Source-linked AI summary
Dynamic similarity promotes interpersonal coordination in joint-action
Piotr Słowiński, Chao Zhai, Francesco Alderisio, Robin Salesse, Mathieu Gueugnon, Ludovic Marin, Benoit G. Bardy, Mario di Bernardo, Krasimira Tsaneva-Atanasova
TL;DR
The paper addresses how to capture individual movement styles and test whether similarity in movement dynamics relates to coordination in joint action. It defines motor signatures from velocity profiles and finds that dynamic similarity is associated with coordination in the mirror game.
Problem
The paper asks how to capture personal kinematic features and identify individuals from movement, and whether people with similar movement dynamics synchronize more during joint tasks.
Source: §1 · p. 2Method
The authors use velocity probability density functions as individual motor signatures, compare profiles with earth mover distance and multidimensional scaling, and measure temporal correspondence with relative position error.
Source: §4 · p. 14, §5.3 · p. 26Results
Solo-motion velocity profiles were stable over time and differed significantly between players, while greater dynamic similarity of solo motions was associated with enhanced coordination in the mirror game.
Source: §4 · p. 14Takeaways & Limitations
The findings support the theory-of-similarity prediction that participants with more similar solo-motion dynamics coordinate more in the mirror game.
Source: §4 · p. 14Relative-phase estimates can incur errors for signals with non-zero local means and are sensitive to amplitude changes when amplitude and phase spectra are not well separated.
Source: §5.9 · p. 36
Abstract
from arXiv · showhide
Human movement has been studied for decades and dynamic laws of motion that are common to all humans have been derived. Yet, every individual moves differently from everyone else (faster/slower, harder/smoother etc). We propose here an index of such variability, namely an individual motor signature (IMS) able to capture the subtle differences in the way each of us moves. We show that the IMS of a person is time-invariant and that it significantly differs from those of other individuals. This allows us to quantify the dynamic similarity, a measure of rapport between dynamics of different individuals' movements, and demonstrate that it facilitates coordination during interaction. We use our measure to confirm a key prediction of the theory of similarity that coordination between two individuals performing a joint-action task is higher if their motions share similar dynamic features. Furthermore, we use a virtual avatar driven by an interactive cognitive architecture based on feedback control theory to explore the effects of different kinematic features of the avatar motion on the coordination with human players.
1 Introduction
The paper addresses how to identify personal movement styles and test whether dynamic similarity relates to coordination in joint tasks. It proposes individual motor signatures and reports that similarity between players’ preferred motions enhances synchronisation in the mirror game.
1 Introduction
- An open problem is how to capture personal movement features and identify individuals from the way they move.The introduction links this problem to testing whether people with similar movements synchronise more during joint tasks.Source: §1 · p. 2
- The theory of similarity predicts enhanced joint-action synchronisation when participants are similar in morphology and movement dynamics and willing to match behaviours.The introduction says this prediction had not been tested in controlled experiments despite previous attempts.Source: §1 · p. 2
- The paper proposes a time-invariant individual motor signature and a measure of dynamic similarity to predict coordination in interactive joint action.The signature captures kinematic features that distinguish individuals.Source: §1 · p. 2
- In the mirror game, similarity between players’ preferred motions enhances synchronisation during interaction.The paper presents dynamic similarity as a complement to qualitative measures of affiliation affecting joint actions.Source: §1 · p. 3
2 Methods
The study uses three experimental scenarios to establish individual motor signatures and examine how dynamic similarity relates to coordination. It derives velocity profiles from movement recordings, compares them with Earth mover’s distance, and uses multidimensional scaling and relative position error for analysis.
