Identifying unique gait phenotypes across neuromotor conditions using wearable inertial sensors and topological data analysis

Abstract

Wearable sensors quantify gait and mobility in detail, but translating high-dimensional data into clinically actionable insights remains challenging in precision rehabilitation. We applied Topological Data Analysis (TDA) to inertial sensor recordings from multiple gait assessments in 81 individuals with stroke, Parkinson’s disease, lower-limb difference, functional neurological disorders, and healthy controls. TDA generated a unified functional map that organized participants based on shared gait patterns across conditions. Within stroke, three phenotypes, corresponding to low, moderate, and high gait function emerged and aligned with clinical outcomes, while Parkinson’s disease shows a smoother transition from low- to high-function phenotypes. Individuals with lower-limb difference were distributed across other conditions which reflected their variable and shared gait patterns. Supervised machine-learning analysis further identified gait signatures for each phenotype. This framework enables mapping new patients into interpretable functional phenotypes, supports targeted intervention planning, and permits clinical decision-making from sensor data.

Introduction

Precision rehabilitation is of major interest in treating mobility disorders because no two patients are alike. It is becoming increasingly clear that effective rehabilitation requires insights into each patient’s impairments and functional presentation to guide tailored treatment strategies. Advancing rehabilitation strategies is pressing given the high prevalence of mobility impairments, affecting 12.2% of U.S. adults and nearly one-third of adults over the age of 75 (2023; www.apa.org/monitor/2023/11/older-adults-disabilities, 2024; www.cdc.gov/disability-and-health/articles-documents/disability-impacts-all-of-us-infographic.html), and the substantial health, economic, and societal burden they impose worldwide¹. Despite its importance, precision rehabilitation is difficult to actually implement using current clinical tools. Traditional patient assessments (mostly clinical scales or performance-based tests) often lack the sensitivity, resolution or linearity to detect subtle changes over time^2–4, and they do not include objective measures of impairment that could serve as early indicators of overall intervention success^5–8. For example, functional assessments such as the 10-Meter Walk Test (10MWT) and the Timed Up and Go (TUG)^9–11 are reliable and easy to administer. However, these tests reduce mobility to simple outcome measures such as walking speed or completion time and cannot capture nuanced gait differences and phenotypes within or among patients^12–15.

In precision rehabilitation, gait phenotyping can bridge the gap between traditional clinical observation and precision insight into walking function and impairments across different mobility-related disorders. Identifying common or unique characteristics among individuals can improve personalized rehabilitation strategies, enhance recovery or progression monitoring, and optimize diagnostic predictions. This advancement is often done by supporting assessments with digital instruments. For example, wearable sensor-based phenotyping has found specific gait biomarkers that distinguish different motor subtypes of Parkinson’s disease, and support their potential for earlier diagnosis and precision treatment strategies across these subtypes while also enabling quantitative symptom monitoring over time¹⁶. Instrumenting gait assessment with low-cost, wearable inertial motion sensors directly records continuous, high-temporal resolution, multi-segment, and quantitative data related to gait mechanics. The explosion of research using wearable sensors for rehabilitation applications has verified their ability to capture subtle and complex gait measures beyond traditional clinical tests^17–20. However, measurement alone is insufficient; integrating these data into robust big-data analytic frameworks is also essential to derive clinically meaningful insights from diverse patient populations and to enable actionable application in clinical practice^21–23. Uncovering latent gait phenotypes from big data has been previously explored through neuromechanical modeling, such as dimensionality reduction approaches²⁴ machine learning²⁵, etc.

Topological Data Analysis (TDA) offers an alternative, novel method to compare the underlying pattern of high-resolution data across diverse populations^26–28. TDA creates a new representation of the data without relying on a specific coordinate system, instead quantifying similarities and differences through unitless “distances.” This makes TDA especially useful for harmonizing mixed biomechanical and biological datasets recorded using different measurement tools²⁹. Moreover, TDA’s robustness to noise and outliers allows it to identify consistent structural patterns in high-dimensional data, such as human movement. A widely used implementation of TDA is the Mapper algorithm³⁰, which creates a visual summary of the data shape and organization, including clusters, connections, loops, and other hidden patterns that conventional exploratory techniques often overlook. This approach has not yet been explored as a technique for phenotyping gait in mixed patient populations.

In this study, we applied advanced multidimensional analysis of gait using TDA to identify gait phenotypes across individuals with a variety of neuromotor conditions, including stroke/cerebrovascular accident (CVA), Parkinson’s disease or functional neurological disorder (PD-FND), or lower limb difference after amputation (LL), as well as healthy individuals (HC) with no known mobility impairments. Our goal was to create a transferable analytical framework that can be applied to other clinical populations and datasets in order to support broader study and advancement of precision rehabilitation.

Results

In this study, 81 research participants were recruited and sorted into four cohorts depending on their diagnosis (Table 1). Anthropometric measurements were performed on each participant prior to completing a set of clinical assessments that targeted upper or lower limb motor function; either condition-specific or common across groups (Tables S1 and S2). Assessment data were captured via clinical scores, inertial measurement unit (IMU) sensors (Fig. 1a), or both. Whole-body kinematic and spatiotemporal parameters were calculated from IMU data during three common functional assessments across all four cohorts (10MWT, TUG, and stair climbing; Fig. 1b) and used in the TDA Mapper algorithm to identify meaningful gait phenotypes.

Table 1.

Basic demographic and clinical characteristics of participants

Variable	CVA (n = 30)	PD-FND (n = 11)	LL (n = 20)	HC (n = 20)	Statistic, p-value
Sex, Female	17	4	6	10	3.976, 0.264
Age (years)	60.0 [16.75]	73.0 [7.0]	58.5 [26.5]	44.0 [33.25]	21.703, <0.001a HC/CVA, 0.044a HC/PD-FND, <0.001a LL/PD-FND, 0.013a CVA/PD-FND, 0.042a
Ethnicity, Hispanic	1	0	4	2	5.245, 0.155
Race	n = 28b	n = 11	n = 18b	n = 20
Asian	2	0	0	2	37.277, <0.001a
Black/African American	21	1	6	2
Middle Eastern	0	0	1	0
White/Caucasian	5	10	11	16
Dominant side	n = 30	n = 11	n = 20	n = 20
Left	2	1	2	1	2.142, 0.906
Right	27	10	18	19
Bilateral	1	0	0	0
Impaired side	n = 30	n = 8b	n = 20	n = 20
Left	17	4	15	10	6.980, 0.323
Right	13	4	4	10
Bilateral	0	0	1	0
Chronicity (years)	9.3 [8.25]	-	12.62 [30.71]	-	0.128, 0.721
Type of stroke, Ischemic	17	-	-	-	-
Assistive device, Present	25	2	7	0	41.615, <0.001a
AFO, Present	16	0	0	0	34.45, <0.001a
Knee cage, Present	1	0	0	0	1.678, 0.642
Power chair, Present	0	0	1	0	2.486, 0.478
Straight cane, Present	12	1	3	0	13.727, 0.003a
Other cane, Present	2	0	2	0	2.233, 0.525
Walker, Present	1	1	1	0	2.998, 0.392
Rollator, Present	2	0	0	0	3.406, 0.333
Scooter, Present	1	0	0	0	1.678, 0.642
Cause of Amputation	-	-	n = 20	-	-
Trauma	-	-	10	-
Vascular disease	-	-	2	-
Infection	-	-	4	-
Cancer	-	-	3	-
Other	-	-	1	-
Amputation level			n = 20		-
Transtibial	-	-	13	-
Before knee	-	-	2	-
Transfemoral	-	-	5	-
Amputation K-level			n = 20		-
K1	-	-	1	-
K2	-	-	1	-
K3	-	-	3	-
K4	-	-	9	-

