and the skin and thus failed to collect valid data.

^{2}matrix in Figure 6 is organized as follows: for each group of parameters, the top row shows the highest correlation among all participants, while the bottom row shows the lowest correlation. Further, the left column shows the participant with the highest correlations among all parameters, while the right column shows the participant with the lowest correlations among all parameters.

#### 5.2.2. Cross-Correlation

#### 5.2.3. MINE Statistics

^{2}(see Section 5.2.1), we use the Maximal Information Coefficient MIC to identify all functional relationships, also including linear ones as issued by R

^{2}. Although a functional relationship between certain combinations of parameters might be obvious (e.g., IBI [ms] = 60,000/HR [beats per hour]), we nonetheless include such combinations herein for reasons of confirmation.

- a, b: LF and VLF derived from ECG measured by BioHarness show a rather low correlation with almost all other parameters
- c, d: IBI measurements, either directly measured or derived from ECG, show a rather high correlation with HR and with IBI from other sensors
- e, f: GSR measurements from VP (high- and low-pass filtered) show a rather low correlation with all other parameters; however, GSR measurements from E4 (high- and low-pass filtered) show a low to moderate correlation with all other parameters.

^{2}coefficient can only quantify linear relationships. By subtracting R

^{2}from the MIC, we compute a measure of nonlinearity [36], which we use to identify the following three classes of relationships as shown in Figure 10:

- “false” linear relationships (R
^{2}is not confirmed by MIC): MIC–R^{2}< 0 - “true” linear relationships (R
^{2}is confirmed by MIC): MIC–R^{2}~ 0 - functional but not linear relationships: MIC–R
^{2}> 0

^{2}matrix shown in Figure 11 provides additional detail to the clustering view. Interestingly, GSR measurements from E4 and VP show rather strong functional but not linear relationships with almost all other parameters (see third and fifth row in Figure 10 and Figure 11). Particularly interesting is the relationship between GSR VP (filtered and moving averaged version, fourth row) and GSR E4 (filtered and moving averaged version, fifth-last column), which shows some highly negative values (see black arrow). These cases indicate a “false” linear relationship. For instance, participant RP 9–17: MIC 0.2 minus R

^{2}0.91 results in −0.71. In other words, the MIC does not confirm the highly linear relationship indicated by R

^{2}; in fact, the MIC indicates that there is almost no relationship. From a physiological point of view, this relationship might be obvious; however, the quantification of this relationship from a data-driven perspective is, to our best knowledge, novel.

#### 5.2.4. Fréchet Distance (Global and Local)

#### 5.2.5. DTW Distance

**.**Figure 16 shows an example of two time series of GSR measurements with rather low similarity (high DTW distance); however, the overall trend is highly similar. The corresponding exploratory plots of the GSR example are shown in Figure 5.

## 6. Discussion and Limitations

^{2}matrix (Figure 6a) together with the cross-correlation matrix (Figure 7a) and comparing the individual result between participants. Further, it allows checking whether that particular pair of parameters has a functional relationship and whether that relationship is stable among other participants by using the MIC–R

^{2}individual matrix (Figure 11). The focus on a particular pair of parameters and participant can be continued to the similarity measures, namely the Fréchet distance and the DTW distance (Figure 12 and Figure 14). Another method of interpretation is to begin at the collective level using the MIC–R

^{2}cluster matrix of pairs of parameters (Figure 10), then drilling-down on a specific parameter combination of interest using the MIC–R

^{2}individual matrix (Figure 11) and contextualizing this matrix with the corresponding exploratory plots as shown in Figure 5.

^{2}with the MIC (Figure 10 and Figure 11). In other words, we confronted a statistic that measures linear relationships against a statistic that measures all types of functional relationships, including linear ones, and thereby classified the relationship as ‘false linear’, ‘true linear’, or ‘functional but not linear’. The results are outstanding: on the one hand, some already expected linear relationships have been confirmed by a purely data-driven approach (for instance, relationships between IBI and VLF, LF, HF); on the other hand, some relationships that were expected to be linear are in fact not linear or functional. For instance, the relationships between GSR measured by E4 and GSR measured by VP (both filtered and moving averaged versions).

