一种紧凑的步态索引前后压力中心表示，用于基于足底垂直地面反作用力的帕金森病分类

# A Compact Stance-Indexed Anterior–Posterior COP Representation for Parkinson’s Disease Classification from Plantar VGRF
Source: [https://arxiv.org/html/2609.22956](https://arxiv.org/html/2609.22956)
Md\. SifatEmail:[mdsifat371@gmail\.com](mailto:[email protected])Affiliation:Department of Computer Science and Engineering, University of Rajshahi, Rajshahi, BangladeshSania AkterEmail:[saniaaker@gmail\.com](mailto:[email protected])Affiliation:Department of Computer Science and Engineering, University of Rajshahi, Rajshahi, BangladeshAkif IslamEmail:[iamakifislam@gmail\.com](mailto:[email protected])Affiliation:Department of Computer Science and Engineering, University of Rajshahi, Rajshahi, BangladeshMd\. Ekramul HamidEmail:[ekram\_hamid@ru\.ac\.bd](mailto:[email protected])Affiliation:Department of Computer Science and Engineering, University of Rajshahi, Rajshahi, Bangladesh

###### Abstract

Parkinson’s disease alters gait and bilateral coordination, but machine\-learning performance also depends on how continuous gait signals are represented\. This study investigates whether preserving anterior–posterior center\-of\-pressure \(AP\-COP\) information at fixed locations across normalized stance provides a compact and informative representation of plantar\-force gait signals\. Bilateral vertical ground reaction force recordings from 165 participants in the Gait in Parkinson’s Disease Database were evaluated using repeated fully nested participant\-level cross\-validation\. We propose AP\-COP10, comprising AP\-COP position and bilateral asymmetry across five stance windows\. AP\-COP10 achieved an AUC of 0\.894 and outperformed three harmonized literature\-derived COP representations under the same evaluation pipeline\. The complementary 25 non\-AP\-COP descriptors alone achieved an AUC of 0\.856, while the complete 35\-feature representation achieved 0\.908\. Removing AP\-COP10 from the complete representation produced a statistically supported loss in discrimination, whereas adding the complementary descriptors to AP\-COP10 yielded only a small, unsupported improvement\. Feature competition indicated that the most informative stance\-indexed descriptors were concentrated in early and early\-mid stance, while source\-study holdout and sensor\-perturbation analyses supported the robustness of the representation\. These findings indicate that stance\-indexed AP\-COP retains discriminative information that is not readily recovered by broader engineered gait descriptors, supporting compact and interpretable representations for machine\-learning analysis of pathological gait\.

###### Keywords:

Parkinson’s disease , plantar vertical ground reaction force , center of pressure , normalized stance , signal representation , interpretable machine learning

## 1Introduction

In machine\-learning analysis of gait, predictive performance depends not only on the choice of classifier but also on how continuous sensor signals are represented\. This issue is particularly relevant in Parkinson’s disease \(PD\), where gait impairment involves changes in pace, rhythmicity, postural stability, variability, and bilateral coordination\[[1](https://arxiv.org/html/2609.22956#bib.bib1),[2](https://arxiv.org/html/2609.22956#bib.bib2),[3](https://arxiv.org/html/2609.22956#bib.bib3)\]\. Quantitative gait measures are increasingly being investigated as digital biomarkers for characterizing mobility impairment and monitoring disease\-related changes\[[4](https://arxiv.org/html/2609.22956#bib.bib4),[5](https://arxiv.org/html/2609.22956#bib.bib5)\]\. Plantar\-force sensing is attractive in this context because instrumented insoles provide direct measurements of foot–ground interaction during walking and support the extraction of temporal, kinetic, and spatial gait information\[[6](https://arxiv.org/html/2609.22956#bib.bib6),[7](https://arxiv.org/html/2609.22956#bib.bib7)\]\. The Gait in Parkinson’s Disease Database \(GaitPDB\), which contains bilateral plantar vertical ground reaction force \(VGRF\) recordings from participants with PD and healthy controls across three source studies, has therefore become a widely used resource for computational gait analysis\[[8](https://arxiv.org/html/2609.22956#bib.bib8)\]\.

Among the quantities derived from plantar\-force measurements, the center of pressure \(COP\) provides an interpretable description of how the resultant plantar load progresses beneath the foot during stance\[[9](https://arxiv.org/html/2609.22956#bib.bib9),[10](https://arxiv.org/html/2609.22956#bib.bib10)\]\. Altered and asymmetric COP behavior has been reported in PD\[[11](https://arxiv.org/html/2609.22956#bib.bib11),[12](https://arxiv.org/html/2609.22956#bib.bib12)\], supporting its relevance for quantitative gait characterization\. COP is fundamentally a continuous trajectory, however, and its information content depends on how that trajectory is represented\. Global statistics, geometric measures, bilateral summaries, and dynamic descriptors compress different aspects of the underlying signal, and whole\-trajectory summaries do not necessarily preserve where within stance a discriminative difference occurs\. Continuous biomechanical analyses have similarly shown that localized effects may be obscured by scalar reduction\[[13](https://arxiv.org/html/2609.22956#bib.bib13)\]\.

This creates a representation\-level problem\. Existing COP\-based studies differ in feature construction, participant selection, prediction task, model choice, and validation procedure, making their reported performance difficult to interpret as evidence that one representation is intrinsically more informative than another\. More fundamentally, it remains unclear whether discriminative COP information is distributed broadly across the trajectory or concentrated within particular portions of stance that may be attenuated when the signal is reduced to whole\-trajectory summaries\. A controlled comparison under a common evaluation framework is therefore needed to isolate the effect of representation content\.

Normalized stance provides a useful middle ground between aggressive whole\-trajectory compression and high\-dimensional waveform modeling\. COP progression is known to vary systematically across different portions of stance and is influenced by walking speed, foot position, and foot structure\[[14](https://arxiv.org/html/2609.22956#bib.bib14),[10](https://arxiv.org/html/2609.22956#bib.bib10),[15](https://arxiv.org/html/2609.22956#bib.bib15)\]\. Retaining COP information at corresponding locations of normalized stance can therefore preserve the location of biomechanical information while remaining low dimensional and interpretable\. This motivates preserving localized anterior–posterior COP information across normalized stance rather than summarizing the trajectory only at the whole\-stance level\. In the present work, five fixed windows are used to derive AP\-COP position and corresponding bilateral asymmetry, yielding a compact 10\-candidate representation termed AP\-COP10\.

We evaluate AP\-COP10 under a common participant\-level repeated fully nested framework against harmonized literature\-derived COP representations and a broader 35\-candidate engineered feature space spanning temporal\-rhythm, dynamic\-support, bilateral\-asymmetry, COP\-rollover, and vertical\-loading descriptors\. To examine how the stance\-indexed descriptors contribute within this broader representation, the remaining 25 non\-AP\-COP descriptors are also evaluated independently\. Together, these comparisons assess the discriminative information retained by the compact stance\-indexed representation, by the complementary engineered descriptors, and by their combined feature space\.

The main contributions are:

1. 1\.A compact stance\-indexed representation of anterior–posterior COP position and bilateral asymmetry across normalized stance\.
2. 2\.A controlled representation\-level evaluation framework that isolates the effect of COP feature design from differences in experimental pipelines\.
3. 3\.An analysis of the discriminative value, compactness, and robustness of localized COP information for participant\-level PD classification\.

## 2Related Work

### 2\.1Plantar\-force and COP analysis in Parkinsonian gait

Plantar force measurements have long been used to characterize gait abnormalities in Parkinson’s disease \(PD\), including altered force distribution and gait variability\[[16](https://arxiv.org/html/2609.22956#bib.bib16),[17](https://arxiv.org/html/2609.22956#bib.bib17)\]\. Subsequent reviews have documented broader spatiotemporal and biomechanical abnormalities in PD gait\[[2](https://arxiv.org/html/2609.22956#bib.bib2),[4](https://arxiv.org/html/2609.22956#bib.bib4)\]\. The center of pressure \(COP\) provides an interpretable spatial description of how the resultant load progresses beneath the foot during stance\. COP trajectories have been characterized using in\-shoe force measurements and normalized stance coordinates\[[9](https://arxiv.org/html/2609.22956#bib.bib9),[10](https://arxiv.org/html/2609.22956#bib.bib10)\], with progression influenced by factors including walking speed, age, sex, and foot structure\[[14](https://arxiv.org/html/2609.22956#bib.bib14),[18](https://arxiv.org/html/2609.22956#bib.bib18),[15](https://arxiv.org/html/2609.22956#bib.bib15)\]\. Altered and asymmetric COP behavior has also been reported in PD\[[11](https://arxiv.org/html/2609.22956#bib.bib11),[12](https://arxiv.org/html/2609.22956#bib.bib12)\]\.

More recent COP, plantar\-pressure, and wearable\-insole studies have expanded analysis to regional pressure dynamics, postural\-sway measures, and larger multidomain feature spaces\[[19](https://arxiv.org/html/2609.22956#bib.bib19),[20](https://arxiv.org/html/2609.22956#bib.bib20),[21](https://arxiv.org/html/2609.22956#bib.bib21)\]\. Together, these studies establish plantar force and COP as useful sources for Parkinsonian gait analysis while showing that the same underlying trajectory can be represented in substantially different ways\.