2 Methods
- Three scenarios provided solo movements to establish motor signatures and human–human or human–virtual-player interactions to examine coordination.Solo data from Scenarios 2 and 3 were also used to measure dynamic similarity between interacting participants.Source: §2 · p. 3
2.1 Experimental Setups and Data Collection
- Scenario 1 recorded nine 60-second solo movement series for each of 15 participants across three sessions separated by at least one week.Participants moved a preferred hand above a Leap Motion sensor; positions were recorded in arbitrary units.Source: §2.1 · p. 3
- Scenario 2 recorded eight dyads moving balls along strings, with solo, leader–follower, and joint-improvisation conditions.Movements were captured at 100 Hz; leader–follower rounds let both participants lead and follow.Source: §2.1 · pp. 3–4
- In Scenario 3, 51 people played as followers with a virtual player driven by adaptive feedback control using a prerecorded reference trajectory.Each participant completed four solo rounds and 12 interaction rounds; the virtual player’s reference was based on solo trials and modified to control similarity.Source: §2.1 · pp. 4–5
2.2 Data processing
- Preprocessing filtered and differentiated position recordings, then represented velocity time series as PDFs and compared profiles using Earth mover’s distance.Velocity PDFs were estimated with normalised histograms; EMD measures the work required to transform one histogram into another.Source: §2.2 · p. 5
- Multidimensional scaling represented distances between velocity profiles, while relative position error measured how well a follower tracked a leader’s movement.Classical MDS was used to visualise relations between profiles while preserving distance information.Source: §2.2 · pp. 5–6
3 Results
The results present individual motor signatures as time-persistent, distinguishable movement profiles, and use distances between them to examine coordination. Smaller signature distances are associated with better coordination in human dyads and human–virtual-player interactions, while cooperative movement can differ from solo preferences.
3.1 Existence of an Individual Motor Signature
- Solo-trial velocity profiles cluster by participant across recordings on three different days, supporting time-persistence, and the ellipses show separation between participants.Figure 1 depicts 15 participants in Scenario 1 and a representative subset from Scenario 3; the latter recordings were collected on a single day.Source: Figure 1 · p. 7, §3.1 · p. 8
- Median ellipse overlap was 0.02 for 15 participants in Scenario 1 and 0.05 for 51 participants in Scenario 3; 45/105 and 418/1275 pairs, respectively, did not overlap.The paper reports that individual signatures can identify participants and measure dynamic similarity.Source: §3.1 · p. 8
- The similarity-space x coordinate correlates with absolute average velocity, while the y coordinate correlates with velocity-segment kurtosis.The paper relates kurtosis to the ratio of high and low velocities in the motion.Source: §3.1 · p. 8
3.2 Behavioural plasticity during social interaction
- Cooperative movement profiles reveal behavioral plasticity: some participants adjust their kinematic characteristics during interaction, and movement dynamics can vary with who leads.Joint-improvisation dynamics differed from leader–follower dynamics in the reported examples.Source: §3.2 · pp. 9–10, Figure 2 · p. 9
3.3 Dynamic similarity enhances coordination in joint action
- ρ=0.3907 (p=0.0066) for the correlation between signature distance and relative position error in human leader–follower trials; the association remained significant after controlling for speed-related factors.Adjusted Spearman correlations were ρ=0.3466 (p=0.0183) controlling for leader velocity and ρ=0.4697 (p=0.0011) controlling for both factors.Source: Figure 4 · p. 12, §3.3 · pp. 12–14
- In human–virtual-player trials, relative position error increased with distance between the player’s solo signature and the virtual player’s reference, but the association disappeared when controlling for preferred-velocity difference.The reference trajectories were made faster by adding a 2.5 Hz sine signal, making this a special case of dynamic similarity.Source: Figure 4 · p. 12, §3.3 · p. 13
4 Discussion and Conclusions
The paper establishes time-invariant individual motor signatures from solo velocity profiles and finds that dynamic similarity is associated with stronger coordination. It also presents an interactive virtual player as a tool for studying joint actions.
4 Discussion and Conclusions
- Solo velocity profiles provide time-persistent individual motor signatures that differ significantly between players, extending motor signatures beyond periodic-motion frequency content.The authors describe the signatures as readily recordable with an off-the-shelf experimental setup.Source: §4 · p. 14
- Greater dynamic similarity between participants’ solo motions is associated with higher coordination in the mirror game, supporting a central prediction of similarity theory.The study measures similarity using distances between velocity profiles and temporal correspondence using relative position error.Source: §4 · p. 14
- The study focuses on direct, intentional human coordination with a designated leader, which differs from spontaneous or unintentional coordination in animal groups.The authors identify extension of animal models to interpersonal interaction as a future research direction.Source: §4 · pp. 14–15
- An interactive cognitive architecture drives a virtual player while maintaining bidirectional coupling, allowing control through reference trajectories and coupling parameters.The authors identify this as a tool for studying joint actions and discuss possible use in social-bonding applications.Source: §4 · p. 15
- The paper introduces quantitative measures for dynamic properties of complex aperiodic movements in human socio-motor interaction.It also introduces an interactive cognitive architecture to drive a virtual player in the mirror game.Source: §4 · p. 15
Funding
The work received support from the European Project AlterEgo and an EPSRC grant.
