Modeling the Heterogeneity of Post-Stroke Gait Control in Free-Living Environments Using a Personalized Causal Network

Post-stroke gait control is a complex, often fail to account for the heterogeneity and continuity of gait in existing gait models. Precisely evaluating gait speed adjustability and gait instability in free-living environments is important to understand how individuals with post-stroke gait dysfunction approach diverse environments and contexts. This study aimed to explore individual causal interactions in the free-living gait control of persons with stroke. To this end, fifty persons with stroke wore an accelerometer on the fifth lumbar vertebra (L5) for 24 h in a free-living environment. Individually directed acyclic graphs (DAGs) were generated based on the spatiotemporal gait parameters at contemporaneous and temporal points calculated from the acceleration data. Spectral clustering and Bayesian model comparison were used to characterize the DAGs. Finally, the DAG patterns were interpreted via Bayesian logistic analysis. Spectral clustering identified three optimal clusters from the DAGs. Cluster 1 included persons with moderate stroke who showed high gait asymmetry and gait instability and primarily adjusted gait speed based on cadence. Cluster 2 included individuals with mild stroke who primarily adjusted their gait speed based on step length. Cluster 3 comprised individuals with mild stroke who primarily adjusted their gait speed based on both step length and cadence. These three clusters could be accurately classified based on four variables: Ashman’s D for step velocity, Fugl-Meyer Assessment, step time asymmetry, and step length. The diverse DAG patterns of gait control identified suggest the heterogeneity of gait patterns and the functional diversity of persons with stroke. Understanding the theoretical interactions between gait functions will provide a foundation for highly tailored rehabilitation.


I. INTRODUCTION
I NDIVIDUALS with stroke frequently experience gait dys- function [1].Post-stroke hemiplegic gait is characterized by a decline in gait speed, shortened step length, longer double support time, and asymmetry of the spatiotemporal parameters [2], [3], [4].Gait speed and instability are important variables for the range of activity, prognosis, fall risk, and impending morbidity and mortality [5], [6], [7], [8].Precisely evaluating gait speed adjustability and gait instability in free-living environments is important in understanding how individuals with post-stroke gait dysfunction approach diverse environments and contexts such as obstacles and inclines.These parameters are typically computed as average measures of distance or time in performance assessments; however, they do not consider the continuity of gait.
With the recent development of inertial sensors, free-living gait control, which is directly reflected in the activity of daily living and quality of life, has been actively reported in older adults and persons with neurological disorders such as stroke [9], [10], [11].Decreased gait speed following stroke is influenced by the severity of hemiplegia, as well as gait instability and asymmetry [12], [13], [14].Experimental interventions to increase gait speed in persons with stroke have been reported to decrease double support, increase instability, and modulate gait asymmetry [12], [15], [16].
Traditionally, several models have provided insights to facilitate the understanding of gait control following stroke, as measured by spatiotemporal parameters.In post-stroke gait control models, gait speed is primarily determined by cadence, [17] but the influence of step length and gait asymmetry on gait speed varies [18], [19].In addition, stroke does not cause individual gait deficits but several stroke-related dysfunctions.Therefore, an individual causal model for gait control should be developed to incorporate the factors related to gait speed and gait instability, as well as their relationships.Gait control phenotypes are important theoretically for understanding the interactions among gait functions and clinically for tracking impairment and treatment efficacy.They also have important clinical implications for highly individualized and precise rehabilitation procedures, as has been emphasized recently [20].
In the present study, we aimed to explore and characterize the causal relationships between different parameters involved in free-living gait control after stroke.To this end, we applied the linear non-Gaussian acyclic model (LiNGAM)-a machine learning approach to causal discovery used to infer the causal relationships among observed variables whose causalities are not revealed-as an individual causal model for discovery-based free-living gait parameters [21].Subsequently, we identified patient groups and syndromes based on individual causal models using unsupervised learning clustering.Finally, Bayesian logistic regression via predictive projection feature selection was applied to interpret the clustering causal model based on the gait parameters and demographics.