## 7. Conclusions and Future Work

^{2}against the Maximal Information Coefficient MIC, in particular, the classification of non-linear correlations, and 2) the quantification of the signals’ temporal and geometric similarity based on well-established distance metrics (DTW distance and Fréchet distance).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Data pre-processing phase—from raw sensor data (

**left**) to sensor data ready to analyse (

**right**).

**Figure 3.**Data analysis workflow—from sensor data ready to analyse (

**left**) to visualizations of exploratory plots and quantitative analysis results to deriving conclusions (

**right**).

**Figure 4.**Participant RP 5–14: time plot (

**a**), scatter plot (

**b**), and cross-correlation plot (

**c**), and cross-correlation plot of moving averages (

**d**) of heart rate HR [beats per minute] measured by Bioharness3 BH sensor and VarioPort VP.

**Figure 5.**Participant RP 3–8: time plots (

**a**), scatter plot (

**b**), cross-correlation plot (

**c**), and cross-correlation plot of moving averages (

**d**) of galvanic skin response GSR measured by Empatica E4 and VarioPort.

**Figure 6.**R

^{2}matrix of pairs of parameter and participants; detail (

**a**) complements Figure 4, detail (

**b**) complements Figure 5; total average of individual pairs among participants is shown in the last column; total average of participants among individual parameter pairs is shown in the last row of each parameter group; colour: red indicates high correlation, blue indicates low correlation.

**Figure 7.**Cross-correlation matrix of pairs of parameters and participants; detail (

**a**) complements Figure 4, detail (

**b**) complements Figure 5; colour: orange indicates positive cross-correlation, blue indicates negative cross-correlation; a cell detail shows lags as small horizontal bars: lag −15 at top, and lag +15 at bottom.

**Figure 8.**Maximum Information Coefficient (MIC) cluster matrix of pairs of parameters (size show averages among all participants, moving averaged versions only); colors: blue (cluster 1): low correlations; orange (cluster 2): moderate correlations; green (cluster 3): high correlations; symbol size in a matrix cell: average MIC among participants; (

**a**–

**f**) highlight special characteristics described in the text.

**Figure 9.**MIC participant-level matrix of pairs of parameters (moving averages only); details of a matrix cell show participants as small vertical bars (order of participants is shown in the legend).

**Figure 10.**MIC–R

^{2}cluster matrix of pairs of parameters (moving averages only); colors: green (cluster 1): “false” linear relationships; yellow (cluster 2): “true” linear relationships; red (cluster 3): functional but not linear relationships.

**Figure 11.**MIC–R

^{2}individual matrix of pairs of parameters (moving averages only); details of a matrix cell show participants as small vertical bars (order of participants is shown in the legend); back arrow points to pairs of parameters with very weak association.

**Figure 13.**Local Fréchet distance of a moving time window (1 min) of selected pairs of parameters (inter beat interval IBI, heart rate HR, galvanic skin response GSR; moving averaged only).

**Figure 15.**Illustration of the Dynamic Time Warping (DTW) distance between two parameters of participant RP 5-14: moving averaged version of heart rate HR from BioHarness BH versus moving averaged version of heart rate HR from VarioPort VP (note the offset of the two y-axes).

**Figure 16.**Illustration of the Dynamic Time Warping (DTW) distance between two parameters of participant RP 3-8: moving averaged version of galvanic skin response GSR from E4 versus moving averaged version of galvanic skin response GSR from VarioPort VP (note the offset of the two y-axes).

VarioPort | Zephyr BioHarness 3 | Empatica e4 | |
---|---|---|---|

HR | X | X | – |

IBI | X | X | X |

ECG | X | X | – |

GSR | X | – | X |

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## Share and Cite

**MDPI and ACS Style**

Sagl, G.; Resch, B.; Petutschnig, A.; Kyriakou, K.; Liedlgruber, M.; Wilhelm, F.H.
Wearables and the Quantified Self: Systematic Benchmarking of Physiological Sensors. *Sensors* **2019**, *19*, 4448.
https://doi.org/10.3390/s19204448

**AMA Style**

Sagl G, Resch B, Petutschnig A, Kyriakou K, Liedlgruber M, Wilhelm FH.
Wearables and the Quantified Self: Systematic Benchmarking of Physiological Sensors. *Sensors*. 2019; 19(20):4448.
https://doi.org/10.3390/s19204448

**Chicago/Turabian Style**

Sagl, Günther, Bernd Resch, Andreas Petutschnig, Kalliopi Kyriakou, Michael Liedlgruber, and Frank H. Wilhelm.
2019. "Wearables and the Quantified Self: Systematic Benchmarking of Physiological Sensors" *Sensors* 19, no. 20: 4448.
https://doi.org/10.3390/s19204448