All metrics are expressed in terms of mean (standard deviation), median [interquartile range], or frequency, corresponding to continuous variables with normal distribution, continuous variables with non-normal distribution, and categorical variables, respectively.

Statistics and p-values are derived from the corresponding statistical test (i.e., ANOVA, Kruskal-Wallis, and chi-squared test, respectively).

^aStatistically significant p-values (p < 0.05).

^bSample sizes for individual variables may differ from the total number of participants due to subsets of missing data (For participants without a clearly identifiable impaired side and participants who did not report their race).

CVA Cerebrovascular Accident (i.e., stroke), HC Healthy Controls, LL Lower Limb difference, N Number, PD-FND Parkinson’s Disease-Functional Neurological Disorder.

Fig. 1. Overview of the TDA on gait parameters.

a Participants were equipped with 17 IMU sensors. b Motion data from clinical assessments were recorded and kinematic and spatiotemporal parameters were calculated for each stride, trial, or stair, depending on the task (10MWT at preferred, slow, and fast speeds; single- and dual-task TUG; stair climbing). c Gait parameters were averaged for each participant to form a structured dataset. This dataset was processed by a PCA to extract top components across four specific cohorts: CVA, PD-FND, LL, or HC. d Principal components across participants were embedded into a lower-dimensional space using the first two components of t-distributed Stochastic Neighbor Embedding (t-SNE), with each data point representing a participant. e Data points were then grouped to identify locally dense regions/clusters. f Clusters were connected to form a network, where nodes represent overlapping groups of similar individuals and edges indicate shared participants between two connected nodes. g Final Mapper algorithm visualization. Two nodes are magnified to show the participant samples within each node. Nodes were defined to contain a minimum of two participants from either the same or different groups.

TDA reveals global gait similarities and differences across neurological conditions

In TDA Mapper, a total of 227 kinematic and spatiotemporal gait parameters (135 from the 10MWT, 50 from TUG, and 42 from stair climbing) were extracted and averaged across strides, trials, and steps as appropriate for each participant (Fig. 1c). These parameters were standardized and used in a principal component analysis (PCA) to reduce dimensionality, mitigate feature collinearity, and retain the most informative variance structure of the gait dataset. Principal components explaining 95% of the cumulative variance were retained, resulting in the first 47 components being used as input for the TDA analysis. Subsequently a systematic hyperparameter exploration was performed within the Mapper framework to empirically evaluate the stability and consistency of emerging cluster structures across different cover resolutions, overlap levels, and clustering parameters. Initial inspection focused on identifying configurations in which coherent participant groups (clusters) were consistently preserved across parameter settings. Configurations were then refined to avoid both excessive fragmentation (isolated notes) and over-smoothing resulting in overly uniform connectivity without identifiable group structure (Fig. 1d–g). In the final configuration, participants were grouped into nodes optimized with 14 cubes (defined sub-regions of the clustering space for node formation), 55% percent overlap among sub-regions, at least two participants within each node, and a distance threshold (ε) of five, which was selected as the smallest value that prevented over-fragmentation of the Mapper graph. Figure 2 shows the distribution of all participants across the Mapper, color coded based on the prevalence of target participants over the total number of participants within each node. HC participants (Fig. 2d) were clustered along the lower region of the graph and formed a dense and bimodal distribution with limited spread across the topology. This group has almost no overlap with individuals with CVA (Fig. 2a), who were in three distinct network regions (red arrows), suggesting the presence of three possible distinct gait phenotypes in the CVA group. Participants with PD-FND (Fig. 2b) and LL (Fig. 2c) were positioned between these two groups. While those with PD-FND formed a clear cluster with two branches (Fig. 2b), participants with LL were scattered across Mapper.

Fig. 2. Topological distribution of participant groups based on gait parameters.

a CVA, b PD-FND, c LL, and d HC. Nodes were generated using principal components from gait spatiotemporal parameters and kinematics derived from 10MWT (preferred, slow, and fast speeds), TUG (single- and dual-tasks), and stair climbing assessments. Node color intensity reflects the prevalence of participants in that node who belong to the target condition. Nodes without any participants from the target group are blank. In the CVA and PD-FND Mappers, three distinct participant regions were visually identified and are indicated with highlighted background and arrows.

Across all hyperparameter settings, the global relationships among the four conditions remained visible, and at higher resolutions, condition-specific regions became more distinct. For example, the three CVA gait patterns identified in Fig. 2a remained spatially coherent across resolutions, either appearing as distinct islands or merged but locally compact regions (Figs. S1–S4). A similar stability was observed in the PD-FND cohort, where participants’ groupings (Fig. 2b) retained their relative neighborhood structure. Two participants (CVA#16 and one HC#12) were excluded from the final Mapper visualization, as their assignment was unstable across different cover and overlap settings and they were classified as noise under the selected configuration. While these participants could be incorporated under alternative parameter choices, the presented Mapper was optimized to provide the clearest and most stable representation for phenotype discovery. Importantly, these participants were retained in all subsequent machine learning analyses. An interactive version (https://xka1z0x.github.io/TDA-Mapper/) of the Mapper can be used to further explore the distribution and location of each participant.

TDA reveals three distinct gait phenotypes in individuals with CVA

For individuals with CVA, TDA revealed three distinct subgroups (Fig. 2a). To explore these subgroups, the Mapper was color coded using the first Principal Component (PC1) scores derived from different combinations of clinical assessments. These scores were not directly used to form the Mapper. Specifically, the Mapper was first color-coded using locomotion and endurance assessments (6MWT distance and 10MWT performed at preferred, slow, and fast speeds; Fig. 3a), second using functional mobility assessments (time to complete the single- and dual-task TUG, Fig. 3b), and third using upper limb motor function assessments (Action Research Arm Test, ARAT, and upper-limb Fugl-Meyer Assessment, FMA, Fig. 3c). The clearest distinction among subgroups was observed in the Mapper colored by locomotion and endurance assessments (Fig. 3a), with the subgroups differentiated by functional performance on these assessments (low, moderate, and high functional level). This indicates strong alignment between the objective multi-assessment gait pattern and function level. For each subgroup, nodes were explored to identify participants and calculate clinical outcome values for each subgroup. Statistical comparisons of these three subgroups also showed significant differences (Fig. 3d–f) with values presented in Table 2.