A. Participants
We recruited 50 individuals with subacute post-stroke (mean age: 68.72±12.16years).The inclusion criteria were as follows: (1) hemorrhagic or ischemic stroke diagnosis confirmed based on computed tomography or magnetic resonance imaging, (2) walking independently with or without a cane in a free-living environment, (3) stroke onset within 180 days, and (4) no known history of stroke.The exclusion criteria were as follows: (1) Mini-Mental State Examination (MMSE) score of <20 and (2) history of lower limb orthopedic diseases.The study protocol conformed to the principles of the Declaration of Helsinki.Each participant provided written informed consent.The Ethics Committee of Nishiyamato Rehabilitation Hospital approved this study (IRB#032, the date of approval: May 5, 2022).With reference to a previous study that post-stroke gait was classified by cluster analysis [22], we determined that a sample size of at least 40 stroke patients was necessary (β = 0.20) [23].

B. Study Design and Procedure
Demographic data such as age, gender, body mass index (BMI), stroke type, hemiparetic side, time post-stroke, and use of a walking cane were collected.Participants were clinically assessed using the MMSE, Fugl-Meyer Assessment (FMA), and National Institutes of Health Stroke Scale (NIHSS).Next, each participant wore a single wearable triaxial accelerometer (Axivity AX3, York, UK) over the fifth lumbar vertebra (L5) for 24 h in a free-living environment and was instructed to continue daily activities as usual [24].The sensor was programmed to record data at 100 Hz with a range of ± 8 g [25].

C. Data Processing and Analysis
We assessed the spatiotemporal gait parameters for free living, (2) developed individual-directed acyclic graphs (DAGs) using LiNGAM, (3) characterized the DAGs using spectral clustering, and (4) interpreted the DAG patterns based on the gait parameters and demographics (Fig. 1).

D. Spatiotemporal Gait Parameters
Acceleration-derived variables were analyzed using custom MATLAB R2021b (MathWorks BV, USA).To ensure that the steady-state gait was analyzed, walking bouts lasting Summary of gait data analysis pipeline.Eighteen gait parameters (i.e., 9 parameters each at the time points t and t-1) are calculated from acceleration data.Spectral clustering is applied using the adjacency matrix for individual-directed acyclic graphs (DAG) of gait parameters.Another spectral clustering was applied to assign cluster labels.Abbreviations: step time asy, step time asymmetry; step length asy, step length asymmetry; RMS-ML, root mean square of the medial-lateral direction; RMS-AP, RMS of the anterior-posterior direction; RMS-SI, RMS of the superior-inferior direction.
for >15 s were discarded.The methodology for the algorithm and segmentation of accelerometer data has been comprehensively detailed in previous studies [25], [26].In brief, the initial and final contacts in the gait cycle were estimated for the spatiotemporal parameters using continuous wavelet transformation for vertical acceleration [26].
We obtained the values for the following nine spatiotemporal gait parameters: step velocity, step length, cadence, double support ratio, step length asymmetry, step time asymmetry, and Root Mean Square (RMS) in the anteroposterior (AP), mediolateral (ML), and superior-inferior (SI) axes for each gait cycle.The values of step velocity and step length were calculated as the mean values of both legs for the gait cycle.Cadence was derived from the step time of both legs.The double support ratio indicated the proportion of double support during the gait cycle.Step length asymmetry and step time asymmetry were used as spatiotemporal gait asymmetries [25].
Step length asymmetry was calculated as the absolute difference between the step lengths of both legs during each gait cycle.
Step time asymmetry was calculated as the absolute difference between the step times of both legs during each gait cycle.Higher values of these asymmetries indicate greater disparities between the gait performances of both legs.RMS represented the average magnitude of trunk accelerations in each axis during each gait cycle [4].Therefore, a higher RMS value indicates greater trunk sway during gait, which is associated with walking on uneven surfaces and a higher risk of falls [27], [28].In this study, the RMS was approximately equivalent to the standard deviation, as the acceleration signals were transformed so that the mean value for each walking bout was zero.Gait cycles with speeds of <0.2 m/s were discarded because they could represent a break.The values of nine gait parameters were calculated at the time points of t and t-1 because gait was continuous and influenced by the control from the previous gait cycle.Therefore, 18 gait parameters were analyzed.Three hundred data samples of these parameters from each patient were randomly selected and used for causal discovery analysis.
For a comprehensive interpretation of the gait parameters, we calculated their medians and ranges of these nine parameters.The range was defined as the difference between the 25th and 75th percentiles of the 300 data samples for each parameter [29].The range of gait parameters indicates their variability.The distributions of daily life gait speed and cadence are known to follow a bimodal distribution, reflecting gait adjustability through two preferred gait controls for adaptation to diverse environments and contexts.The fitting of the bimodal distributions for the step velocity and cadence were assessed using Ashman's D (Supplemental Fig. 1a and 1b) [29], [30].An Ashman's D value greater than 2 indicated a bimodal distribution.Ashman's D is calculated using the following formula (Equation 1): where µ 1 and µ 2 are the means of each gait parameter in the lower and higher gait speed distributions, respectively, and σ 1 and σ 2 are the standard deviations from each of these means.