### 2\.2COP representations for machine\-learning gait analysis

Machine\-learning studies have used several forms of COP representation\. Global statistics such as mean and standard deviation provide compact summaries of overall COP position and dispersion\[[22](https://arxiv.org/html/2609.22956#bib.bib22)\]\. Bilateral and geometric descriptors, including AP\-COP dispersion and COP\-path symmetry, retain information about inter\-limb relationships and overall COP behavior\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]\. Other approaches use richer dynamic or nonlinear descriptors, including COP velocity, acceleration, jerk, path efficiency, and entropy\-related measures\[[24](https://arxiv.org/html/2609.22956#bib.bib24)\]\.

Trajectory\- and phase\-resolved analyses provide a complementary approach by retaining information across the progression of stance\[[13](https://arxiv.org/html/2609.22956#bib.bib13)\]\. Biomechanical studies have shown that COP characteristics vary across normalized stance\[[14](https://arxiv.org/html/2609.22956#bib.bib14),[10](https://arxiv.org/html/2609.22956#bib.bib10),[15](https://arxiv.org/html/2609.22956#bib.bib15)\], suggesting that both COP position and its location within the stance cycle may be informative\. Bilateral asymmetry provides another complementary property, as inter\-limb differences in COP behavior have been reported in PD\[[11](https://arxiv.org/html/2609.22956#bib.bib11),[23](https://arxiv.org/html/2609.22956#bib.bib23)\]\. Together, these studies indicate that both AP\-COP behavior and its localization within stance may be informative, while existing representations differ substantially in the trajectory information they preserve\.

Existing studies, however, use different feature definitions and experimental pipelines, making their reported performance difficult to compare directly\. A controlled representation\-level comparison can therefore provide a clearer assessment of the information retained by different COP encodings\.

### 2\.3Machine learning on the Gait in Parkinson’s Disease Database

GaitPDB has also been studied using a broad range of machine\-learning approaches beyond COP\-specific features\. Earlier work used engineered VGRF, temporal, and frequency\-domain descriptors with classical classifiers\[[25](https://arxiv.org/html/2609.22956#bib.bib25),[26](https://arxiv.org/html/2609.22956#bib.bib26),[27](https://arxiv.org/html/2609.22956#bib.bib27)\], while other studies focused on stance\-related force characteristics or disease\-stage classification\[[28](https://arxiv.org/html/2609.22956#bib.bib28),[29](https://arxiv.org/html/2609.22956#bib.bib29)\]\. More recent work has increasingly used deep learning, including convolutional models, explainable architectures, and graph\-based approaches for multichannel plantar\-force data\[[30](https://arxiv.org/html/2609.22956#bib.bib30),[31](https://arxiv.org/html/2609.22956#bib.bib31),[32](https://arxiv.org/html/2609.22956#bib.bib32)\]\.

These studies demonstrate the predictive richness of GaitPDB, but their different representations, model designs, and validation strategies make published performance difficult to interpret as evidence for the superiority of one representation\. The present study therefore focuses on the controlled comparison of interpretable COP representations under a common participant\-level framework, with particular attention to the information preserved by stance\-indexed AP\-COP\.

## 3Materials and Methods

### 3\.1Study Design and Dataset

The study was designed to isolate the effect of representation content on participant\-level Parkinson’s disease classification\. Three representation groups were evaluated under a common machine\-learning pipeline: the proposed 10\-candidate stance\-indexed AP\-COP representation \(AP\-COP10\), three literature\-derived COP representations, and a complete 35\-candidate engineered multidomain representation \(Full35\)\. The 25 non\-AP\-COP descriptors contained within Full35 were also evaluated independently\. All representations used the same participants, signal preprocessing, outer data partitions, training\-only feature selection, and final classifier\. This design allows differences in predictive performance to be interpreted primarily in terms of representation content rather than differences in the surrounding experimental pipeline\. Figure[1](https://arxiv.org/html/2609.22956#S3.F1)summarizes the study workflow\.

Figure 1:Study workflow from bilateral plantar VGRF preprocessing and feature construction through fully nested participant\-level evaluation\.The proposed representation was evaluated in two complementary comparisons\. First, it was compared with COP descriptors derived from Alam et al\.\[[22](https://arxiv.org/html/2609.22956#bib.bib22)\], Jin\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\], and Tong et al\.\[[24](https://arxiv.org/html/2609.22956#bib.bib24)\], each harmonized to the common participant\-level pipeline\. Second, AP\-COP10 was evaluated as a strict subset of Full35, allowing the contribution of additional temporal, support, bilateral, COP\-rollover, and vertical\-loading descriptors to be examined without changing the evaluation framework\. The remaining 25 descriptors were additionally evaluated on their own to assess their predictive information in the absence of stance\-indexed AP\-COP\.

#### 3\.1\.1Dataset and participant\-level prediction task

Experiments used GaitPDB from PhysioNet\[[8](https://arxiv.org/html/2609.22956#bib.bib8)\]\. The database provides bilateral plantar VGRF signals from eight individual force sensors beneath each foot plus left and right total\-force channels, sampled at 100 Hz\. The database documentation lists 93 participants with idiopathic PD and 73 healthy controls collected across three studies\. In the present analysis, one\_01usual\-walking recording was retained per participant from the Ga, Ju, and Si source studies\. One control listed in the demographic table lacked a matching\_01signal file, leaving an analytic cohort of 165 participants: 93 PD and 72 controls\.

Source\-study counts were 47 for Ga, 54 for Ju, and 64 for Si\. Participant characteristics are shown in Table[1](https://arxiv.org/html/2609.22956#S3.T1)\. The participant was the prediction and analysis unit\. Individual samples, gait cycles, stances, windows, and repeated steps were used only to construct participant\-level descriptors and were never treated as independent machine\-learning observations\. This participant\-level design prevents repeated measurements from the same individual from contributing independent observations to model evaluation\.

Table 1:Participant characteristics by source study and diagnosis\. Continuous variables are median \[IQR\]\.

### 3\.2Signal Processing and Feature Construction

#### 3\.2\.1Signal preprocessing and stance extraction

The first and final 10 s of each recording were removed\. Left and right total VGRF were clipped at zero and median filtered using a five\-sample window\. Foot contact was detected independently with a 20\-N threshold\. Contact interruptions lasting at most five samples were closed, runs shorter than 20 samples were removed, and candidate stances were restricted to 0\.30–2\.00 s\. Participants were required to have at least eight valid stances for each foot\. The retained left\- and right\-foot stance runs were ordered chronologically, and one boundary stance was removed from each end of the active walking interval\.

For timing and multidomain descriptors, contact onset defined the step event\. Consecutive events separated by less than 0\.20 s were excluded\. Alternating\-foot step intervals were restricted to 0\.25–1\.50 s; same\-foot stride, stance, and swing durations were restricted to 0\.50–2\.50, 0\.30–2\.00, and 0\.05–1\.50 s, respectively\. Body force for normalization of vertical\-loading descriptors was estimated as the median bilateral total force among samples where combined force exceeded 100 N\.

#### 3\.2\.2Sensor\-coordinate COP reconstruction and AP stance normalization

Negative individual\-sensor force values were clipped to zero\. AP\-COP was derived independently for each foot using fixed anterior–posterior sensor coordinates

sj=\[−800,−400,−400,0,0,400,400,800\]\.s\_\{j\}=\[\-800,\-400,\-400,0,0,400,400,800\]\.For sensor forcefj​\(t\)f\_\{j\}\(t\), the raw force\-weighted AP load\-center coordinate was

qraw​\(t\)=∑j=18fj​\(t\)​sj∑j=18fj​\(t\),q\_\{\\mathrm\{raw\}\}\(t\)=\\frac\{\\sum\_\{j=1\}^\{8\}f\_\{j\}\(t\)s\_\{j\}\}\{\\sum\_\{j=1\}^\{8\}f\_\{j\}\(t\)\},\(1\)when the summed individual\-sensor force exceeded10−810^\{\-8\}\. The resulting coordinate is scaled to\[0,1\]\[0,1\],

q⁡\(t\)=qraw​\(t\)\+8001600,q\(t\)=\\frac\{q\_\{\\mathrm\{raw\}\}\(t\)\+800\}\{1600\},\(2\)and is interpreted as a sensor\-coordinate AP load\-center proxy rather than an anatomical COP distance, because the underlying coordinates represent discrete sensor locations rather than measured anatomical distances\.

Within each detected stance, non\-finite AP\-COP values were removed\. A stance was discarded from AP\-COP analysis when fewer than 30 finite samples remained\. Accepted AP\-COP trajectories were linearly resampled to 101 points corresponding to 0–100% normalized stance and smoothed using an 11\-point, second\-order Savitzky–Golay filter with interpolation\-based edge handling\[[33](https://arxiv.org/html/2609.22956#bib.bib33)\]\.

For literature\-derived descriptors requiring two\-dimensional COP, the same force\-weighted reconstruction was applied using the sensor\-plane coordinates adopted for the corresponding reference representations, and the resulting ML and AP trajectories were summarized under the harmonized stance extraction described above\. This common preprocessing was intentional: the goal was to compare representation content rather than reproduce the original studies’ entire signal\-processing pipelines\.