Fig. 3. Topological representation and clinical comparison of gait characteristics in individuals with CVA.

Mappers visualizing participants with CVA (n = 29), colored by first principal components (PC1) scores from (a) 10MWT at preferred, slow, and fast speeds and 6MWT distance (locomotion and endurance), b single- and dual-task TUG times (functional mobility), and c ARAT and FMA scores (upper limb motor function). In all panels, lighter colors indicate participants with worse performance in the corresponding tests. Based on the topological structure in (a) and inspection of the Mapper in other hyperparameter configuration, all participants were grouped into three distinct gait subgroups (n = 30). When labeled with clinical scores, these regions corresponded to functional level: high gait function (n = 12), moderate gait function (n = 6), and low gait function level (n = 12), highlighted in (a). d-h Clinical gait or upper-limb assessments across the three gait function levels, shown using kernel density plots. Dashed lines represent group means. Statistical comparisons using Kruskal-Wallis tests followed by Dwass-Steel-Critchlow-Fligner post-hoc tests confirmed significant differences across groups (*p < 0.05, **p < 0.005, ***p < 0.001).

Table 2.

Clinical assessment performance across topological CVA groups

	Topological gait function groups
Assessment	High gait function	Moderate gait function	Low gait function
10MWT, preferred speed (m/s)	0.87 [0.31]	0.68 [0.17]	0.35 [0.21]
10MWT, slow speed (m/s)	0.69 [0.25]	0.58 [0.03]	0.40 [0.17]
10MWT, fast speed (m/s)	1.21 [0.23]	0.99 [0.37]	0.55 [0.24]
6MWT distance (m)	266.70 [131.82]	252.45 [99.07]	129.90 [84.25]
TUG, single-task time (s)	14.62 [5.01]	19.98 [5.01]	24.50 [14.52]
TUG, dual-task time (s)	15.43 [2.82]	20.57 [3.80]	33.13 [12.49]
ARAT score	6.0 [24.3]	2.5 [4.5]	37.5 [55.3]
FMA score	25.5 [19.5]	10.0 [11.0]	50.0 [47.5]

Measures of locomotion (10MWT at preferred, slow, and fast speeds), endurance (6MWT), functional mobility (single- and dual-task TUG), and hand function (ARAT and FMA) were obtained for individuals with CVA and grouped according to gait function classification derived from topological Mapper graphs.

Data represent median [Interquartile range].

10MWT 10-Meter Walk Test, 6MWT 6-Minute Walk Test, TUG Timed Up and Go, ARAT Action Research Arm Test, FMA Fugl-Meyer Assessment Sections A-D.

Color-coding of the Mapper with functional mobility (Fig. 3b) was consistent with the three regions, but it could only highlight the low gait function region. However, this trend was not observed for upper-limb motor function color-coding (Fig. 3c). The correlation between three identified gait pattern regions and upper-limb motor function assessments was weak, as these regions displayed more mixed color distributions, indicating less alignment between gait patterns and upper-limb motor function (Fig. 4c). This is consistent with the non-significant statistical comparison of upper-limb motor function across these three groups shown in Fig. 4g, h and Table 2. Mappers were also color-coded by performance on each clinical assessment for the CVA group separately (no PCA performed) and plotted in Fig. S5.

Fig. 4. Feature importance analysis distinguishing CVA gait function groups.

SHAP violin plots showing the top 20 most influential gait features contributing to the classification of participants into a high, b moderate, and c low gait function groups, based on the support vector classifier model. Features are ordered by their importance for the corresponding group classification. Positive SHAP values indicate a greater contribution to classifying a participant into that gait function group whereas negative SHAP values indicate a greater contribution of the feature magnitude to classifying a participant into the other two gait function groups. Color gradients reflect the relative magnitude of each feature (darker for high values, lighter for low values).

To assess whether TDA-informed subgroups were meaningfully separable, and to find the most influential features that distinguish the three gait function groups plotted in the Mapper, multiple machine learning classifier algorithms were deployed to test the performance of kinematic and spatiotemporal features to classify the three identified CVA groups. The best-performing classifier applied to the TDA input data, and utilizing the high, moderate, and low gait function regions as labels (support vector machine, test F1-score = 0.87, cross-validation F1-score = 0.89) revealed different contributing factors for each predicted class. Specifically, spatiotemporal parameters extracted from the 10MWT (shorter stance and relatively longer swing length) were the primary contributors to the organization of participants in the high gait function subgroup (Fig. 4a); parameters from stair climbing task (lower knee flexion angle and greater maximum foot clearance asymmetry during ascent) contributed most to the moderate gait function subgroup (Fig. 4b); and TUG-related features (longer duration and increased number of steps during the turn phases) predominantly influenced the organization of participants to the low gait function subgroup (Fig. 4c).

PD-FND gait function exhibits a bidirectional Mapper structure

The TDA analysis of the PD-FND cohort revealed a central region within the Mapper that bridges HC and CVA distributions (Fig. 2b). Within this region, participants formed two converging branches rather than fully distinct clusters. These branches originate from higher-functioning participants and merge toward a region associated with lower gait function (Fig. 5a). The single participant diagnosed with FND is located at the extremity of one branch (Fig. 5a). Although this participant exhibited moderate-to-severe impairment based on the Movement Disorder Society – Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) Part III (Fig. 5a), their gait pattern was corresponded to relatively higher functional performance within the PD-FND group (Fig. 5b–d) and overlaps with the higher-function spectrum of the HC group (Fig. 7a). Similar gradients are visible when Mapper nodes were further color-coded using PC1 scores derived from domain-specific clinical assessments, including locomotion and endurance (10MWT speed at preferred, slow, and fast trials, and 6MWT distance; Fig. 5b), functional mobility (single- and dual-task TUG time; Fig. 5c), and balance (Mini Balance Evaluation System Test [MiniBESTest] score; Fig. 5d). In addition, Mapper visualizations were generated using individual clinical assessment scores (without PCA) for the PD-FND group, as shown in Fig. S6.

Fig. 5. Topological representation of gait characteristics in individuals with PD-FND.

a Mapper showing individuals with PD (n = 10) and FND (n = 1), colored by MDS-UPDRS severity score. Green arrows show the direction of the transition of gait function from high to low. Three Mappers of the individuals colored by first principal component (PC1) scores from b 10MWT speed and 6MWT distance (locomotion and endurance), c single- and dual-task TUG times (functional mobility), and d MiniBESTest scores (balance). In all Mappers, lighter tones indicate participant(s) with lower performance on the corresponding tasks.

Fig. 7. Topological and clinical characterization of gait in HC participants.