E. LiNGAM
LiNGAM identifies the causal structure variables with causal relationships by utilizing non-Gaussian distributions.We employed direct LiNGAM, a method that robustly determines the causal sequence of variables by iteratively removing the influence of each independent component from the dataset within the model [21], [31].Prior knowledge was set that there were no time-reversal links (from the time point of t to t-1).The DAGs were developed using 18 gait parameters of 300 data samples for each participant.Edges showed independence between error variables (p<0.05) and >50% bootstrap probability after 1000 bootstrap sampling [32].

F. Similarity Between Individual DAG
The dice similarity coefficient (DSC) measures the similarity of DAGs between two participants and is calculated as follows (Equation 2): where |D A | and | D B | are the cardinalities of edges in the DAGs of participants A and B, respectively.A higher DSC indicates greater similarity between the DAGs of the two participants, with 0 indicating no similarity and 1 indicating complete similarity.The DCSs of the DAGs were calculated for all possible pairs of participants.The resulting values were populated into an adjacency matrix, with each entry representing the similarity between the corresponding pair of participants.For example, the entry in row A and column B, or row B and column A, represented the DCS between participants A and B (Fig. 1).The matrix provided a comprehensive overview of the similarities between participants.

G. Spectral Clustering
We examined the structure of personal relationships using clustering techniques tailored for network data.Spectral clustering, a promising method, leverages the eigenvalues of the adjacency matrix of a graph and is commonly executed with the k-means algorithm [33], [34].Spectral clustering in this study involved two phases.For the first phase, we created the co-occurrence matrix by repeating the spectral clustering 1000 times on the adjacency matrix.The co-occurrence matrix has more robust spectral properties and separability, as repeated clustering ensures a consistent accumulation of evidence from the data samples.The second phase entailed applying spectral clustering to the co-occurrence matrix to assign cluster labels to each participant [35].The optimal number of clusters k was determined by the spectral gap based on the eigenvalues.The spectral gap is typically defined as the discrepancy between the k-th and (k + 1)-th eigenvalues of the normalized Laplacian matrix of the co-occurrence matrix.A higher spectral gap indicates clearer separation between clusters.Therefore, we compared the spectral gaps for different numbers of clusters and selected the number of clusters that exhibited relatively high spectral gap values.The Fruchterman-Reingold force-directed algorithm was used to visualize the matrix [36].
To verify the fit of the average model for all the participants and each model for clusters, the Bayesian Information Criterion (BIC) was derived for each participant.The model with the lowest BIC had the best fit for the DAGs.We compared each model above using a Bayesian model comparison in the VBA toolbox and adopted a random-effects approach, assuming that the optimal model could have different outputs across participants [37].This method can verify whether a single model, as in previous studies or each clustering model, is optimal as a post-stroke gait model.