#### 3\.2\.3Proposed stance\-indexed AP\-COP representation

The proposed representation preserves AP\-COP position and bilateral asymmetry at five fixed windows distributed across normalized stance:

W=\{5​–​15,25​–​35,45​–​55,65​–​75,85​–​95\}%\.W=\\\{5\\text\{\-\-\}15,\\;25\\text\{\-\-\}35,\\;45\\text\{\-\-\}55,\\;65\\text\{\-\-\}75,\\;85\\text\{\-\-\}95\\\}\\%\.The windows specify*when*within normalized stance AP\-COP is summarized rather than fixed physical locations on the foot\. They were fixed before the reported classification runs and were not selected by searching PD–control results\. The windows provide approximately uniform coverage from early to late stance without concentrating all descriptors in a single phase\.

For participantii, footF∈\{L,R\}F\\in\\\{L,R\\\}, stancerr, and windoww=\[a,b\]w=\[a,b\], the stance\-level AP\-COP position was

mi,F,r\(w\)=1b−a\+1​∑k=abqi,F,r​\(k\),m\_\{i,F,r\}^\{\(w\)\}=\\frac\{1\}\{b\-a\+1\}\\sum\_\{k=a\}^\{b\}q\_\{i,F,r\}\(k\),\(3\)and repeated stances were summarized separately for the two feet:

Qi,F\(w\)=medianr⁡mi,F,r\(w\)\.Q\_\{i,F\}^\{\(w\)\}=\\operatorname\{median\}\_\{r\}m\_\{i,F,r\}^\{\(w\)\}\.\(4\)The participant\-level bilateral position descriptor was

Pi\(w\)=Qi,L\(w\)\+Qi,R\(w\)2\.P\_\{i\}^\{\(w\)\}=\\frac\{Q\_\{i,L\}^\{\(w\)\}\+Q\_\{i,R\}^\{\(w\)\}\}\{2\}\.\(5\)To quantify left–right differences on a relative scale, we used a Robinson\-type symmetry index based on the absolute bilateral difference normalized by the mean magnitude of the two side\-specific coordinates, a widely used class of discrete gait\-symmetry measures\[[34](https://arxiv.org/html/2609.22956#bib.bib34),[35](https://arxiv.org/html/2609.22956#bib.bib35)\]\. The corresponding bilateral asymmetry descriptor was

Ai\(w\)=\|Qi,L\(w\)−Qi,R\(w\)\|0\.5​\(\|Qi,L\(w\)\|\+\|Qi,R\(w\)\|\)\.A\_\{i\}^\{\(w\)\}=\\frac\{\\left\|Q\_\{i,L\}^\{\(w\)\}\-Q\_\{i,R\}^\{\(w\)\}\\right\|\}\{0\.5\\left\(\\left\|Q\_\{i,L\}^\{\(w\)\}\\right\|\+\\left\|Q\_\{i,R\}^\{\(w\)\}\\right\|\\right\)\}\.\(6\)The primary asymmetry formulation expresses bilateral AP\-COP separation relative to the mean magnitude of the two side\-specific coordinates, providing a dimensionless measure that can be compared across stance windows\. Becauseq⁡\(t\)q\(t\)is expressed on a heel\-anchored\[0,1\]\[0,1\]scale, this normalization depends on the chosen coordinate origin\. Two origin\-invariant alternatives were therefore evaluated as sensitivity variants: the absolute bilateral difference\|Qi,L\(w\)−Qi,R\(w\)\|\\left\|Q\_\{i,L\}^\{\(w\)\}\-Q\_\{i,R\}^\{\(w\)\}\\right\|, already expressed in normalized AP\-coordinate units, and the same difference divided by the participant\-level AP range\.

Both foot summaries were finite for all participants and windows in the reported analysis\. Repeating the procedure over five windows yielded five position and five asymmetry descriptors, for 10 participant\-level candidates\. Figure[2](https://arxiv.org/html/2609.22956#S3.F2)illustrates the construction\. The exact feature identifiers are provided in Supplementary Table S1\.

Figure 2:Construction of the stance\-indexed AP\-COP representation\. \(a\) Each accepted AP\-COP stance trajectory is normalized to 0–100% stance and sampled within five fixed windows\. \(b\) Window values are aggregated across repeated stances separately for the two feet, then combined into one bilateral position and one bilateral asymmetry descriptor per window\. The five windows therefore yield 10 participant\-level candidate features\.
#### 3\.2\.4Complete engineered multidomain representation

The complete engineered representation \(Full35\) contained 35 unique participant\-level candidates spanning six descriptor families: six temporal\-rhythm descriptors, four dynamic\-support descriptors, four bilateral asymmetry descriptors outside the AP\-COP family, six broader COP\-rollover descriptors \(AP range, path length, median COP speed, COP\-speed coefficient of variation, monotonicity, and early slope\), five vertical\-loading descriptors, and the 10 stance\-indexed AP\-COP descriptors defined in Section[3\.2\.3](https://arxiv.org/html/2609.22956#S3.SS2.SSS3)\. Candidate definitions are summarized in Table[2](https://arxiv.org/html/2609.22956#S3.T2); the complete feature dictionary is provided in Supplementary Table S2\.

Full35 denotes a candidate feature space rather than a 35\-variable fitted model and contains AP\-COP10 as a strict subset\. The complementary representation, termed*Non\-AP\-COP25*, was obtained by removing the 10 stance\-indexed AP\-COP candidates from Full35\. It therefore retained six temporal\-rhythm, four dynamic\-support, four non\-AP\-COP bilateral\-asymmetry, six broader COP\-rollover, and five vertical\-loading descriptors\. The same training\-only feature\-selection procedure and six\-feature maximum were applied to Non\-AP\-COP25 as to the other representation spaces\. Full35 and Non\-AP\-COP25 therefore denote candidate pools rather than fixed high\-dimensional fitted models\.

Table 2:Descriptor families in the complete 35\-candidate engineered multidomain representation\.
#### 3\.2\.5Literature\-derived COP reference representations

All literature\-derived sets were defined before their controlled runs and were evaluated with the same downstream nested procedure as the proposed representation\. They should be interpreted as*harmonized reimplementations of published COP descriptor definitions*, not as reproductions of the original papers’ complete classifiers\.

Alam\-derived COP4\.Alam et al\. used mean and standard deviation of COP coordinates as machine\-learning features\[[22](https://arxiv.org/html/2609.22956#bib.bib22)\]\. The direct reference therefore contained four left\-foot descriptors: mean ML\-COP, SD ML\-COP, mean AP\-COP, and SD AP\-COP\. Stance\-level quantities were summarized under the common participant aggregation\. Because the proposed representation is bilateral, an eight\-candidate bilateral extension of the same descriptor types was also evaluated as a sensitivity analysis to confirm that the primary result was not an artifact of the single\-foot formulation\.

Jin\-derived COP7\.The Jin\-derived COP representation contained seven COP\-specific descriptors\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]: AP\-COP SD for the left and right feet, ML\-COP SD for the left and right feet, two\-dimensional COP path length for the left and right feet, and bilateral COP\-path symmetry\. Forefoot\-to\-rearfoot loading ratio was deliberately excluded because it is a regional plantar\-loading descriptor rather than a COP descriptor\. This distinction is important because Jin reported moderate\-to\-large group effects for forefoot\-to\-rearfoot loading and identified it as an influential gait\-derived quantity in the broader analysis\. The present Jin7 comparator therefore isolates the COP dispersion/path/symmetry family by design and should not be interpreted as Jin’s complete gait feature set\.

Tong\-derived COP18\.Tong et al\. described linear and nonlinear characteristics extracted from COP trajectories\[[24](https://arxiv.org/html/2609.22956#bib.bib24)\]\. The primary controlled Tong\-derived set contained nine reproducible descriptor types retained separately for the left and right feet: RMS ML\-COP, RMS AP\-COP, RMS total COP coordinate magnitude, RMS two\-dimensional COP velocity, RMS acceleration, RMS jerk, COP path efficiency, ML\-COP sample entropy, and AP\-COP sample entropy, yielding 18 candidates\. COP path efficiency was defined as direct start\-to\-end COP displacement divided by actual COP path length during stance\.

Descriptors that could not be deterministically reconstructed from the source description—COP\-track intersection measures \(CSIP/CISP\), whose intersection algorithm was not specified sufficiently for reliable reimplementation—were excluded rather than approximated, and source\-specific downstream procedures such as persistent\-homology processing, oversampling, and SVM classification were omitted, as the present comparison isolates COP descriptor representation under a common downstream classifier\. Sample entropy used embedding dimensionm=2m=2and tolerancer=0\.20×SDr=0\.20\\times\\mathrm\{SD\}, disclosed because the source article does not specify this parameterization\. Secondary sensitivities \(a nine\-candidate bilateral summary, an AP\-focused eight\-candidate set, and a generous axis\-expanded 30\-candidate set\) are reported in Results\. The complete feature\-level reproduction and harmonization record is provided in Supplementary Table S3\.

Literature\-derived COP union\.To evaluate whether combining descriptor families from more than one source study captures additional information relative to any single comparator, an 11\-candidate union of non\-duplicated Alam\- and Jin\-derived COP descriptors was constructed\. This set was assembled for the present comparison and was not used verbatim in any single prior paper; it is reported alongside, but separately from, the three primary literature contrasts\.