Mappers of HC participants (n = 20) colored by the PC1 scores from a 10MWT at preferred, slow, and fast speeds and 6MWT distance (locomotion and endurance), b single- and dual-task TUG time (functional mobility), and c ARAT score (upper-limb motor function). Nodes with lighter colors indicate participants with worse performance in the corresponding tasks. Three potential variants of gait function in HC are highlighted in purple areas.

Gait phenotypes in LL cohort are diverse

TDA applied to the LL group revealed a broad and heterogeneous distribution of gait patterns (Fig. 2c). Unlike other cohorts, the LL group did not form distinct gait phenotypes but rather spanned a wide range of gait phenotypes, extending from patterns resembling low gait function CVA group to those similar to HC group with the highest gait function scores (Fig. 7a). Due to this dispersed structure, no specific region was identified, and therefore, subsequent machine learning classification and statistical analyses were not conducted.

Similar to the other cohorts, Mapper nodes were color-coded using PC1 scores derived from three separate PCA analyses: locomotion and endurance (Fig. 6a), functional mobility (Fig. 6b), and functional ambulation capacity (AMP with Prosthesis [AMPPro] score and K-level; Fig. 6c). In the TDA Mappers colored by the locomotion and endurance and functional mobility domains, a continuous spectrum of gait function is observed. Participants in the LL group positioned closer to the HC region exhibited the highest gait function, whereas progression toward the upper regions of the Mapper and closer proximity to CVA phenotypes was associated with decreasing gait function (Fig. 6a). Participants with moderate to low gait function (orange and yellow nodes) overlapped with CVA phenotypes corresponding to similar functional levels (Fig. 3a, b). Notably, the individual with the lowest gait function in the LL group (yellow nodes; n = 1) clustered near low-function CVA participants (Fig. 3a), indicating comparable gait characteristics. This low-function LL participant also exhibited K-levels of 1 (Fig. 6c), whereas the remaining participants showed higher functional levels spanning K-levels 2–4. However, the AMPPro and derived K-level classification did not clearly separate K-levels 3 and 4, which appeared partially overlapping and did not form distinct regions within the Mapper. For each motor domain and assessment, separate Mappers are presented in Fig. S7.

Fig. 6. Topological representation of gait characteristics in participants with LL difference.

Topological graphs show participants with LL difference (n = 20) colored by a first principal component (PC1) scores derived from their 10MWTs at preferred, slow, and fast speeds and 6MWT distance (locomotion and endurance), b single- and dual-task TUG time (functional mobility), and c clinical assessments: K-level and AMPPro scores (Functional ambulation capacity). Two yellow arrows show the transition direction of gait function form high to low. Lighter nodes indicate participant(s) with worse performance/score in the corresponding tasks. Participants with K-levels of 1 (n = 1) and 2 (n = 1) are highlighted in yellow areas.

HC participants exhibit multiple adjacent gait phenotype clusters

In contrast to the clinical cohorts, TDA in the HC group revealed the densest at one corner of the Mapper marks one end point of the spectrum and highest gait function across all participants (Fig. 2d). The Mapper of HC, although, is not uniform but separated by bridges connecting the highest gait function participants isolated at the corner of the Mapper to a lower gait function group overlapping with CVA, PD, and LL groups. Color-coding the Mapper nodes based on PC1 scores from locomotion and endurance assessments (Fig. 7a) and functional mobility assessments (Fig. 7b) showed smooth gradients in clinical performance across three clusters. Individuals with slightly lower scores in these domains tended to align more closely with the gait regions corresponding to other cohorts, whereas those with better performance remained more centrally located and further from other cohorts.

As shown in Fig. 7c, all participants scored the maximum value on the ARAT and resulted in no variation in this domain. Due to the low number of participants in two out of three HC gait function groups (n = 2 and 4), statistical comparisons were not performed. For additional Mapper visualization of each individual assessment, refer to Fig. S8.

Discussion

This paper presents a TDA-based framework that identifies and inspects gait phenotypes in kinematic and spatiotemporal data from a battery of assessments on a mixed-cohort of individuals affected by mobility impairments, with the goal of supporting personalized and optimized rehabilitation strategies. Our main finding demonstrates that using TDA on high-dimensional spatiotemporal and kinematic gait data effectively organizes the dataset into distinct structures and highlights a transition pattern of gait function across neurotypical and neurological groups. When embedded into a single Mapper, these structures highlight within-cohort gait phenotypes and visualize cross-cohort similarities and differences across these various phenotypes.

The distribution of gait patterns revealed consistent and interpretable separation across clinical conditions (Fig. 2), indicating that the observed structure is intrinsic to the data rather than an artifact of model tuning (Figs. S1–S4). Previous studies have used various unsupervised techniques on gait or motor data, from linear dimensionality reduction³¹, nonlinear embeddings³², traditional clustering methods²⁴, and self-organizing maps³³ to separate healthy from pathological gait or to examine subgroups in clinical populations. However, traditional clustering methods typically require fixed partitions and subgroup definitions, that are not well-suited for analyzing heterogeneous populations with overlapping phenotypes and variable numbers of subgroups across conditions. These approaches often convert gait patterns and traits into discrete clusters and mask the continuum and transition that exist in motor impairment of such clusters. In contrast, the TDA Mapper algorithm integrates dimensionality reduction, clustering, and network analysis to map high-dimensional gait data into a two-dimensional network of connected points, while still preserving gradients and transitions among identified groups. In our study, the Mapper network organized gait patterns of all four cohorts and placed HC and CVA at two corners of the Mapper, which can be interpreted as the two sides of the gait function spectrum and the contrast in gait quality and functionality between these two groups (Fig. 2a–d). The isolation and contrast of gait function are even more evident in moderate to low-function individuals with CVA, where clusters form branches sprouting from the Mapper, which suggests a distinct and unique phenotype. While HC and high gait function CVA regions are largely distinct, a small overlapping area in the center of the Mapper suggests shared gait characteristics between HC and CVA phenotypes and indicates that tailored rehabilitation strategies may be required for these specific participants.

PD-FND and LL groups appeared to occupy intermediate adjacent spaces based on their gait function level (Fig. 2b, c). Specifically, PD-FND is characterized by a relatively symmetrical and progressive motor deterioration, while LL represents a more localized and often mechanically compensated deficit, even if extremely heterogeneous depending on the level and severity of the amputation, as demonstrated by a larger spread of nodes for participants in the LL group. Therefore, the power of TDA resides in its dual capacity to reveal the continuum of motor behavior across clinical populations while also highlighting the presence of distinct, clinically meaningful regions that characterize specific gait patterns.