H. Hyperlink-Induced Topic Search Centrality
Graph centralities are used to identify essential nodes in complex networks and premier methods for evaluating the topological positions of individual network entities [38].Hyperlink-Induced Topic Search (HITS) centrality, which is used to determine the hub and vectors for authority and centrality of the nodes [39], was calculated for the DAGs of all participants and each cluster.

I. Statistical Analyses
R version 4.3.1 (R Foundation, Vienna, Austria) was used for the statistical analyses.In examining the demographic characteristics of the clusters, analysis of variance (ANOVA) was applied to age, BMI, MMSE score, time post-stroke, FMA score, and NIHSS score while the Chi-squared (X 2 ) test was applied to gender, stroke type, hemiparetic side, and use of a walking cane.Multiple comparisons with Holm corrections were applied to demographic variables with significant differences revealed by ANOVA or the X 2 test [40].Statistical significance was set at p<0.05.
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TABLE I SAMPLE CHARACTERISTICS AND COMPARISONS OF VARIABLES AMONG CLUSTERS
A predictive projection feature selection was used for the DAG pattern (i.e., cluster) from the candidate clusters.This method involved variable selection within a Bayesian framework, which delivers both predictive performance and inference [41].First, we fitted a Bayesian multinomial logistic regression as the reference model and the DAG pattern from the candidate cluster explanation.The candidate cluster variables consisted of 26 parameters; these included 20 gait variables (9 median parameters, 9 ranges of parameters, Ashman's D of step velocity, and Ashman's D of cadence) and 6 continuous demographic variables (age, BMI, MMSE, time post-stroke, FMA, and NIHSS).
We utilized weakly informative normal priors for both slopes and intercepts.We implemented four chains, each comprising 4000 iterations, with 2000 iterations designated for warmup as sampling.Additionally, we employed predictive projection feature selection to establish a submodel with fewer variables, aiming to yield predictions similar to the full model and leveraging the projpred package [41].The predictive performances of the submodels were evaluated and compared using the expected log predictive density (ELPD) and acquired through leave-one-out cross-validation using Pareto-smoothed importance sampling (PSIS-LOO-cv) [42].The optimal submodel selected the smallest variables with ELPDs within one standard error of the reference model.We used Bayesian R 2 to assess the model performance [43].

A. Spectral Clustering
According to the results of the spectral gap analysis in Fig. 2a, three primary clusters were derived from the gait data analysis using spectral clustering.Utilizing the Fruchterman-Reingold force-directed algorithm, the visualization arranged participants with similar characteristics nearer to each other on the graph (Fig. 2b).A few individuals (e.g., patients 4, 13, and 28) were intermediate between the clusters.Fig. 2c shows that each participant had the highest probability for the model of the cluster to which they were classified.Table I presents the demographic characteristics of the clusters.Only the ANOVA of the FMA score revealed a statistically significant difference.The multiple comparisons showed that the FMA score for Cluster 1 was significantly lower than those for Clusters 2 and 3. Supplemental Fig. 2 illustrates the results from the inter-cluster comparison of gait parameters.Cluster 1 was characterized by lower median values for step velocity and step length and higher medians for step time asymmetry, step length asymmetry, and RMS-SI.In contrast, Cluster 2 had higher median values for step velocity, step length, and RMS-AP and lower medians for double support, step time asymmetry, and step length asymmetry.Additionally, Cluster 2 showed a broader range of RMS-SI and a higher Ashman's D for step velocity.No significant differences were observed in the median cadence across the three clusters.
The DAG and HITS centralities for all the participants and three clusters are shown in Figs. 3 and 4, respectively.For all the participants, step length (t-1) and step time asymmetry (t-1) were prominent hubs for DAG, whereas step velocity (t) and cadence (t) were prominent authorities for DAG related to HIT centrality (Figs.3a, 4a, and 4b).Cluster 1 (n = 14) was characterized by low weight of the edge between step velocities and edges from step length to step velocity, loss of edges between step length asymmetries, and poor degree of nodes for step length but not cadence at contemporaneous and temporal points (Fig. 2b).In addition, the RMS-ML (t-1) was the most important hub for DAG, whereas cadence (t) and step length asymmetry (t) were authorities for the DAG over step length (t) for HIT centrality (Fig. 4a and b).Cluster 2 (n = 15) was characterized by a high weight of the edge from step length to step velocity, high connectivity with temporal autoregression, and high degree of node for step length but not cadence at contemporaneous and temporal points (Fig. 3c).RMS-SI (t-1) was described as the hub of the DAG and step length (t) as the authority of the DAG rather than cadence (t) (Figs.4a and b).Cluster 3 (n = 21) had a low weight of the edges between the step velocities, high weight of the edge from step length to step velocity and cadence to step velocity, and a loss of edges between the double supports (Fig. 3d).It had step time asymmetry as the hub of the DAG and step length (t) as the authority of the DAG over cadence (t) (Figs.4a and b).The DAGs for all the participants deviated from the results for each cluster; point step length asymmetry (t-1) was relatively important, which was similar to the hub (Figs.4a and b).