### 3\.3Model Development and Evaluation

#### 3\.3\.1Fully nested feature selection and validation

The entire feature\-selection and model\-development process was nested within the outer training data so that no held\-out participant influenced feature eligibility, feature ranking, hyperparameter selection, or model fitting, avoiding the optimistic bias that arises when feature or model selection is performed outside the validation loop\[[36](https://arxiv.org/html/2609.22956#bib.bib36),[37](https://arxiv.org/html/2609.22956#bib.bib37)\]\. Inner folds were used exclusively for model development, whereas outer folds were used only for performance estimation\. Identical outer partitions were applied to every representation, enabling paired participant\-level comparison\.

All model development occurred within each outer\-training partition\. Missing values were median\-imputed and candidates standardized using training\-only statistics\. Elastic\-net logistic hyperparameters\[[38](https://arxiv.org/html/2609.22956#bib.bib38)\]were selected by inner five\-fold cross\-validation stratified jointly by diagnosis and source study\. NineCCvalues logarithmically spaced from10−210^\{\-2\}to10110^\{1\}andl1​\_​ratio∈\{0\.25,0\.50,0\.75,1\.00\}\\mathrm\{l1\\\_ratio\}\\in\\\{0\.25,0\.50,0\.75,1\.00\\\}were evaluated using mean inner ROC AUC, with effective ties favoring stronger regularization\.

Using the selected hyperparameters, feature stability was estimated from 100 stratified subsamples containing 75% of the outer\-training participants, following the general principle that subsampling\-based stability can make variable selection less dependent on a single fitted sample\[[39](https://arxiv.org/html/2609.22956#bib.bib39)\]\. A candidate was retained when its elastic\-net coefficient was nonzero in at least 60% of subsamples\. If no feature met that threshold, the most stable candidate was retained\. Redundancy was then pruned using training\-only absolute Spearman correlation: when two retained descriptors had\|ρ\|≥0\.85\|\\rho\|\\geq 0\.85, the less stable member was removed\. Remaining candidates were ordered by stability and at most six entered the final class\-balanced L2\-regularized logistic regression classifier \(C=1C=1,liblinear\)\. No outer\-test participant contributed to imputation, scaling, hyperparameter selection, stability estimation, redundancy pruning, feature ordering, or fitting\.

Performance was estimated using 20 repetitions of five\-fold participant\-level cross\-validation \(100 outer folds\)\. Outer partitions were stratified jointly by diagnosis and source study, and the exact same outer splits were used for every representation\. Each participant therefore received one out\-of\-fold probability per repetition; the 20 probabilities were averaged to obtain a final participant\-level prediction\. ROC AUC was the primary metric\. Balanced accuracy, sensitivity, specificity, and Brier score were secondary metrics, with a fixed probability threshold of 0\.5 for threshold\-based measures\.

### 3\.4Statistical Analysis and Robustness

#### 3\.4\.1Statistical analysis

AUC confidence intervals were obtained from 5,000 participant\-level bootstrap resamples stratified by diagnosis\. The three direct literature comparisons—proposed vs Alam\-derived COP4, Jin\-derived COP7, and Tong\-derived COP18—used matched participant\-level bootstrap resampling within source\-study\-by\-diagnosis strata\. Two\-sidedppvalues used a plus\-one correction\. Family\-wise error across this three\-comparison primary literature family was controlled using Holm’s sequentially rejective procedure\[[40](https://arxiv.org/html/2609.22956#bib.bib40)\]\.

The nested contrast between the complete and compact representations, comparisons involving Non\-AP\-COP25, the literature\-derived COP union, and all remaining comparisons were treated as secondary analyses and were not included in the primary multiplicity family\. Comparisons involving Non\-AP\-COP25 used the same matched participant\-level bootstrap procedure within source\-study\-by\-diagnosis strata\.

For stance\-window characterization, Hedges’gg, bootstrap confidence intervals, direction\-agnostic univariable AUC, and outer\-fold retention frequencies were examined\. Additional sensitivity analyses assessed the coordinate\-origin dependence of the relative asymmetry metric, predictive information beyond walking speed, feature\-budget and final\-cap compactness, simulated sensor gain variation and dropout, classifier family, and leave\-one\-source\-study\-out performance\. These analyses were used to probe robustness and interpretation rather than to redefine the proposed 10\-candidate representation\.

#### 3\.4\.2Secondary robustness analyses

Feature\-budget analysis truncated the training\-derived stability ordering of the complete representation at maximum budgetsk∈\{1,…,6\}k\\in\\\{1,\\dots,6\\\}and refitted the final model, so the analysis evaluates at mostkkdescriptors rather than independent exact\-kkselection;k=6k=6reproduces the primary complete\-representation result by construction\. Final\-cap sensitivity separately reran fold\-specific stability selection with maximum final\-feature caps of 4, 6, 8, 10, and 12\. Classifier\-family sensitivity evaluated the fold\-specific selected descriptors with radial\-basis\-function support vector machine, random forest, and histogram gradient boosting alongside logistic regression\. Sensor perturbation applied independent multiplicative gains with mean 1 and standard deviation 0\.05, 0\.10, or 0\.20 to the 16 individual plantar sensor channels before COP extraction, together with random single\- and two\-sensor dropout, using five random realizations per condition; models were trained only on clean outer\-training data and evaluated on perturbed outer\-test features\. Source\-study robustness held out Ga, Ju, and Si in turn, with all feature development restricted to the remaining cohorts, and was applied to both the complete and the compact representation\.

## 4Results

### 4\.1Cohort and feature completeness

All 165 participants contributed complete values for AP\-COP10, Non\-AP\-COP25, Full35, and the three direct literature\-derived COP representations\. No missing feature cells were present in these representations\. Within Full35, every candidate had at least 23 distinct observed values, providing a basic check against degenerate or nearly constant engineered features\.

### 4\.2Representation performance

The complete 35\-candidate engineered representation \(Full35\) achieved participant\-level ROC AUC 0\.908 \(95% CI 0\.862–0\.948\), balanced accuracy 0\.817, sensitivity 0\.828, specificity 0\.806, and Brier score 0\.125\. The compact 10\-candidate stance\-indexed AP\-COP representation \(AP\-COP10\) achieved AUC 0\.894 \(0\.843–0\.937\), balanced accuracy 0\.828, sensitivity 0\.796, specificity 0\.861, and Brier score 0\.135 \(Table[3](https://arxiv.org/html/2609.22956#S4.T3)\)\. Neither representation dominated across all metrics: Full35 gave the highest AUC and the lowest Brier score, whereas AP\-COP10 gave higher fixed\-threshold balanced accuracy and specificity\.

In the secondary nested representation analysis, adding the complementary 25 non\-AP\-COP descriptors to AP\-COP10 increased AUC by 0\.013, from 0\.894 to 0\.908 \(95% CI−0\.015\-0\.015to 0\.043;p=0\.361p=0\.361\)\. Non\-AP\-COP25 evaluated independently achieved AUC 0\.856 \(0\.796–0\.910\), balanced accuracy 0\.751, sensitivity 0\.753, specificity 0\.750, and Brier score 0\.154\. Adding AP\-COP10 to Non\-AP\-COP25 increased AUC by 0\.051 \(95% CI 0\.015–0\.089;p=0\.0028p=0\.0028\)\. AP\-COP10 itself was numerically higher than Non\-AP\-COP25 by 0\.038 AUC \(95% CI−0\.011\-0\.011to 0\.090;p=0\.134p=0\.134\), although this direct difference was not statistically supported\. Thus, removing AP\-COP10 from Full35 produced a supported reduction in discrimination, whereas adding the complementary descriptors to AP\-COP10 produced only a small, unsupported increase\.

Figure[3](https://arxiv.org/html/2609.22956#S4.F3)places these results alongside the literature\-derived comparators\.

Figure 3:Participant\-level ROC AUC across the main engineered and literature\-derived representation spaces under the same fully nested evaluation\. Error bars show 95% bootstrap confidence intervals\.Table 3:Participant\-level performance under repeated fully nested validation\.HHolm\-adjusted across the three direct literature\-derived COP comparisons\.SSecondary nested representation comparison; not included in the Holm\-adjusted literature\-comparison family\.

### 4\.3Controlled literature\-grounded comparisons

Under the identical pipeline, Alam\-derived COP4 achieved AUC 0\.809 \(0\.742–0\.871\), Jin\-derived COP7 achieved 0\.784 \(0\.714–0\.852\), and Tong\-derived COP18 achieved 0\.746 \(0\.665–0\.821\)\. AP\-COP10 achieved higher AUC, balanced accuracy, and specificity, and a lower Brier score than all three literature\-derived representations \(Table[3](https://arxiv.org/html/2609.22956#S4.T3)\)\.

The paired gain over Alam\-derived COP4 wasΔ\\DeltaAUC=0\.085=0\.085\(95% CI 0\.037–0\.135\), over Jin\-derived COP7 it was 0\.110 \(0\.050–0\.171\), and over Tong\-derived COP18 it was 0\.148 \(0\.084–0\.213\)\. Each raw bootstrapppvalue was 0\.0004; after Holm correction across the three direct literature comparisons, all remained significant atpHolm=0\.0012p\_\{\\mathrm\{Holm\}\}=0\.0012\.