This approach could transform our understanding of motor variability within and among patient populations, ultimately informing precision rehabilitation and personalization of care. Clinicians increasingly aim to match interventions to a patient’s specific functional profile in order to improve outcomes. In this context, our study demonstrates how TDA can help identify such profiles by characterizing distinct gait function subgroups, providing actionable insights for personalized rehabilitation. For example, individuals with CVA in a high gait function subgroup may benefit from speed-enhancing and mobility refinement interventions, such as task‑oriented treadmill training or speed‑based gait training programs that emphasize gait symmetry and cadence³⁴. In contrast, those in the moderate gait function subgroup, whose key distinguishing features emerged during challenging tasks like stair ascent, may benefit from targeted balance, strength, and stair navigation training to address specific deficits revealed by the analysis³⁵. In practice, clinicians could perform a brief instrumented baseline assessment, project a patient’s data onto the Mapper, and then use the resulting topological location to select interventions aligned with the dominant parameters of the corresponding gait phenotype and the underlying muscle groups involved.

Beyond inter-condition relationships, TDA also provided insights into the internal organization and variability within each condition. Among individuals with CVA, the topological representation revealed three distinct gait phenotypes which appear closely linked to function (Fig. 3). These regions closely aligned with typical clinical ambulation categories (community, limited community, household ambulators) and were consistent with the main findings of prior unsupervised gait studies in stroke^36–38. While the exact number and boundaries of subgroups vary across the literature, a recurring pattern is the appearance of fast, moderate, and slow walkers that mirror the clinical spectrum of mobility. Unlike traditional classification derived from single assessments, these phenotypes were defined by connecting high-dimensional, full-body motion data recorded during traditional gait assessments. The clear boundaries of the TDA-derived CVA subgroups further enabled a classification analysis to validate their reproducibility and internal generalizability (cross-validation score = 0.89, F1-score = 0.87). This classification analysis was used for subgroup analyses to assess the internal reproducibility and feature-level interpretability of the TDA-derived regions. Machine learning and feature importance analyses in the CVA group indicated that the TDA-derived gait phenotypes were primarily driven by lower-body sensor data. This aligns with biomechanical expectations of our gait assessments and suggests that the identified TDA phenotypes are less influenced by upper-body measurements. Due to the exploratory approach of this study, we did not perform sensor ablation analyses; however, these findings motivate future work to systematically evaluate reduced sensor configurations or targeted inclusion of upper-body assessment to capture whole-body functional phenotypes in neurological conditions.

Although gait and functional mobility assessments were statistically different among three gait function phenotypes (Fig. 3d–h), this distinction was not dominated solely by one assessment (Fig. S5). Rather, it emerged when visualizing the principal components of assessment scores (Fig. 3a–c). Further classification reports showed that for the high gait function subgroup, the most informative kinematic and spatiotemporal parameters were 10MWT-related features such as stance and swing phase durations (Fig. 4a). For the moderate gait function subgroup, more challenging tasks such as stair ascent revealed key patterns (Fig. 4b). For the low gait function subgroup, dynamic tasks like turning during the TUG were most distinguishing (Fig. 4c). Through the application of TDA on wearable sensor data, we identified gait patterns that are not captured by traditional assessment scores alone, revealing subtle and previously unrecognized distinctions across gait function levels. Such insights underscore the value of integrating multi-dimensional data sources within a unified analytic framework and provide essential information for precision rehabilitation, where therapeutic strategies can be tailored based on an individual’s position within the continuous landscape of motor function rather than on a single test outcome.

The need for multidimensional assessment was also confirmed from the analysis of the individuals with PD: the TDA Mapper revealed a bidirectional gait phenotype cluster corresponding two higher gait function regions overlapping with high gait function HC participants and converging into a low gait function region overlapping with high function CVA individuals (Fig. 5a, c, d). At the individual level, the topological analysis highlighted an overlapped area between the highest gait function PD-FND and HC individuals that brought attention to a specific participant who had initially been diagnosed with PD (Fig. 5a). Upon further review, this individual was identified as having FND, rather than idiopathic PD. This particular case illustrates the potential of topological gait phenotyping to cluster FND individuals overlapped with HC phenotypes to support more refined diagnostic pathways, especially in situations where the interpretation of clinical assessments remains challenging (Fig. 5a).

The analysis of individuals with LL difference revealed a very high heterogeneity in gait patterns, with the TDA Mapper showing a broad spectrum of phenotypes, from CVA-like to near-typical gait patterns (Fig. 6a). This diversity is consistent with prior reports that gait in individuals with LL difference is influenced by many individual factors, including amputation level (transfemoral vs. transtibial), residual limb characteristics, prosthetic components, and compensatory strategies^39–42. The region that emerges the most from both clinical perspective and gait pattern is the low gait function region, spatially organized close to the low gait region of the CVA (Fig. 6d), and identified by the individual with K1 level. Although the number of participants in this subgroup was limited, the separation of their corresponding region (Fig. 6a–c) highlights their marked differences in mobility, functional capacity, biomechanical compensation, and motor adaptation challenges. The remaining participants (all K3 and K4) were mostly dispersed homogeneously across the Mapper (Fig. 6a). This dispersion suggests the ceiling effect of the AMPPro, which often shows no significant score differences between K3 and K4 ambulators⁴³, and is consistent with biomechanical studies reporting only subtle gait distinctions between these groups⁴⁴.

The HC cohort established the benchmark for understanding the Mapper distribution and drawing comparisons within and among the clinical cohorts. The HC group localized to one corner of the Mapper, with the highest-functioning individuals forming two dense isolated clusters at the periphery, within nodes not shared by other conditions. In contrast, HC individuals with lower gait function overlap with CVA, PD–FND, and LL groups (Fig. 7). This density of participants in one side of the Mapper matches previous topological gait analyses showing that healthy adults exhibit a single distinct distribution of gait parameters, while clinical groups present with multimodal distributions²⁶. In our results, HC nodes are presumed to be reference control points, and atypicality and contrast of gait phenotypes can be evaluated based on the topological distance of the target condition from these nodes; for example, participants in the PD-FND group exhibited a gait phenotype more similar to HC than participants in the CVA group.

Taken together, our findings emphasize the way in which kinematic and spatiotemporal gait phenotyping supported by TDA enables identification of subtle functional characteristics that may remain undetected using standard clinical assessments. By organizing these features within a topological framework, TDA not only outlines distinct phenotypes but also quantifies their relationships, similarities, and transitions. Importantly, we believe this structure can also inform the selection of meaningful subgroups for the development of robust computational and machine learning models. This is a critical and non-trivial decision to be made during model development, since composition of the training data is a primary driver of the model’s potential use case in the real world. Indeed, our previous work showed n that population- or device-specific training data can improve model accuracy, but an often-unresolved question is: how specific does the training data need to be?^19,45,46 TDA offers a method to identify phenotypically similar data for targeted model development, or to examine the similarity among various training datasets and new patient data to select models that will provide the most accurate outcomes.