Funding
- The work was funded by European Project AlterEgo FP7 ICT 2.9, grant 600610, and K.T-A’s research was supported by EPSRC grant EP/L000296/1.European Project AlterEgo is identified as Cognitive Sciences and Robotics.Source: Funding · p. 16
Earth’s movers distance
Earth’s movers distance (EMD) compares probability distributions by measuring the area between their cumulative distribution functions. The paper uses it to compare velocity-profile distributions, including cases that share the same first four moments.
Earth’s movers distance
- EMD is a metric on PDFs, satisfying positive definiteness, symmetry, and the triangle inequality.The paper notes that EMD is non-parametric and quantifies partial matches.Source: Earth’s movers distance · pp. 16–17
- EMD compares distributions beyond selected moments, which may not uniquely parameterize a probability density function.For univariate PDFs, EMD is the area between their cumulative distribution functions; it is a special case of Wasserstein distance.Source: Earth’s movers distance · pp. 16–17
- The example velocity-profile histogram and Pearson-system histogram share the same estimated first four moments, yet EMD distinguishes them.Figure 5 illustrates the CDF gap as the shaded area between the distributions.Source: Earth’s movers distance · pp. 17–18, Figure 5 · p. 17
- Empirical CDFs are computed from normalized cumulative histogram counts using 101 equidistant bins over a fixed velocity range.EMDs are normalized by the maximum EMD for the support, given as its length.Source: Earth’s movers distance · p. 18
Similarity space
The similarity space maps solo velocity profiles into a geometric representation of their proximities. Its dimensions relate to participants’ average speed and the kurtosis of their velocity segments, while the combined space separates individuals better than either correlate alone.
Similarity space
- Mean kurtosis of velocity segments describes direction changes: low kurtosis indicates sudden changes, whereas high kurtosis indicates slower changes.The segments are portions of the velocity time series between consecutive zero-velocity points.Source: Similarity space · pp. 18, 20
- The similarity-space x coordinate is strongly correlated with average solo speed, while y is correlated with mean kurtosis of normalized velocity segments.Figure 6 reports x versus mean absolute velocity (R2=0.9993, ρ=0.9979) and y versus average kurtosis (R2=0.5657, ρ=0.5685).Source: Similarity space · p. 18, Figure 6 · p. 19
- The similarity-space coordinates separate participants better than a plane defined by their correlates, and mean absolute velocity alone is insufficient to separate them.The space is derived by multidimensional scaling of EMDs between velocity profiles.Source: Similarity space · pp. 18, 20
Relative position error
Relative position error (RPE) estimates follower–leader position difference using shared motion direction when both players move together, and absolute distance when they move oppositely. Its sign also indicates whether the designated follower is behind or ahead.
Relative position error
- RPE combines signed position difference during shared motion with absolute position difference during opposite motion, treating the follower as behind in the latter case.The definition assumes that changes in direction are initiated by the leader.Source: Relative position error · pp. 20–21
- Positive RPE means the follower is behind; negative RPE means the designated follower is ahead, suggesting the designated leader is tracking them.RPE is asymmetric because it is defined relative to a designated leader and follower.Source: Relative position error · pp. 20–21
5 Supplementary Information
The supplementary methods derive velocity profiles and curve-segment measures, then compare how well they separate individuals and represent motion similarity. Velocity profiles separate participants better than segment skewness and kurtosis, while the latter still describe short-timescale motion characteristics.