Additional sensitivity analyses indicated that these gaps did not depend on narrow encoding choices\. A bilateral eight\-candidate extension of the Alam descriptor types achieved AUC 0\.828 \(0\.762–0\.889\), with a paired difference of 0\.066 \(0\.025–0\.110;p=0\.0024p=0\.0024\)\. For the Tong family, the bilateral\-summary Tong9 representation achieved AUC 0\.767, the AP\-focused Tong8 representation 0\.758, and the axis\-expanded Tong30 sensitivity 0\.741; giving that descriptor family fewer, more AP\-focused, or more axis\-explicit candidates did not approach 0\.894\. The 11\-candidate literature COP union achieved AUC 0\.828 \(0\.764–0\.887\), 0\.066 below AP\-COP10 \(0\.022–0\.110;p=0\.0024p=0\.0024\)\.

### 4\.4Source\-study holdout robustness

Leave\-one\-source\-study\-out evaluation removed each acquisition protocol entirely from model development in turn\. AP\-COP10 achieved pooled AUC 0\.907 \(0\.860–0\.947\), with 0\.837 \(0\.713–0\.939\) when Ga was held out, 0\.937 \(0\.865–0\.988\) for Ju, and 0\.946 \(0\.890–0\.986\) for Si\. Full35 achieved pooled AUC 0\.872 \(0\.813–0\.921\), with 0\.807 \(0\.670–0\.920\) for Ga, 0\.932 \(0\.859–0\.983\) for Ju, and 0\.867 \(0\.767–0\.948\) for Si \(Figure[4](https://arxiv.org/html/2609.22956#S4.F4)\)\.

AP\-COP10 had higher point estimates than Full35 in every held\-out protocol and in the pooled estimate\. Its pooled holdout AUC \(0\.907\) was slightly above its repeated within\-cohort estimate \(0\.894\), whereas Full35 declined from 0\.908 to 0\.872 under the same procedure\.

Figure 4:Leave\-one\-source\-study\-out robustness within GaitPDB\. ROC AUC and 95% bootstrap confidence intervals are shown for Full35 and AP\-COP10 when each source study is excluded from model development\.
### 4\.5External context: comparison with Jin’s gait\-only model

As external context for the source\-study holdout results, Table[4](https://arxiv.org/html/2609.22956#S4.T4)places the AP\-COP10 per\-protocol holdout AUCs alongside the gait\-only sensitivity model reported by Jin\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]\. AP\-COP10 remained between 0\.837 and 0\.946 across the three held\-out protocols \(mean 0\.907\), while Jin’s gait\-only model ranged from 0\.500 to 0\.845 \(mean 0\.726\)\. The comparison is descriptive rather than statistically paired: Jin’s evaluation used a single 75/25 holdout split rather than repeated nested cross\-validation, and the gait\-only feature set retains non\-COP demographic and contextual variables rather than being restricted to COP descriptors alone\.

Table 4:Cross\-protocol leave\-one\-source\-study\-out holdout AUC for the proposed AP\-COP10 representation and the gait\-only sensitivity model reported by Jin\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]\.aRetains non\-clinical demographic/contextual variables \(age, weight, height, walking speed, trial index\) alongside gait\-derived features; not restricted to COP descriptors\.

### 4\.6Information across normalized stance

The strongest marginal PD–control differences occurred in early and early\-mid stance\. AP\-COP position at 25–35% showed Hedges’g=1\.303g=1\.303and direction\-agnostic univariable AUC 0\.828, while position at 5–15% showedg=1\.217g=1\.217and univariable AUC 0\.810\. Bilateral asymmetry at 5–15% showedg=0\.842g=0\.842\. AP\-COP position at 65–75% showed no statistically supported marginal separation \(g=−0\.198g=\-0\.198, 95% CI−0\.490\-0\.490to 0\.095;p=0\.192p=0\.192\) yet was retained in 96% of outer folds within AP\-COP10, and deleting it reduced AUC by 0\.019 \(95% CI−0\.000\-0\.000to 0\.041;p=0\.053p=0\.053\)\.

Within AP\-COP10, outer\-fold retention frequencies were 100% for 5–15% asymmetry, 100% for 5–15% position, 100% for 25–35% position, 96% for 65–75% position, 72% for 65–75% asymmetry, and 60% for 25–35% asymmetry\. Position at 45–55% was retained in 29% of folds, while the remaining late\-window candidates were selected less frequently\. Figure[5](https://arxiv.org/html/2609.22956#S4.F5)summarizes marginal effects and stand\-alone retention\.

Figure 5:AP\-COP information across normalized stance\. \(a\) Hedges’ggwith 95% confidence intervals for AP\-COP position and bilateral asymmetry\. \(b\) Outer\-fold retention frequencies within the stand\-alone AP\-COP10 representation\.Figure 6:Feature competition within the complete 35\-candidate engineered representation\. Bars show final outer\-fold retention after training\-only stability selection, redundancy pruning, and the six\-feature cap\. Stance\-indexed AP\-COP descriptors are highlighted\.The literature\-derived selections provide a face\-validity comparison\. In Alam\-derived COP4, AP\-COP SD and AP\-COP mean were retained in every outer fold, while the ML quantities were less stable\. In Jin\-derived COP7, left AP\-COP SD was retained in every fold and right AP\-COP SD in 98%, while the remaining path and ML descriptors were rarely retained\. In Tong\-derived COP18, AP\-coordinate and AP\-entropy/velocity quantities were among the most stable\. Across distinct representation families, the AP direction therefore repeatedly emerged as informative; AP\-COP10 differs by preserving AP\-COP*location across stance*rather than compressing it primarily into whole\-trajectory summaries\.

Table 5:Outer\-fold retention of the 10 stance\-indexed AP\-COP descriptors under competition within Full35, with the most frequently retained descriptors from other families for context\.
### 4\.7Feature competition within the complete representation

Placing all 10 stance\-indexed descriptors in the same candidate pool as 25 descriptors from five other biomechanical families allows direct competition under training\-only selection\. Final models retained a mean of 5\.92 descriptors per outer fold \(median 6\), with mean pairwise Jaccard similarity of 0\.62 between fold\-specific selections \(median 0\.71\)\.

The stance\-indexed AP\-COP family was represented in every outer\-fold final model, contributing a mean of 3\.73 of the 5\.92 selected descriptors \(Table[5](https://arxiv.org/html/2609.22956#S4.T5)\)\. That contribution was highly concentrated rather than distributed across the family\. Three descriptors dominated: bilateral asymmetry at 5–15% \(99% retention\), position at 25–35% \(99%\), and position at 5–15% \(90%\)\. Asymmetry at 25–35% was retained in 40% of folds and position at 65–75% in 23%, while the remaining five stance\-indexed descriptors were retained in at most 15% of folds\. Among descriptors outside the AP\-COP family, double\-support proportion was retained in 90% of folds and step\-interval irregularity in 72%; the six broader COP\-rollover descriptors were retained in at most 31% of folds \(AP range\), with COP path length at 5% and median COP speed at 3%\.

The retention profile for position at 65–75% differs markedly between the two settings: 96% within the stand\-alone AP\-COP10 representation and 23% under Full35 competition, displaced once double\-support and temporal\-rhythm descriptors enter the same pool \(Figure[6](https://arxiv.org/html/2609.22956#S4.F6)\)\.

### 4\.8Attribution and speed sensitivity

Secondary attribution analyses examined the relative contribution of position and asymmetry descriptors within AP\-COP10\. A five\-position\-only representation achieved AUC 0\.857, whereas the five asymmetry descriptors alone achieved 0\.746\. Adding only the early 5–15% asymmetry descriptor to the five position features increased AUC to 0\.900\. Attribution therefore points to broad stance\-indexed position coverage as the primary source of discriminative information, with early\-stance asymmetry contributing complementary value beyond position alone\. This pattern is consistent with the retention profile observed under Full35 competition, where the three most frequently retained stance\-indexed descriptors were early\-stance asymmetry and the 25–35% and 5–15% positions\.

Walking speed alone achieved AUC 0\.772, and age with speed 0\.767\. Adding speed to AP\-COP10 increased AUC to 0\.919, and adding both age and speed yielded 0\.922\.

The relative asymmetry index is coordinate\-origin dependent\. Replacing it with the absolute bilateral AP\-COP difference produced AUC 0\.896, and the AP\-range\-normalized bilateral difference produced 0\.894\.

### 4\.9Compactness, classifier family, and sensor sensitivity

Within Full35, AUC rose from 0\.802 with a one\-descriptor maximum to 0\.865 with two, 0\.885 with three, 0\.901 with four, 0\.906 with five, and 0\.908 with six\. The paired gain of the six\-descriptor budget over three descriptors was 0\.022 \(0\.002–0\.045;p=0\.033p=0\.033\), whereas its gains over four and five descriptors were not statistically supported \(0\.006,p=0\.264p=0\.264; 0\.001,p=0\.699p=0\.699\)\. Rerunning fold\-specific selection with maximum final\-feature caps of 4, 6, 8, 10, and 12 produced AUCs of 0\.901, 0\.908, 0\.908, 0\.905, and 0\.903; none of the larger caps improved on six \(cap 6 minus cap 8:−0\.001\-0\.001,p=0\.864p=0\.864; minus cap 10: 0\.002,p=0\.543p=0\.543; minus cap 12: 0\.005,p=0\.211p=0\.211\) \(Supplementary Table S8\)\.