IV. DISCUSSION
In this study, we explored and characterized individual causal relationships of the parameters for free-living gait control of persons with stroke.Repeated spectral clustering identified three main clusters in the DAGs based on gait data, which were visualized using the Fruchterman-Reingold force-directed algorithm (Fig. 3a).The DAGs and HITS centrality revealed key features of each cluster, such as step length, cadence, and step time asymmetry.To identify the characteristics of each cluster based on gait parameters and demographics, we performed predictive projection feature selection.Four variables were extracted from the 26 potential clustering variables: Ashman's D of step velocity, FMA score, median step time asymmetry, and median step length.The submodel with these four selected variables sufficiently mimicked the classification performance of a comprehensive reference model that included all variables.
With the spectral clustering, most participants were classified into specific clusters; however, some participants were not clearly clustered because they belonged to two or more overlapping clusters (Fig. 2b).This suggests that these participants had a DAG of gait control similar to those of other participants in other clusters.Spectral clustering, a method based on geometric and statistical considerations, was also useful in this study to classify gait control impairments.The results are supported by model fitting using a Bayesian model comparison (Fig. 2c).None of the patients with stroke had the highest probabilities for the model of all participants.The model for gait after a stroke cannot be adequately explained by a single model, suggesting the existence of specific patterns.The individual DAG created by LiNGAM was the model causally related to gait control, considering the continuity of gait (time points t and t-1).According to the DAG for each cluster and HITS centrality (Figs. 3 and 4), gait speed appeared to have the highest authority; various gait parameters were controlled to adjust gait speed.Therefore, this discussion focuses on gait speed as the pivot.
Gait speed depends on step length and cadence at the contemporaneous point [45].Cluster 1 had a low FMA score, low weight of the edges from step length to step velocity, and a poor degree of node for step length but not cadence at contemporaneous and temporal points.Cluster 2 had a high FMA score, a high weight of the edge from step length to step velocity, and a high degree of node for step length but not cadence at contemporaneous and temporal points.Cluster 3 had a relatively high FMA score, a high number of nodes for step length, and a high cadence at contemporaneous and temporal points.These results indicate the contribution to gait speed, with Clusters 1, 2, and 3 demonstrating higher contributions from cadence, step length, and both step length and cadence, respectively.This finding is further supported by the HIT centrality results.The finding that the impact of step length and cadence for adjusting gait speed varied among persons with stroke is crucial to understanding gait control in persons with stroke.Previous studies have reported that persons with stroke increase cadence rather than step length when instructed to walk beyond a comfortable pace [17], [46].Increasing step length requires higher joint movements, whereas reductions or absence of ankle plantar flexion significantly diminishes the capacity to generate the propulsive force necessary for enhancing step length [3], [47].For gait following stroke, an increased step length leads to decreased stability margins.Therefore, persons with stroke should strategically adjust their gait speed with cadence to maintain stability [48].
Our results also show that step time asymmetry and step length asymmetry are characteristics of post-stroke gait.They affect gait speed through step length and cadence.However, the edge from asymmetry to cadence was not observed for Cluster 2. Increasing the step time asymmetry and step length asymmetry contributed to an increase in step length, whereas reducing this asymmetry increased cadence, in turn, increased gait speed.These results explain the inconsistency in gait asymmetry manipulating gait speed, as reported by previous studies [16], [18], [49].
Step length asymmetry for Cluster 3, but not for Clusters 1 and 2, may also affect speed.However, the present results also revealed that the contribution of gait asymmetries to step length and cadence is low, making its relative contribution to gait speed low as well.For Cluster 1, the edges from RMS to gait speed or step length at contemporaneous points were limited.In contrast, there was connectivity between RMS-AP and RMS-SI for Cluster 2 and RMS-SI for Cluster 3.For all the clusters, increased RMS-SI and RMS-AP of the previous gait cycle contributed to increased gait speed and/or step length in the subsequent gait cycle, whereas increased RMS-ML contributed to decreased gait speed and/or step length.The increase in the center of mass motions in the AP and SI axes is closely associated with an increase in gait speed but not in the ML axis [50].In addition, RMS-ML is more reflective of gait instability [51], [52].Thus, our results suggest that increased gait instability in the ML axis reduces gait performance in the subsequent gait cycle.For each cluster, the RMSs were unaffected by other parameters at contemporaneous and temporal points and independent of connectivity.Moreover, the DAG for Cluster 2 demonstrated high connectivity with temporal autoregressions, but those for Clusters 1 and 3 had low or no connectivity with temporal autoregressions.Temporal autoregression of the DAG may also reflect the variability of gait parameters.