5.1 Preprocessing
- Velocity profiles capture whole-trial motion while avoiding physical position-range constraints; the authors found univariate velocity distributions sufficient for this study.They estimate velocities from preprocessed positions and use normalized histograms to represent the velocity distributions.Source: §5.1 · p. 22
5.2 Earth’s movers distance
- Earth Mover’s Distance (EMD) measures distances between velocity profiles, and multidimensional scaling places profiles in a similarity space where closer points indicate more similar profiles.The MDS coordinates approximate EMD distances, allowing pairwise profile relationships to be visualized geometrically.Source: §5.3 · pp. 24, 26
5.3 Multidimensional scaling
- Classical MDS transforms the matrix of pairwise profile distances into coordinates, using the first two dimensions because they were sufficient for the analysis.The procedure double-centres squared distances, eigendecomposes the resulting matrix, and uses leading eigenvectors and eigenvalues to obtain coordinates.Source: §5.3 · p. 25
5.4 Moments of a curve
- Curve moments are computed over time-normalized velocity segments, describing curve shape rather than the moments of sampled velocity values.Skewness indicates acceleration–deceleration asymmetry, while kurtosis describes uniformity of maximal velocity; higher kurtosis generally accompanies higher maximum velocity.Source: §5.4 · p. 27
5.5.1 Overlap
- Ellipse overlap quantifies separation between individuals’ regions in either representation, with zero indicating no overlap and one indicating complete overlap.Ellipses are fitted to participant coordinates using a 0.7 probability mass; the overlap ratio is dimension-independent.Source: §5.5.1 · pp. 29–30
5.5.2 Comparison
- Median ellipse overlap was lower in similarity space than the skewness–kurtosis plane in both scenarios: 0.02 vs 0.2 in Scenario 1 and 0.05 vs 0.1 in Scenario 3.In Scenario 1, 45 of 105 pairs did not overlap in similarity space versus none in the skewness–kurtosis plane; in Scenario 3, the counts were 418 versus 183 of 1378 pairs.Source: §5.5.2 · p. 30
5.5 Comparison of velocity segments and velocity profiles
- Velocity-segment skewness and kurtosis describe short-timescale motion, but their substantial overlap across individuals makes them insufficiently specific for studying dynamic similarity.The moments cluster by person and persist over time, yet overlap prevents reliable distinction between participants.Source: §5.5 · p. 29, §5.5.2 · p. 30
5.6 Velocity segments of movement generated by ICA
The analyses compare movement kinematics and measures of coordination, finding that avatar-led velocity segments largely resemble human movement and that RPE is useful for assessing leader–follower interaction. They also distinguish similarity in movement dynamics from coordination in time.
5.6 Velocity segments of movement generated by ICA
- In most trials, ICA-driven avatar leaders’ velocity segments had skewness and kurtosis similar to human players, with stronger skewness linked to followers’ rapid correction after direction changes.Some avatar-leader skewness values were higher because the avatar tracked a fast-changing reference while leading.Source: §5.6 · pp. 32–34
5.7 Correlations and partial correlations between different variables and RPE
- Dynamic similarity remained significantly associated with RPE after controlling for the leader’s average absolute velocity, so leader speed alone did not explain RPE variability.Adding a 2.5 Hz sinusoid to solo trajectories also increased the reference trajectory’s average absolute velocity.Source: §5.7 · p. 34
5.8 Statistical tests
- Spearman’s rank correlation tested associations, Pearson’s R² illustrated linear dependence, and Kolmogorov–Smirnov tests assessed differences between distributions.The authors selected these tests because their data were not normally distributed.Source: §5.8 · p. 36
5.9 Relative phase
- Wavelet coherence supplied relative-phase estimates from correlated time-frequency regions, avoiding Hilbert-transform phase jumps caused by changing local means.The wavelet estimate’s sign matched the designated leader’s role; it uses signal components that are measurably correlated and modelled with periodic functions.Source: §5.9 · pp. 36–37
5.10 Comparison of different measures of temporal correspondence
- For complicated mirror-game trajectories with a designated leader, RPE was the most useful measure: it showed a stronger association with movement dynamics than relative phase.Wavelet-based relative phase may help in leaderless joint improvisation, where RPE cannot be used.Source: §5.10 · pp. 39–40
5.11 On the relation between temporal correspondence and dynamic similarity
- Similar velocity profiles can occur without coordinated position trajectories (nontrivial dynamic similarity), whereas coordination necessarily entails similar velocity profiles (trivial dynamic similarity).The distinction arises because velocity profiles do not retain temporal information.Source: §5.11 · pp. 40–42, Figure 8 · p. 41