Classifier\-family sensitivity on the same fold\-specific descriptors produced AUC 0\.913 for histogram gradient boosting, 0\.908 for logistic regression, 0\.899 for RBF\-SVM, and 0\.898 for random forest\. Calibration slopes were 1\.01 for logistic regression and 0\.73 for histogram gradient boosting \(Supplementary Table S9\)\.

Simulated sensor\-gain variation produced graded degradation: mean AUC fell from 0\.908 on clean input to 0\.907 at 5% gain variation, 0\.902 at 10%, and 0\.881 at 20%\. Random single\-sensor dropout reduced mean AUC to 0\.858 and two\-sensor dropout to 0\.802\. Under 10% gain variation, the five position descriptors retained median Spearman agreement ranging from 0\.985 to 0\.996 with their clean values, whereas the five asymmetry descriptors ranged from 0\.865 to 0\.921\. Under single\-sensor dropout, position descriptors ranged from 0\.831 to 0\.966, while asymmetry descriptors ranged from 0\.544 to 0\.618 \(Supplementary Figure S1; Supplementary Table S10\)\.

## 5Discussion

### 5\.1Principal finding: representation matters

The central result is a controlled representation effect\. When the classifier, outer splits, feature\-selection procedure, and participant cohort were held constant, AP\-COP10 provided higher discrimination than three distinct COP descriptor families derived from prior GaitPDB studies\. The gain was 0\.085 AUC over Alam\-derived global coordinate statistics, 0\.110 over Jin\-derived dispersion/path/symmetry descriptors, and 0\.148 over the primary Tong\-derived dynamic/nonlinear descriptor set; all three differences remained significant after Holm correction\. The result does not rely on comparing our cross\-validation AUC with the published headline accuracy of another paper\. It instead addresses a narrower and more defensible question: how much predictive information is retained by different COP representations when evaluated under the same machine\-learning procedure\.

This distinction matters because the source studies address different scientific questions\. Alam et al\. combined COP with temporal and force features\[[22](https://arxiv.org/html/2609.22956#bib.bib22)\]\. Jin’s full model included clinical severity and demographic variables, and even the gait\-only sensitivity included non\-COP quantities such as walking speed\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]\. Tong et al\. addressed multiclass severity classification with topological processing and oversampling\[[24](https://arxiv.org/html/2609.22956#bib.bib24)\]\. Their reported performance therefore cannot be ranked directly against the present binary participant\-level experiment\. The harmonized reimplementation isolates the COP representation itself\.

### 5\.2Compactness within a complete engineered feature space

The nested representation comparisons strengthen the compactness result\. Full35 achieved AUC 0\.908, AP\-COP10 achieved 0\.894, and Non\-AP\-COP25 achieved 0\.856\. Adding the 25 non\-AP\-COP descriptors to AP\-COP10 increased AUC by only 0\.013 \(95% CI−0\.015\-0\.015to 0\.043;p=0\.361p=0\.361\)\. In the reverse comparison, adding AP\-COP10 to Non\-AP\-COP25 increased AUC by 0\.051 \(95% CI 0\.015–0\.089;p=0\.0028p=0\.0028\)\. AP\-COP10 was also numerically higher than Non\-AP\-COP25 by 0\.038 AUC, although that direct difference was not statistically supported \(p=0\.134p=0\.134\)\. The results therefore do not indicate that the complementary 25 descriptors contain no predictive information; their stand\-alone AUC of 0\.856 clearly shows that they do\. Rather, they suggest substantial overlap between the information captured by AP\-COP10 and the broader engineered descriptors, while the supported loss after removing AP\-COP10 indicates that part of the stance\-indexed information is not readily recovered by the complementary feature bank\. No equivalence margin was prespecified, so the Full35–AP\-COP10 null contrast remains a null result rather than evidence of equivalence\.

The feature\-budget, selection, and cap analyses reinforce this interpretation\. Non\-AP\-COP25 selected a mean of 5\.91 descriptors per outer fold \(median 6\), indicating that its lower AUC was not caused by systematically sparse final models\. Within Full35, stance\-indexed AP\-COP appeared in every final model and contributed a mean of 3\.73 of the 5\.92 retained descriptors\. Four to six retained descriptors recovered nearly all available Full35 discrimination, and allowing 8, 10, or 12 final descriptors produced no supported improvement over six\. Together, these results indicate that substantial discriminative information in the broad engineered gait bank can be represented using a small number of interpretable descriptors, with stance\-indexed AP\-COP accounting for a large share of the selected features\.

The classifier\-family analysis points in the same direction\. Histogram gradient boosting produced only a small numerical AUC increase over logistic regression \(0\.913 versus 0\.908\), while RBF\-SVM and random forest achieved 0\.899 and 0\.898, respectively\. Calibration favored the linear reference, with a slope of 1\.01 for logistic regression compared with 0\.73 for histogram gradient boosting\. This should not be interpreted as evidence against deep or graph\-based gait models, which have demonstrated strong VGRF discrimination\[[30](https://arxiv.org/html/2609.22956#bib.bib30),[31](https://arxiv.org/html/2609.22956#bib.bib31),[32](https://arxiv.org/html/2609.22956#bib.bib32)\]\. Rather, for this controlled representation\-comparison task, careful feature construction concentrated substantial predictive information without requiring a highly flexible final classifier\.

### 5\.3Which stance locations survive competition

Under nested competition within Full35, the stance\-indexed family appeared in every final model, but its contribution was concentrated in three descriptors: early\-stance asymmetry, position at 25–35%, and position at 5–15%\. Position at 25–35% was retained in 99% of outer folds, ranking above every temporal, support, loading, and broader\-COP descriptor in the candidate pool\. This provides strong evidence that stance\-localized AP\-COP position retains information that is not fully displaced by the other engineered descriptors with which it competes\. The complete outer\-fold retention profiles are provided in Supplementary Tables S4–S5\.

The remaining seven stance\-indexed descriptors were selected less often under full competition, and one case is particularly informative\. Position at 65–75% was retained in 96% of folds within AP\-COP10 but only 23% within Full35\. Removing it from AP\-COP10 reduced AUC by 0\.019 \(95% CI−0\.000\-0\.000to 0\.041;p=0\.053p=0\.053\)\. This descriptor also showed no statistically supported univariable separation on its own \(Hedges’g=−0\.198g=\-0\.198\), illustrating that marginal effect size and multivariable usefulness are not necessarily equivalent\. A plausible interpretation is that the descriptor contributes conditional information about later stance when only AP\-COP descriptors are available, whereas other temporal or support descriptors may capture overlapping information once they enter the broader candidate pool\. This also cautions against interpreting stand\-alone retention frequency as evidence of intrinsic descriptor importance\.

The broader COP\-rollover descriptors behaved differently from the localized positions\. AP range was retained in 31% of folds, whereas path length, median speed, speed variability, monotonicity, and early slope were retained much less frequently under Full35 competition\. This pattern is consistent with the controlled literature comparisons, although correlation and competition among candidates mean that retention frequencies should not be interpreted as independent evidence that whole\-trajectory summaries are inherently less informative\.

### 5\.4From global AP\-COP summaries to stance\-indexed position

The literature\-derived results show substantial agreement rather than contradiction\. Across the Alam\-, Jin\-, and Tong\-derived feature sets, AP\-direction descriptors were repeatedly more consistently informative than many ML or path\-based alternatives\. Jin identified reduced AP\-COP dispersion as one of the strongest biomechanical effects in GaitPDB\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\], while Tong reported that COP quantities in the walking direction were important for severity differentiation\[[24](https://arxiv.org/html/2609.22956#bib.bib24)\]\. The present results support the same broad biomechanical direction but extend it representationally: instead of summarizing only how much AP\-COP varies, how long its path is, or how irregular its derivatives are, AP\-COP10 preserves*where*the AP load center is at multiple fixed locations across normalized stance\.

Independent waveform evidence from Jin also supports the broader premise that plantar\-force differences can be localized rather than uniform across stance\. Jin’s statistical\-parametric analysis of VGRF—a different signal from COP—identified significant PD–control clusters in early stance \(approximately 0–13% on the left and 6–12% on the right\), midstance on the right \(approximately 34–55%\), and late stance \(approximately 90–96%\)\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]\. These intervals should not be interpreted as validating the present COP windows, but they independently reinforce the rationale for retaining stance location rather than relying only on whole\-trajectory scalars\.

The present study does not claim that examining COP across stance is itself novel\. COP progression has long been analyzed as a trajectory, across stance conditions, and within stance subregions\[[9](https://arxiv.org/html/2609.22956#bib.bib9),[10](https://arxiv.org/html/2609.22956#bib.bib10),[14](https://arxiv.org/html/2609.22956#bib.bib14),[15](https://arxiv.org/html/2609.22956#bib.bib15),[13](https://arxiv.org/html/2609.22956#bib.bib13)\]\. Recent plantar\-pressure studies have likewise explored regional and multidomain representations for PD\[[20](https://arxiv.org/html/2609.22956#bib.bib20),[21](https://arxiv.org/html/2609.22956#bib.bib21)\]\. The contribution here is the compact five\-window AP\-COP encoding, its controlled comparison with multiple GaitPDB\-derived COP summary families, and its behavior when placed in direct competition with a broader engineered feature space\.