Only 4 of the 26 potential clustering variables, determined using predictive projection feature selection, were sufficient to mimic the forecasts of an extensive reference model encompassing all 26 variables.Participants who showed a bimodal distribution of step velocity, high FMA score, low step time asymmetry, and high step length were allocated to Cluster 2. These characteristics of Cluster 2 gait parameters were consistent with those of Supplemental Fig. 2. The performance of the optimal four-variable submodel measured by the Bayesian R 2 was slightly worse than that of the model based on all 26 variables.The similar predictions between the submodel, featuring only four variables, and the reference model with 26 variables do not imply that the other 22 variables lack relevance to cluster classification.The chosen four variables in the projected submodel hold theoretical significance for gait research.Specifically, the first variable, Ashman's D of step velocity, pertains to the fitting of the bimodal distribution of step velocity, adding depth to the analysis in the field (Supplemental Fig. 1a).
This indicates that the participants had two preferred gait speeds.Quantifying gait speed distribution in this manner preserves the breadth of information rather than simplifying it to a single mean and standard deviation.It is plausible that the lower preferred speed corresponds to short walking bouts in confined spaces, whereas the higher preferred speed aligns with longer bouts in more open areas.Functional impairment, inferred from the bimodal distribution of gait speed, may restrict the freedom to select speeds, as observed in individuals with a history of falls and some with Parkinson's disease [29], [53].This study also represents the first investigation of the distribution of gait speeds in free-living persons with stroke.Our findings revealed that the bimodality of gait speed was impaired in individuals with moderate or mild hemiparesis.The second and third variables selected in the submodel were the FMA score and median step time asymmetry.The findings of this study support those shown in several previous studies indicating the importance of lower limb dysfunction in gait control by persons with stroke [54], [55].The last variable selected for the submodel was step length.Cluster 2 was distinct because the contribution of step length to gait speed was higher than that for the other clusters in the DAGs for gait control.Previous studies have reported that individuals with stroke increase cadence rather than step length to achieve higher walking speeds [17], [46], but our results suggest that the contributions of step length and cadence to gait speed are heterogeneous after stroke.
The findings of this study should be interpreted considering some limitations.First, the sample size for this study was comparatively limited, which necessitates caution in interpreting our findings.Second, the persons with subacute stroke recruited in this study had varied time post-stroke.There were no significant differences in stroke onset duration between clusters.Due to differences in the recovery process of hemiplegia and other factors, unifying the duration of onset may yield different results.Third, acceleration data can identify the initial and final contacts of both legs, allowing for the calculation of spatiotemporal gait parameters, which we used in this study.However, it is impossible to determine which leg is the right or left limb based solely on this data.As a result, although gait asymmetry can be calculated, the specific gait parameters of the hemiplegic limb could not be determined.Distinguishing between hemiplegic and non-hemiplegic limbs for gait parameters can provide deeper insights for clinical practice.Future studies need to analyze the gaits of both hemiplegic and nonhemiplegic legs by attaching inertial sensors to both feet.
In summary, Cluster 1 comprised persons with moderate stroke who showed high gait asymmetry and gait instability and primarily adjusted their gait speed based on cadence.Cluster 2 comprised individuals with mild stroke who regulated gait speed mainly by increasing step length through enhanced anterior-posterior and vertical center-of-mass displacements.Cluster 3 comprised individuals with mild stroke who strategically adjusted their gait speed based on both step length and cadence.These clusters were explained by the bimodal distribution of step velocity, high FMA score, low step time asymmetry, and high step length.Our study group had mild-to-moderate hemiplegia; thus, the results can only be generalized to persons with similar symptoms.The diverse DAG patterns of gait control identified suggest the heterogeneity of gait patterns, and persons with stroke are functionally different.Understanding the theoretical interactions between gait functions would provide a foundation for highly tailored rehabilitation.By deciphering the individual networks for gait control, we can develop precise interventions that target specific gait parameters, such as step length or gait asymmetry, which are associated with desired functional Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
improvements like increased walking speed.This approach will allow for a more tailored and effective treatment strategy.