It is important to state that TDA is often computationally intensive, which limits its applicability in real-time or large-scale settings⁴⁷, and resulting interpretations can be challenging, especially when applied to complex datasets. Beyond these considerations, Mapper-based analyses involve methodological choices related to parameter selection, feature dimensionality, missing data handling, and sensor-derived measurement uncertainty such as sampling rate, sensor noise and bias, and sensor-to-body alignment. In this study, these factors were addressed through empirically guided parameter selection, implicit dimensionality reduction via PCA to mitigate collinearity and attenuate noise, cohort-specific imputation of sparse missing values, manufacturer-provided sensor fusion, and manual quality control of the gait segmentation. While these steps partially reduce sensitivity to measurement variability, they do not fully account for all sources of acquisition-related uncertainty. Importantly, the primary goal of this work was to introduce and demonstrate the utility of TDA as an exploratory framework for gait phenotyping and clinical interpretation and systematic evaluation of the impact of acquisition parameters on the resulting topological structures was beyond the scope of this study. Systematic comparison of alternative parameterizations, feature reduction strategies, imputation methods, and sensing modalities represents an important direction for future research as TDA continues to mature as a translational tool in rehabilitation science.

In conclusion, we demonstrated that TDA is well-suited to capture and visualize complex motor behavior. By projecting high-dimensional kinematic and spatiotemporal data into an interpretable two-dimensional space, it facilitates the exploration of both global patterns and localized variations, thus allowing for a nuanced analysis at both the population and individual level. This positions TDA as a powerful instrument for clinical decision-making, complementing traditional assessment measures by simplifying multi-dimensional sensor data and enabling applications that span diagnostic assessment, prognostic modeling, and personalized intervention planning.

Methods

Participants

Eighty-one participants, who were able and willing to provide written consent and comply with study procedures, participated in this study. Participants were recruited and sorted into four cohorts depending on their diagnosis, including CVA, (n = 30), PD-FND (n = 11), LL (n = 20), HC (n = 20). Individuals who were pregnant, nursing, or with skin allergies that prevented safe use of sensors were excluded. All participants could safely walk ten meters with or without assistance. This study was performed in accordance with the Declaration of Helsinki; it is registered on ClinicalTrial.gov (NCT05471375), starting on March 19th, 2022, and all participants provided informed consent prior to study participation, in compliance with Northwestern University IRB guidelines (NU IRB, IL, USA; STU00216350).

Study design and data acquisition

This cross-sectional observational study involved a range of functional and movement-related rehabilitation assessments using wearable sensors. During a single-day visit, demographic information, medical history, and anthropometric measurements were collected from participants (Table 1 and S1). They also completed a series of upper- and lower-limb motor assessments that yielded either clinical outcome scores, sensor-based motion data, or both (Table 3 and S2). The assessments spanned five motor domains: locomotion and endurance, functional mobility, balance, upper-limb motor function, and global motor severity. While several of these assessments were shared across all participant cohorts, others were specific to conditions represented by each cohort.

Table 3.

Clinical motor assessments

Motor domain	Test	Number of trials	Type of data	Cohort
				CVA	PD-FND	LL	HC
Locomotion and endurance	10MWT, preferred speed	3	Clinical	x	x	x	x
			Instrumented	x	x	x	x
	10MWT, slow speed	3	Clinical	x	x	x	x
			Instrumented	x	x	x	x
	10MWT, fast speed	3	Clinical	x	x	x	x
			Instrumented	x	x	x	x
	6MWT	1	Clinical	x	x	x	x
	Stair climbing	3	Instrumented	x	x	x	x
Functional mobility	TUG, single-task	2	Clinical	x	x	x	x
			Instrumented	x	x	x	x
	TUG, dual-task	2	Clinical	x	x	x	x
			Instrumented	x	x	x	x
	FGA	1	Clinical	x
Balance	MiniBESTest	1	Clinical		x		x
	AMPPro	1	Clinical			x	x
			Instrumented			x	x
Upper limb motor function	ARAT	1	Clinical	x			x
	FMA	1	Clinical	x
Motor severity	MDS-UPDRS	1	Clinical		x

Each row lists a functional assessment grouped by motor domain, along with the number of trials performed, type of data collected (clinical score, sensor-based/instrumented, or both), and participant cohort involvement.

10MWT 10-Meter Walk Test, 6MWT 6-Minute Walk Test, AMPPro Amputee Mobility Predictor with Prosthesis, ARAT Action Research Arm Test, BBS Berg Balance Test, FGA Functional Gait Assessment, FMA Fugl-Meyer Assessment Sections A-D, MDS-UPDRS Unified Parkinson’s Disease Rating Scale Part III, MiniBESTest Mini Balance Evaluation System Test, TUG Timed Up and Go.

Sensor-based data were collected using motion capture and a full-body Xsens MVN Awinda system (Xsens Technologies B.V., Enschede, Netherlands) at Shirley Ryan AbilityLab (Chicago, IL). This inertial motion capture system includes 17 tri-axial IMU sensors attached via a fitted Lycra shirt and 12 adjustable straps placed on rigid body segments following the XSens MVN guidelines (https://www.movella.com/hubfs/User_Manual_Xsens%202025.pdf). A diagram of these locations is shown in Fig. 1A. Prior to calibration, individuals’ anthropometric measurements (Table S1) were entered into the MVN Analyze software (version 2022.0). After sensor calibration, motion data were recorded at 60 Hz, and processed using the HD processing pipeline in MVN Analyze software to extract 3D data, including body segment position, velocity, acceleration, orientation, and joint angles, for use in downstream analyses.

Data processing - segmentation

For all instrumented data, the processing included two main phases of segmentation and feature extraction. Sensor-based kinematic and spatiotemporal data were segmented to extract key phases within each functional task. For the 10MWT (three trials each for preferred, slow, and fast), individual stride cycles were segmented for each body side. These strides were identified using a threshold-based peak detection method applied to the sagittal-plane model-estimated foot position estimated by the manufacturer HD processing pipeline. This approach has been previously validated against optical motion capture⁴⁸ and was selected to avoid direction-dependent sign inversion associated with the global reference frame of angular velocity signals. During stair climbing trials, participants ascended and descended a flight of five stairs. These trials were segmented into step ascent and descent cycles for each body side. Steps were manually identified by marking the local minima in the vertical trajectory of each foot. For both the 10MWT and stair climbing, each segmented stride was visually inspected using model-estimated foot and toe position and vertical velocity signals to confirm heel-strike, toe-off and consequently the beginning of each stride. Segments exhibiting high-frequency noise or trials with low-frequency drift were excluded to ensure conservative segmentation quality.

For both single- and dual-task TUG assessments, data were segmented into four distinct phases: sit-to-stand, first turn, second turn, and stand-to-sit. TUG segmentation relied on trunk pitch angular velocity to delineate the four functional phases, following the established method⁴⁹. All segmentation was performed on earth-referenced position signals estimated by the manufacturer-provided HD processing pipeline, which applies proprietary sensor fusion of acceleration and orientation information to obtain drift-mitigated representations prior to segmentation.

