Is gait more individual at slow speed?
Knee-flexion cycles of 52 healthy adults walking at five speeds, analysed with participant-level statistics: re-identification, variance decomposition, functional PCA, grouped cross-validation and clustering stability.
- One knee cycle identifies its owner among 52 people 63 % of the time at spontaneous speed, but only 53 % at very slow and 51 % at slow speed (paired difference C2 − C4: −11.9 points, 95 % CI −19.9 to −3.6). Slow walking does not make gait more individual. The drop itself is specific to raw curves: after removing each cycle's offset, or with DTW, no slow-speed difference excludes zero, so the robust conclusion is “not more individual”, not “less individual”.
- It makes it more variable: within-participant SD rises from 2.8° to 4.5°, between-participant SD from 4.0° to 6.5°, so the ICC stays between 0.64 and 0.68 at every speed.
- The "first bump" grows with speed: its excursion (maximum flexion in the first 25 % of the cycle minus flexion at heel strike) rises from 4.4° (very slow) to 17.9° (fast): +10.5° per m/s within a participant, positive in 52 of 52; it is absent in 37 % of very-slow cycles.
- Speed class from one time-normalised cycle: 70% with participant-grouped CV (chance 20 %). Cycle-level CV would have reported 60% for 1-NN DTW instead of 48%.
Why it matters
Clinical gait analysis compares a patient's curves with a reference band, and the original course project concluded that asking patients to walk slowly could expose individual abnormalities. That claim deserves a test before it shapes a protocol. In these data slow walking adds stride-to-stride noise at both levels without making individual signatures more distinctive.
Data
Five MATLAB files, one per speed instruction, each holding knee flexion-extension
time-normalised to 101 samples per cycle (heel strike to heel strike) plus spatio-temporal
parameters. Participants are keyed by their position in the files because one label
(SS2014004) is shared by two different people; 16 very-slow cycles that duplicate another stride of the same person
are removed. Ages 19–67, 29 men.
| condition | instruction | cycles | speed (m/s) | stance (% cycle) | cadence (steps/min) |
|---|---|---|---|---|---|
| C1 very slow | 0-0.4 m/s | 504 | 0.29 | 74.4 | 42 |
| C2 slow | 0.4-0.8 m/s | 512 | 0.61 | 68.3 | 72 |
| C3 medium | 0.8-1.2 m/s | 510 | 0.98 | 65.0 | 100 |
| C4 spontaneous | self-selected | 514 | 1.15 | 64.0 | 108 |
| C5 fast | self-selected fast | 504 | 1.63 | 61.4 | 128 |
1. Does slow walking make gait more individual?
A cycle is matched to its nearest neighbour among all other cycles at the same speed (leave-one-cycle-out); accuracy is the share matched to the right participant. Intervals are participant-level bootstrap percentiles (2,000 resamples), and condition differences are paired on the same resampled participants.
Same-speed re-identification from one cycle (52 participants)
Raw curves identify people best at spontaneous and fast speed. Registering toe-off narrows the gap; DTW with a 10 % band (a common default, not tuned on these data) stays between 49 % and 54 % at every speed, 8 to 10 points below raw Euclidean at spontaneous and fast speed. A narrower 2 % band, checked post hoc, beats Euclidean at every speed: light warping helps, wider warping removes timing differences that are part of a person's signature.
Variance components, averaged over the cycle
Slow walking widens both spreads by a similar factor, so the share of variance that belongs to the person (ICC) does not change.
Pointwise ICC along the gait cycle
Pointwise ICC: at medium to fast speed the person shows most in loading response (10-15 % of the cycle) and least around toe-off and terminal swing. At slow speed that peak flattens, together with the loading bump itself.
Re-identification across speeds (raw curves)
A signature transfers only between C3 and C4, whose speed ranges overlap (42 % to 46 %); every other pair, neighbours included, is at 3 % to 20 % (13 % on average off the diagonal).
2. How does speed deform the curve?
Mean knee flexion per speed (95 % CI over participants)
Faster walking raises loading-response flexion and peak swing flexion and shortens stance (toe-off moves earlier).