### 5\.5Source\-protocol robustness

As shown in Section[4\.5](https://arxiv.org/html/2609.22956#S4.SS5), Jin’s gait\-only sensitivity model\[[23](https://arxiv.org/html/2609.22956#bib.bib23)\]reached AUC 0\.500 when the Ju protocol was held out, despite retaining non\-COP demographic and contextual variables alongside gait\-derived features\. In the present study, AP\-COP10 remained between 0\.837 and 0\.946 across the three held\-out source studies, with pooled AUC 0\.907, and its point estimate was higher than Full35 in every holdout\. Full35 declined from AUC 0\.908 under repeated within\-resource validation to 0\.872 under source\-study holdout, whereas AP\-COP10 changed from 0\.894 to a pooled holdout AUC of 0\.907\.

One possible interpretation is that a larger candidate pool provides more opportunity to select descriptors whose behavior is associated with source\-study characteristics, whereas restricting the representation to one signal family may limit that exposure\. The present results do not establish this mechanism, however, and the confidence intervals overlap\. Moreover, Ga, Ju, and Si are all contained within GaitPDB and share the same general sensing platform and sensor geometry\. Leave\-one\-source\-study\- out evaluation therefore measures robustness to acquisition protocol within one database and should not be interpreted as external validation\. Independent cohorts and different sensing layouts remain necessary\.

### 5\.6Asymmetry, walking speed, and measurement robustness

Bilateral asymmetry is biologically plausible in PD because motor manifestations are often lateralized, and postural and gait asymmetry have been reported previously\[[41](https://arxiv.org/html/2609.22956#bib.bib41),[42](https://arxiv.org/html/2609.22956#bib.bib42),[11](https://arxiv.org/html/2609.22956#bib.bib11)\]\. In AP\-COP10, asymmetry is aligned to the same stance windows as position\. Early\-stance asymmetry was retained in 99% of Full35 outer folds and provided complementary information when added to the five position features, whereas the five asymmetry descriptors alone were substantially weaker than the position\-only representation\. The relative asymmetry index also depends on coordinate origin\. Origin\-invariant variants produced nearly identical AUCs, supporting the overall representation conclusion without implying that the relative asymmetry index itself is an origin\-invariant biomechanical measure\.

Walking speed is an important interpretive issue because COP progression changes with speed\[[14](https://arxiv.org/html/2609.22956#bib.bib14)\], and PD gait rhythmicity is also speed dependent\[[43](https://arxiv.org/html/2609.22956#bib.bib43)\]\. Speed alone achieved AUC 0\.772, whereas AP\-COP10 combined with speed achieved 0\.919\. These results indicate that AP\-COP10 contains predictive information beyond that provided by walking speed alone\. They do not establish causal independence from speed, age, disease severity, or other participant characteristics, and the representation should not be interpreted as a pure disease mechanism\.

The sensor perturbation analysis provides a separate measurement perspective\. Under single\-sensor dropout, AP\-COP position descriptors were more stable overall, with median Spearman agreement ranging from 0\.831 to 0\.966, than the asymmetry descriptors, which ranged from 0\.544 to 0\.618\. The terminal\-stance position descriptor was more sensitive than the other position features\. Early\-stance asymmetry remained important predictively, being retained in 99% of Full35 outer folds, but its dropout stability was onlyρ=0\.618\\rho=0\.618\. The lowest asymmetry stability occurred at 65–75% stance \(ρ=0\.544\\rho=0\.544\)\. Predictive usefulness and measurement robustness are therefore distinct properties, particularly for bilateral asymmetry features\. These simulations held contact detection and stance segmentation fixed and used five random realizations per condition; they should be interpreted as a first\-order robustness check rather than device\-failure testing\.

### 5\.7Limitations

Several limitations define the scope of the findings\. First, all participants were drawn from one historical public database and one plantar\-sensor platform\. Although GaitPDB contains three source studies, leave\-one\-source\-study\-out evaluation remains internal to the same resource and does not constitute external validation\. Only one usual\-walking recording was retained per participant, so test–retest reliability was not assessed\. Independent cohorts, repeated measurements, and different sensing platforms are therefore needed to establish broader generalizability\[[5](https://arxiv.org/html/2609.22956#bib.bib5),[7](https://arxiv.org/html/2609.22956#bib.bib7)\]\.

Second, participant characteristics may contribute to the observed discrimination\. Walking speed alone was predictive, and the present speed and age analyses assess predictive information rather than causal covariate adjustment\. Effects of walking speed, age, disease severity, medication state, comorbidities, and other cohort characteristics therefore cannot be excluded\. The reported representation should consequently not be interpreted as isolating a PD\-specific biomechanical mechanism\.

Third, AP\-COP was reconstructed as a sensor\-coordinate force\-weighted load\-center proxy tied to the GaitPDB insole geometry rather than as an anatomical COP distance from a continuous pressure field\. The five stance windows were fixed before the reported classification analyses, but their optimal locations and widths have not been established\. Transfer to other sensor geometries or alternative stance\-window definitions may therefore require additional validation\.

Finally, the literature\-derived comparators are harmonized reimplementations of reproducible COP descriptor definitions rather than exact replications of the complete published pipelines, and Full35 and Non\-AP\-COP25 represent finite engineered feature banks rather than all possible gait representations\. The supported loss after removing AP\-COP10 therefore applies to the engineered descriptors tested here and does not exclude additional information in richer waveform\-based or learned representations\. Sensor perturbations were also simulated rather than tested on physically degraded hardware\. More broadly, the task is established PD versus healthy control classification and should be interpreted as an evaluation of representation quality rather than as validation of a clinical diagnostic system\.

## 6Conclusion

This study demonstrates that how plantar\-force signals are represented can substantially influence the information available for machine\-learning analysis of Parkinsonian gait\. Preserving anterior–posterior COP position at corresponding locations across normalized stance produced a compact representation that consistently performed strongly against conventional COP summaries and remained informative when placed in competition with a broader engineered gait feature space\. The complementary representation analyses further indicate that the information carried by stance\-indexed AP\-COP is not readily recovered when these descriptors are removed, even though the remaining temporal, support, asymmetry, COP\-rollover, and loading features retain substantial discriminative information\.

The findings therefore support a shift from treating COP primarily as a trajectory to be summarized globally toward preserving*where*its informative behavior occurs during stance\. In this representation, AP\-COP position provides the main discriminative structure, with bilateral asymmetry contributing complementary information, particularly in early stance\. Overall, AP\-COP10 provides a compact and interpretable way to retain localized gait information without relying on a large engineered feature bank\. Validation in independent cohorts and different sensing platforms is the necessary next step before broader clinical or translational conclusions can be drawn\.

## Data and code availability

The GaitPDB dataset is publicly available through PhysioNet\[[8](https://arxiv.org/html/2609.22956#bib.bib8)\]\. The analysis notebooks and derived result archives used for the complete engineered representation can be made available from the authors upon reasonable request\. The reported analyses were executed with Python 3\.10\.19, NumPy 1\.26\.4, and pandas 2\.3\.3 on Linux\. Participant\-level predictions, feature\-selection summaries, paired comparisons, and supporting numerical outputs are retained by the authors\.

## Ethics statement

This study is a secondary analysis of deidentified, publicly available data\. No new participants were recruited and no intervention was performed\. Ethics approval and informed\-consent procedures for the original data collections are described in the source\-study publications and database documentation\.

## CRediT authorship contribution statement

The authors’ contributions are described according to the Contributor Roles Taxonomy \(CRediT\):

Md\. Sifat:Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing – original draft, Writing – review & editing\.

Sania Akter:Data curation, Investigation, Validation, Writing – review & editing\.

Akif Islam:Methodology, Validation, Resources, Writing – review & editing\.

Md\. Ekramul Hamid:Supervision, Project administration, Writing – review & editing\.

All authors have read and approved the final version of the manuscript and agree to be accountable for all aspects of the work\.

## Supplementary Material

## S1Scope and reproducibility

This supplement has two purposes\. First, it records the exact candidate\-feature identifiers used in the final analyses and documents the literature\-derived COP reference sets\. Second, it provides supporting analyses that probe compactness, selection stability, classifier dependence, sensor perturbation, asymmetry normalization, covariate sensitivity, and source\-study robustness\. The Holm\-adjusted literature\-comparison family comprises AP\-COP10 versus the three literature\-derived COP representations\. The AP\-COP10–Full35 and Non\-AP\-COP25 contrasts are secondary nested representation analyses and were not included in that Holm\-adjusted family\. All supporting model analyses retain the same separation between model development and outer\-fold performance estimation used in the main manuscript\[[36](https://arxiv.org/html/2609.22956#bib.bib36),[37](https://arxiv.org/html/2609.22956#bib.bib37)\]\.

## S2Feature dictionary

### S2\.1Proposed stance\-indexed AP\-COP10

The proposed representation contains five bilateral AP\-COP position descriptors and five bilateral asymmetry descriptors at fixed normalized\-stance windows

W=\{5​–​15,25​–​35,45​–​55,65​–​75,85​–​95\}%\.W=\\\{5\\text\{\-\-\}15,\\;25\\text\{\-\-\}35,\\;45\\text\{\-\-\}55,\\;65\\text\{\-\-\}75,\\;85\\text\{\-\-\}95\\\}\\%\.
The identifiers below are the exact feature\-column names used in the final analysis\.