Data processing - feature extraction

Feature extraction involved computing kinematic and spatiotemporal parameters from the segmented gait and movement components described in the previous section. Features were derived from segmented strides in the 10MWT, step ascent and descent in stair climbing, and the sit-to-stand, first turn, second turn, and stand-to-sit phases of the TUG assessments. For 10MWT and stair climbing, features were extracted separately for the left and right sides of the body where applicable. For these features, the symmetry index was calculated using Eq. 1, and corresponding percent asymmetry measures were added to the rest of the parameters:

$$\mathit{Symmetry}\mathit{Index}=\frac{\left|{\mathit{Feature}}_{\mathit{left}}-{\mathit{Feature}}_{\mathit{right}}\right|}{0.5\times ({\mathit{Feature}}_{\mathit{left}}+{\mathit{Feature}}_{\mathit{right}})}\times 100\mathrm{\%}$$ 1

In the 10MWT, features spanned the full body–including upper limbs, trunk, and lower limbs–while stair climbing features also covered both ascent and descent. For non-alternating stair patterns, all parameters were normalized to reflect values per single step. Each feature was calculated per stride, step, or phase and then averaged across trials to yield a single representative value per participant. For the TUG, features included phase durations, step characterization during the turns (e.g., number of steps, average step duration), and description of the trunk movement during the sit-to-stand phases (e.g., anterior-posterior mean and maximum trunk acceleration amplitude), distinguishing a leaning phase from an active trunk engagement⁵⁰. Missing values were imputed using the cohort-wise mean for the corresponding parameter. A complete list and description of extracted features is provided in Table 4. Signal segmentation and feature extraction were manually inspected for each segmented component (strides and steps for the 10MWT and stair climbing; sit-to-stand, stand-to-sit, and turning phases for the TUG) for every participant, with 10MWT and stairs climbing assessments reviewed by one investigator and TUG assessments by a second investigator. All signal segmentation and feature extraction procedures were performed in MATLAB (version R2021a).

Table 4.

Gait kinematic and spatiotemporal parameters

Test	Parameter	Description
10MWT	Cadence (step/min)	Number of steps per minute.
	Stance (% Gait Cycle)	Percentage of the gait cycle spent with the foot in contact with the ground.
	Swing (% Gait Cycle)	Percentage of the gait cycle spent with the foot off the ground.
	Single limb support (% Gait Cycle)	Percentage of the gait cycle when only the targeted foot is in contact with the ground.
	Terminal double limb support (% Gait Cycle)	Percentage of the gait cycle when both feet are in contact with the ground simultaneously.
	Maximum foot clearance (m)	Maximum vertical distance between the foot and ground during the swing phase.
	Stride length (m)	Anterior-posterior distance between the heel contacts of two successive strides by the same foot during walking.
	Stride duration (s)	Time elapsed between two consecutive initial contacts of the same foot.
	Stride velocity (m/s)	Average forward speed calculated as stride length divided by stride duration.
	Toe off angle (degrees)	Angle between the foot and ground at the moment the toe leaves the ground during gait.
	Toe out angle (degrees)	Average transverse angle between the foot’s longitudinal axis and the direction of walking during the stance phase.
	Foot strike angle (degrees)	Angle between the foot and ground in the sagittal plane at the moment of initial contact.
	Foot circumduction (m)	Maximum lateral deviation of the foot during the swing phase, measured as the peak horizontal displacement.
	Lumbar coronal range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the L3 segment during consecutive right and left strides in the coronal plane.
	Lumbar sagittal range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the L3 segment during consecutive right and left strides in the sagittal plane.
	Lumbar transverse range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the L3 segment during consecutive right and left strides in the transverse plane.
	Trunk coronal range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the T8 segment during consecutive right and left strides in the coronal plane.
	Trunk sagittal range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the T8 segment during consecutive right and left strides in the sagittal plane.
	Trunk Transverse range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the T8 segment during consecutive right and left strides in the sagittal plane.
	Arm swing velocity (m/s)	Average angular velocity of the forearm segment in the sagittal plane during consecutive right and left strides.
	Arm swing range of motion (degrees)	Difference between the maximum and minimum orientation angles of the forearm segment in the sagittal plane during consecutive right and left strides.
Stair climbing	Stair climb time (s/stair)	Time taken to climb or descend one stair step.
	Cadence (stair/min)	Number of stairs climbed or descended per minute.
	Stride length (m)	Anterior-posterior distance between successive foot contacts of the same foot on consecutive steps.
	Maximum foot clearance (m)	Maximum vertical displacement of the foot from one step to the next during ascent or descent.
	Knee flexion (degrees)	Maximum flexion angle of the knee joint during stair ascent of descent.
	Hip abduction (degrees)	Maximum abduction angle of the hip joint during stair ascent of descent.
	Trunk coronal range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the T8 segment during consecutive step ascent or descent in the coronal plane.
	Trunk sagittal range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the T8 segment during consecutive step ascent or descent in the sagittal plane.
	Trunk transverse range of motion (degrees)	Maximum difference between the peak and lowest orientation angles of the T8 segment during consecutive step ascent or descent in the transverse plane.
TUG	Turn; duration (s)	Duration of the turn phase. Calculated for both the first and second turn of the task.
	Turn; max angular velocity (degrees/s)	Maximum trunk angular velocity on the vertical axis observed during the turn. Calculated for both the first and second turn of the task.
	Turn; step count	Number of steps calculated during the turn. Calculated for both the first and second turns of the task.
	Turn; longest step duration (s)	Duration of the longest step observed during the turn. Calculated for both the first and second turns of the task.
	Turn; average step duration (s)	Mean duration of the steps observed during the turn. Calculated for both the first and second turns of the task.
	Turn; duration of last step before turn (s)	Duration of the last step observed during the turn. Calculated for both the first and second turns of the task.
	Turn; double step count	Number of double steps calculated during the turn. Calculated for both the first and second turns of the task.
	Sit-to-stand; duration (s)	Duration of the turn phase. Calculated for both the sit-to-stand and stand-to-sit phases of the task.
	Sit-to-stand; leaning anterior-posterior jerk (g/s)	Slope of the trunk anterior-posterior acceleration during the leaning sub-phase of the sit-to-stand. Calculated for both the sit-to-stand and stand-to-sit phases of the task.
	Sit-to-stand; leaning anterior-posterior acceleration maximum amplitude (g/s)	Maximum amplitude of the trunk anterior-posterior acceleration during the leaning sub-phase of the sit-to-stand. Calculated for both the sit-to-stand and stand-to-sit phases of the task.
	Sit-to-stand; leaning anterior-posterior acceleration mean amplitude (g/s)	Mean amplitude of the trunk anterior-posterior acceleration during the leaning sub-phase of the sit-to-stand. Calculated for both the sit-to-stand and stand-to-sit phases of the task.
	Sit-to-stand; trunk change anterior-posterior acceleration slope (g/s)	Slope of the trunk anterior-posterior acceleration during the trunk change sub-phase of the sit-to-stand. Calculated for both the sit-to-stand and stand-to-sit phases of the task.
	Sit-to-stand; trunk change anterior-posterior acceleration maximum amplitude (g/s)	Maximum amplitude of the trunk anterior-posterior acceleration during the trunk changes sub-phase of the sit-to-stand. Calculated for both the sit-to-stand and stand-to-sit phases of the task.
	Sit-to-stand; trunk change anterior-posterior acceleration mean amplitude (g/s)	Mean amplitude of the trunk anterior-posterior acceleration during the trunk change sub-phase of the sit-to-stand. Calculated for both the sit-to-stand and stand-to-sit phases of the task.