Loading-response excursion per participant
Each grey line is a participant. The first bump grows with speed in all 52 participants; Friedman chi2 = 192, p = 2e-40.
| comparison | mean change (deg) | participants up | Holm p |
|---|---|---|---|
| C2 - C1 | +2.0 [+1.4, +2.7] | 44 / 52 | 2.8e-07 |
| C3 - C2 | +4.9 [+4.1, +5.8] | 51 / 52 | 1.4e-09 |
| C4 - C3 | +2.0 [+1.4, +2.6] | 43 / 52 | 2.8e-07 |
| C5 - C4 | +4.6 [+4.0, +5.3] | 52 / 52 | 1.4e-09 |
Functional PCA on participant-by-speed mean curves: the first component explains 58 % of the variance and correlates with measured speed at Spearman rho = 0.92; the next components are almost speed-free (|rho| ≤ 0.13).
3. Can one cycle tell the speed?
Each participant contributes cycles to every class, so folds are grouped by participant: the model is always tested on people it has never seen. The cycle-level split is shown only to measure the leakage.
Speed class from one cycle
Stance duration alone reaches 55%; the curve shape lifts it to 70%. Errors fall almost only between neighbouring speeds, mostly C3 and C4, whose instructions overlap. The leaky split flatters the nearest-neighbour model most (+11 points) because it can recognise the person.
| model | grouped CV | cycle-level CV | gap |
|---|---|---|---|
| Stance duration only (logistic) | 54.7% (51.7% to 57.7%) | 55.2% | +0.5 pts |
| 8 FPCA scores (logistic) | 70.1% (66.7% to 73.3%) | 71.4% | +1.4 pts |
| Gradient boosting, 101 samples | 66.7% (63.8% to 69.7%) | 72.9% | +6.2 pts |
| 1-NN, DTW band 10 % | 48.4% (45.6% to 51.0%) | 59.5% | +11.2 pts |
4. Clustering, revisited
DTW k-medoids on all cycles
At k = 5 the DTW k-medoids clusters agree with the speed labels at ARI only 0.15, and only k = 2 survives participant resampling (median ARI 0.86, against 0.55 at k = 5). Strides of one participant at one speed mostly share a cluster (77 %, against 51 % for random strides of the same speed): the clusters follow people more than speed instructions.
Re-running the original course pipeline (DTW k-medoids on spontaneous cycles, distances to the three medoids, k-means with k = 5) gives ARI 0.17 against the speed labels. Its headline "within-person variance" (26.88 at very slow versus 8.31 at fast speed, a ratio of 3.2) is not reproduced in absolute value (the original picked its medoids from an unconverged initialisation and did not seed k-means) but its ratio is: 392 versus 133, a ratio of 2.9. Its "lowest at fast speed" is not: the minimum is at C3 (96). That number is the variance of a distance to spontaneous-speed medoids: slow cycles sit far from those medoids, so their distances, and the spread of those distances, are larger. Scaled by the mean distance, the spread is the same at both speeds (coefficient of variation 0.15 versus 0.16).
Limitations
- Healthy adults only. Nothing here measures or diagnoses pathology; whether slow walking helps to expose an abnormality is a different question that needs patients.
- One session per participant: re-identification uses strides from the same session and the same marker placement, so part of the "signature" may be a placement offset (removing each cycle's mean costs 4 to 13 points of accuracy depending on speed).
- Re-identification intervals resample the query participants with the 52-person gallery held fixed, so they are conditional on this gallery.
- The loading-response excursion is a per-cycle maximum over a window, so where no clear peak exists (37 % of very-slow cycles) it partly measures stride noise and is biased upward: the very-slow mean curve rises only about 2.6° over the same window.
- Knee flexion only, one joint and one plane; time-normalised cycles hide cycle duration, which by itself would reveal speed.
- The speed classes overlap by design (C3 is 0.8–1.2 m/s, spontaneous is about 1.15 m/s), which caps classification accuracy.
- Provenance: the files match the protocol of Schreiber and Moissenet (2019), but they come from a course distribution (52 participants rather than the 50 of the public release); the exact correspondence was not verified.
References
- Schreiber C., Moissenet F. (2019). A multimodal dataset of human gait at different walking speeds established on injury-free adult participants. Scientific Data 6, 111. doi:10.1038/s41597-019-0124-4
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