Table S1:Exact feature identifiers for AP\-COP10\.For each window, stance\-level AP\-COP is averaged within the window; repeated stances are summarized separately for the two feet by their median; bilateral position is the mean of the two side\-specific summaries; and bilateral asymmetry is computed using the primary relative index defined in the main manuscript\.

Table S2:Complete Full35 feature dictionary grouped by descriptor family\.Table S3:Literature\-derived COP reproduction record\.

## S3Literature\-derived COP feature reproduction

The literature\-derived sets are harmonized reimplementations of published COP descriptor definitions, not reproductions of the original end\-to\-end classifiers\. The common participant\-level aggregation, preprocessing, nested feature selection, and final classifier are those of the main manuscript\.

An 11\-candidate Alam–Jin union was also assembled as a secondary comparison and was not included in the Holm\-adjusted literature\-comparison family\. Additional encoding sensitivities were evaluated for the Alam and Tong descriptor families\. The bilateral Alam8 extension achieved AUC 0\.828 \(95% CI 0\.762–0\.889\), with AP\-COP10 higher by 0\.066 AUC \(0\.025–0\.110;p=0\.0024p=0\.0024\)\. Tong9, Tong8, and Tong30 achieved AUCs of 0\.767, 0\.758, and 0\.741, respectively\. The 11\-candidate literature COP union achieved AUC 0\.828 \(0\.764–0\.887\), with AP\-COP10 higher by 0\.066 \(0\.022–0\.110;p=0\.0024p=0\.0024\)\. These were secondary sensitivity comparisons and were not part of the Holm\-adjusted three\-comparison family\.

## S4Selection stability and feature\-family competition

Across 100 Full35 outer folds, the mean final model size was 5\.92 descriptors and the median was 6\. Pairwise Jaccard similarity had mean 0\.620 and median 0\.714\. At least one stance\-indexed AP\-COP descriptor appeared in every outer\-fold final model, with a mean of 3\.73 AP\-COP descriptors selected per fold\. The descriptor\-level retention pattern is summarized in Table[S5](https://arxiv.org/html/2609.22956#S4.T5a), with early\-stance asymmetry and AP\-COP position at 5–35% among the most consistently selected candidates\.

Within AP\-COP10 evaluated alone, outer\-fold retention was 100% for position at 5–15%, 100% for position at 25–35%, 29% for position at 45–55%, 96% for position at 65–75%, and 8% for position at 85–95%\. Corresponding asymmetry retention was 100%, 60%, 9%, 72%, and 5%\. Position at 65–75% had weak marginal separation \(g=−0\.198g=\-0\.198, 95% CI−0\.490\-0\.490to 0\.095;p=0\.192p=0\.192\), yet deleting it from AP\-COP10 reduced AUC by 0\.019 \(95% CI−0\.000\-0\.000to 0\.041;p=0\.053p=0\.053\)\. These results illustrate that marginal separation and multivariable retention are not identical\.

Table S4:Feature\-family representation across Full35 final models\.Table S5:Outer\-fold retention of the 10 stance\-indexed AP\-COP descriptors within Full35 final models\.
## S5Complementary Non\-AP\-COP25 representation

Non\-AP\-COP25 was defined exactly as Full35 minus the 10 stance\-indexed AP\-COP candidates\. It therefore contains the six temporal/rhythm, four dynamic\-support, four non\-AP\-COP bilateral\-asymmetry, six broader COP\-rollover, and five vertical\-loading descriptors listed in Table[S2](https://arxiv.org/html/2609.22956#S2.T2)\. This complementary representation used the same 20 repetitions×\\times5 outer folds, five\-fold inner tuning, 100 stability\-selection subsamples, 0\.60 stability threshold,\|ρ\|≥0\.85\|\\rho\|\\geq 0\.85redundancy pruning, six\-feature maximum, final class\-balanced L2 logistic regression, and participant\-level probability averaging used for the primary engineered representations\.

Table S6:Performance of the complementary Non\-AP\-COP25 representation under the common nested evaluation\.Matched participant\-level bootstrap comparisons gave Full35 minus Non\-AP\-COP25Δ\\DeltaAUC=0\.051=0\.051\(95% CI 0\.015–0\.089;p=0\.0028p=0\.0028\), AP\-COP10 minus Non\-AP\-COP25Δ\\DeltaAUC=0\.038=0\.038\(−0\.011\-0\.011to 0\.090;p=0\.134p=0\.134\), and Full35 minus AP\-COP10Δ\\DeltaAUC=0\.013=0\.013\(−0\.015\-0\.015to 0\.043;p=0\.361p=0\.361\)\. Thus, removing AP\-COP10 from Full35 produced a statistically supported loss, whereas adding the complementary descriptors to AP\-COP10 produced only a small, unsupported increase\. These contrasts are secondary nested representation analyses and were not included in the Holm\-adjusted literature\-comparison family\.

Non\-AP\-COP25 final models selected a mean of 5\.91 descriptors per outer fold \(median 6; range 3–6\), and 94 of 100 outer folds reached the six\-feature cap\. The most frequently retained candidates are shown in Table[S7](https://arxiv.org/html/2609.22956#S5.T7)\. The similar final\-model size indicates that the lower stand\-alone AUC was not attributable simply to systematically smaller selected models\.

Table S7:Most frequently retained descriptors within the stand\-alone Non\-AP\-COP25 representation\.
## S6Secondary robustness analyses

### S6\.1Feature\-budget and final\-feature\-cap sensitivity

Table S8:Full35 compactness sensitivity\.The six\-descriptor budget exceeded the three\-descriptor budget byΔ\\DeltaAUC 0\.022 \(95% CI 0\.002–0\.045;p=0\.033p=0\.033\), while gains over four and five descriptors were not supported\. The larger final caps did not improve on six\.

### S6\.2Classifier\-family sensitivity

Table S9:Classifier\-family sensitivity using the same fold\-specific Full35 feature sets\.Histogram gradient boosting produced the highest descriptive AUC \(0\.913\), followed by logistic regression \(0\.908\), RBF\-SVM \(0\.899\), and random forest \(0\.898\)\. Calibration slopes were 1\.01 for logistic regression and 0\.73 for histogram gradient boosting\. No paired inferential claim is made for the classifier\-family AUC differences in this supplement\.

### S6\.3Sensor perturbation and descriptor stability

Table S10:Full35 performance under simulated sensor perturbations\.Under 10% gain variation, the five AP\-COP position descriptors retained median Spearman agreement ranging from 0\.985 to 0\.996 with their clean values, whereas asymmetry descriptors ranged from 0\.865 to 0\.921\. Under one\-sensor dropout, position descriptors ranged from 0\.831 to 0\.966 and asymmetry descriptors from 0\.544 to 0\.618\. The lowest asymmetry stability occurred at 65–75% stance \(ρ=0\.544\\rho=0\.544\), while early\-stance asymmetry hadρ=0\.618\\rho=0\.618; the terminal\-stance position descriptor was the least stable position feature \(ρ=0\.831\\rho=0\.831\)\.

![Refer to caption](https://arxiv.org/html/2609.22956v1/Supplementary_Figure_S1_Sensor_Robustness_Final.png)Figure S1:Simulated sensor robustness and AP\-COP descriptor stability\. Left: Full35 performance under sensor perturbations\. Right: AP\-COP descriptor stability under sensor perturbations\.
### S6\.4Asymmetry and covariate sensitivity

Table S11:Sensitivity and attribution analyses for AP\-COP10\. AUC differences are reported for the listed representation minus the stated comparator\.The asymmetry\-definition sensitivities address coordinate\-origin dependence of the primary relative index\. The attribution and covariate analyses are secondary analyses and did not redefine AP\-COP10\. The speed analyses are predictive sensitivities rather than causal covariate adjustment\.

### S6\.5Source\-study holdout and study\-wise calibration

Leave\-one\-source\-study\-out AUCs were 0\.837, 0\.937, and 0\.946 for AP\-COP10 and 0\.807, 0\.932, and 0\.867 for Full35 when Ga, Ju, and Si were held out, respectively\. The pooled values were 0\.907 for AP\-COP10 and 0\.872 for Full35\. This analysis remains internal to GaitPDB and is not independent external validation\.

Table S12:Leave\-one\-source\-study\-out AUC with 95% bootstrap confidence intervals\.Study\-wise repeated\-CV Full35 AUCs were 0\.918 for Ga, 0\.934 for Ju, and 0\.888 for Si\. The overall Full35 calibration slope was 1\.01; study\-wise slopes were 1\.25, 1\.15, and 0\.87\.

## S7Reproducibility configuration

Table S13:Fixed configuration values used in the verified analyses\.The exact feature identifiers in Tables[S1](https://arxiv.org/html/2609.22956#S2.T1)and[S2](https://arxiv.org/html/2609.22956#S2.T2)are the column names used in the final feature matrices and analysis notebooks\. Participant\-level predictions, paired contrasts, fold\-level selections, selection\-stability summaries, and supporting numerical outputs are retained by the authors and can be made available from the authors upon reasonable request\. The numerical results required to interpret the manuscript are reported in the main text and this supplement\.

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