Fig
Fig. 1.Summary of gait data analysis pipeline.Eighteen gait parameters (i.e., 9 parameters each at the time points t and t-1) are calculated from acceleration data.Spectral clustering is applied using the adjacency matrix for individual-directed acyclic graphs (DAG) of gait parameters.Another spectral clustering was applied to assign cluster labels.Abbreviations: step time asy, step time asymmetry; step length asy, step length asymmetry; RMS-ML, root mean square of the medial-lateral direction; RMS-AP, RMS of the anterior-posterior direction; RMS-SI, RMS of the superior-inferior direction.

Fig. 2 .
Fig. 2. Individual spectral clustering.(a) Spectral gap for various k values.(b) Graph visualization of the co-occurrence matrix for gait parameters.Darker black color links persons frequently clustered together.(c) Individual model probabilities.The best probabilities are provided by the model by which each participant was clustered.

Fig. 3 .
Fig. 3. Directed acyclic graph (DAG) visualization for all persons and each cluster.(a) DAG for all the participants.(b) DAG for Cluster (c) DAG for Cluster 2. (d) DAG for Cluster 3. Node color represents degree of the node, edge color represents the weight of the edge, and edge width represents the occupancy ratio (i.e., the proportion of persons within the cluster have each edge).Abbreviations: step time asy, step time asymmetry; step length asy, step length asymmetry; RMS-ML, root mean square of the medial-lateral direction; RMS-AP, RMS of the anterior-posterior direction; RMS-SI, RMS of the superiorinferior direction.

Fig. 4 .
Fig. 4. Hyperlink-Induced Topic Search (HITS) centrality and ranking of all participants and each cluster.(a) Hub of HITS centrality.(b) Authority of HITS centrality.Abbreviations: step time asy, step time asymmetry; step length asy, step length asymmetry; RMS-ML, root mean square of the medial-lateral direction; RMS-AP, RMS of the anterior-posterior direction; RMS-SI, RMS of the superior-inferior direction.

Fig. 5 .
Fig. 5. Predictive projection feature selection trajectory.(a) Change in expected log predictive density as more variables are entered into submodel.(b) Scatterplot of clusters classified by the submodel (four variables) and those classified by the reference (22 variables).(c) Credible intervals for variables from the submodel of Cluster 1 for Cluster 2. (d) Credible intervals variables from the submodel of Cluster 3 for Cluster 2. Marginal posterior distributions of variables selected for the submodel.