Unsupervised Clustering of Heartbeat Dynamics Allows for Real Time and Personalized Improvement in Cardiovascular Fitness

Figures

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  Figure 1. ACF plot of HR for a single running session. The blue shaded region is the confidence interval with a value of α = 0.05 calculated with Bartlett’s formula [29]. Anything within this range represents a value that has no significant correlation with the most recent value for the HR. In this case, we observe significant correlations from 0 to 80 s. The red point is the intersection between the ACF function and the upper confidence threshold. Correlations subsequent to that point are no longer significant.

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  Figure 2. Unsupervised k-means clustering method. (a) Number of clusters vs. average silhouette score for k-means clustering on sample data. The red dashed line indicates the maximum average score for k = 4 clusters. (b) Visualization of clustered data for k = 4 in the ΔE vs. ΔHR plane. The clusters have been named with the respective signs of ΔE and ΔHR variations: +/+ cluster (yellow), −/− cluster (black), −/+ cluster (blue), and +/− cluster (green). The −/+, +/+, +/−, and −/− in the figure represent the centroids of the corresponding cluster.

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  Figure 3. (a) ΔHR boxplots for every cluster; (b) ΔE boxplots for every cluster; (c) heart rate (up) and energy (down) in running fragments belonging to different clusters. The clustering analysis assigns the belonging of these fragments to different clusters coherently with the sign of both ΔHR and ΔE. p-value annotation legend: ns: 5.00 × 10−2 < p ≤ 1.00 × 100; **: 1.00 × 10−3 < p ≤ 1.00 × 10−2; ***: 1.00 × 10−4 < p ≤ 1.00 × 10−3; ****: p ≤ 1.00 × 10−4. Color legend: yellow: +/+ cluster; black: −/− cluster; blue: −/+ cluster; green: +/− (see Figure 2 in Section 3.1).

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  Figure 4. Bar plots with bar errors (red) of cluster frequencies in four different running sessions acquired three months apart from each other. −/+ cluster (blue) and −/− cluster (black) cluster frequencies seem, respectively, to increase and decrease with time.

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  Figure 5. VO2max vs. cluster frequencies for every cluster: (a) cluster −/−; (b) cluster −/+; (c) cluster +/−; (d) cluster +/+. A positive correlation between VO2max and cluster −/+ and a negative correlation between VO2max and cluster +/+ can be observed. Legend: Pearson correlation coefficient (r), p-value (p). Color legend: yellow: +/+ cluster; black: −/− cluster; blue: −/+ cluster; green: +/− (see Figure 2 in Section 3.1).

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  Figure 6. (a) Projection of the clusters along HR, speed, and altitude time series related to a running session acquired in June 2021. The normalized time between 0 and 1 is shown on the x axis. The vertical red lines divide the time series into the three sections “start” (from 0 to 0.33), “middle” (from 0.33 to 0.66), and “end” (from 0.66 to 1). Color legend: yellow: +/+ cluster; black: −/− cluster; blue: −/+ cluster; green: +/− (see Figure 2 in Section 3.1.); cluster frequency boxplots in the three different running sections for cluster −/− (b), cluster −/+ (c), cluster +/− (d), and cluster +/+ (e). p-value annotation legend: ns: 5.00 × 10−2 < p ≤ 1.00 × 100; *:1.00 × 10−2 < p ≤ 5.00 × 10−2; **: 1.00 × 10−3 < p ≤ 1.00 × 10−2; ***: 1.00 × 10−4 < p ≤ 1.00 × 10−3.

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  Figure 7. (a) RQA determinism boxplots in three different running sections; a representative RP of HR time series during an exemplary running session. In “middle” (b) and “end” (c) sections a larger number of black points (recurrence points) can be seen with respect to the “start” section (d). p-value annotation legend: ns: 5.00 × 10−2 < p ≤ 1.00 × 100; *: 1.00 × 10−2 < p ≤ 5.00 × 10−2; ***: 1.00 × 10−4 < p ≤ 1.00 × 10−3.