Data analysis – TDA analysis

The goal of the TDA was to introduce a framework for representing high-dimensional gait features as a two-dimensional descriptive point cloud (Fig. 1g). Six assessments were performed by all cohorts, including 10MWT at preferred, slow, and fast speed, stair climbing, single- and dual-task TUG. These six assessments were recorded with wearable sensors and used as the primary source for data processing and topological analysis.

For each participant, 227 gait features were computed, averaged across trials or steps to form a single parameter for each participant. Prior to TDA, the feature set was standardized and subjected to principal component analysis (PCA). This step was introduced to mitigate feature collinearity, reduce noise by discarding low-variance components, and improve stability of distance-based topological representations. Top principal components explaining cumulative 95% of the total variance were retained and used as input for subsequent analysis. Then, TDA was applied using the Mapper algorithm, implemented through KeplerMapper⁵¹. The Mapper framework consists of four key steps: dimensionality reduction, covering, clustering, and graph reconstruction. The PCA-transformed data from all participants were first projected non-linearly into a two-dimensional space (dimensionality reduction) using t-distributed Stochastic Neighbor Embedding (t-SNE), with a perplexity of 40, a fixed random state for reproducibility, and 2000 iterations (Fig. 1d). To create overlapping subsets of the projected data (covering), the two-dimensional space was partitioned into regions (spanning between 10 and 20 cubes) with different percentages of overlap between adjacent regions (50% to 65%). Within each region, data points were clustered using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) (ε = 5, minimum samples = 2), which identifies dense clusters while designating outliers as noise (Fig. 1e). The resulting clusters were represented as nodes in a graph G, with edges established among clusters sharing at least one participant data point across overlapping regions (graph reconstruction) (Fig. 1g). This process is summarized in Eq. 2.

$$xf\to R^2\mathit{Cover}\to \left\{U_i\right\}\mathit{Clustering}\to \left\{C_{\mathit{ij}}\right\}\mathit{Graphconstruction}\to G$$ 2

Where $f$ represents the t-SNE projection and edges in G are defined by cluster intersections. Consistent with prior Mapper-based studies^52,53, parameters for covering and clustering were selected through an empirically comparative grid to produce a coherent graph structure with minimal isolated islands or too dense and uniform structure. These parameters primarily control the resolution of the topological summary rather than predictive accuracy, and were selected based on structural stability across a range of cover resolutions and overlap values, rather than optimization of a single configuration. Due to the inherent robustness of the Mapper algorithm to noise and parameter variation, the global structure of the resulting graph remained stable across a range of hyperparameters. These Mappers, although, were visually assessed under different cover and overlap settings to confirm the consistency of the main topological clusters. To interpret clinical relevance within the Mapper, nodes were color-coded based on the prevalence of participants’ condition, clinical assessment scores, or principal component scores derived from them. To allow consistent visual comparison across participants and cohorts, color gradients were normalized within each analysis by rescaling target participants’ assessment or principal component scores to a range of zero to one; these scores were averaged across target participants within each node to represent a single value for each node. A standardized color scheme interpretation was then applied across all target nodes, where lighter colors represent lower gait function and darker colors indicate higher gait function.

Data analysis - statistical analysis and machine learning

Statistical analyses were performed to focus on group comparisons in demographic information and clinical assessment scores. Chi-squared tests were used with categorical variables, while t-test or Mann–Whitney tests were applied for comparison of continuous variables between two groups, in the case of normally and non-normally distributed variables, respectively, and ANOVA or Kruskal-Wallis tests were performed for comparison of continuous variables among multiple groups, in the case of normally and non-normally distributed variables, respectively. Post-hoc tests were run, if applicable, to assess the differences within severity groups. Normality was tested using the Shapiro-Wilk test, and, for all the tests, statistical significance was defined as p < 0.05.

To further interpret and quantitatively assess the structure identified by TDA, supervised machine learning classifiers and statistical analyses were applied to characterize subgroups identified through the TDA Mapper. Mapper regions are not defined to maximize separation between groups, and separability of these regions using the original gait features is neither guaranteed nor generalizable across hyperparameter choices, as illustrated by variations in regional connectivity and separation observed under different Mapper configurations. When the Mapper algorithm revealed distinct regions within cohorts, participants within these regions were labeled, and multiple classifiers were trained and tested to assess whether the topological organization reflected discriminative and recoverable structure in the feature space. Feature attribution analyses were then used to identify gait parameters contributing most to this separability to provide functional interpretability beyond the topological representation alone.

For machine learning analyses of the CVA group, we used a 3-fold nested cross-validation, with participant-level splitting such that data from the same participant were never included in both the training and test sets at any cross-validation level; the inner loop served for hyperparameter optimization of multiple classifier algorithms such as random forest, logistic regression, k-nearest neighbor, decision tree, XGboost, and support vector machine, and the external loop was reserved for testing. All algorithms were performed with feature standardization parameters estimated from the training data at each cross-validation fold and applied unchanged to the corresponding test data. The F1 score of the best-performing model was reported as the performance metric. SHapley Additive exPlanations (SHAP)⁵⁴ were applied to the test set predictions to determine which features contributed most to classification. SHAP assigns each feature a contribution value for each individual prediction, which allows us to quantify and visualize how specific gait parameters influence the likelihood of a participant belonging to a given region. All machine learning, statistical analysis and TDA were performed in Python (version 3.10.0).

Author contributions

Conceptualization: S.D., S.C., M.O., A.J., and R.L. Methodology: S.D. and S.C. Investigation: R.M. Visualization: S.D. and S.C. Funding acquisition: R.L. Project administration: S.D., S.C., M.O., and A.J. Supervision: M.O. and A.J. Writing (Original Draft): S.D. and S.C. Writing (Review and Edit): S.D., S.C., R.M., M.O., R.L., and A.J.

Data availability

The data collected and analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

The underlying TDA code in this study is available in [www.github.com/xKA1Z0x/Topological-Data-Analysis-Mapper] and can be downloaded via this link [https://doi.org/10.5281/zenodo.17717057].

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41746-026-02940-8.