User-Behaviour Based Dynamic Clustering Optimisation Algorithm for True Demand Prediction of Shared Bikes

1. Introduction

1.1. Global Growth and Future Potential of Shared Mobility

Shared mobility, particularly bike-sharing systems, has become an important component of sustainable urban transportation strategies aimed at reducing congestion, lowering emissions, and improving last-mile connectivity. Numerous studies have highlighted the rapid expansion of bike-sharing systems and their role in reshaping urban mobility patterns [1,2,3]. Early bike-sharing initiatives began in the 1960s, such as the White Bicycle Plan in Amsterdam, and gradually evolved into more structured station-based systems deployed in cities including Paris (Vélib), London (Santander Cycles), and New York (Citi Bike) [3,4]. With the development of GPS-enabled bicycles and smartphone-based unlocking technologies, dockless bike-sharing systems have expanded rapidly since the mid-2010s, enabling flexible bike pickup and drop-off without fixed stations [1,2]. Recent policy reports and industry analyses further confirm that shared micromobility has become a key element in urban transportation planning and smart-city mobility strategies worldwide [2,5].

The growth in shared bike usage has been dramatic. In 2024, the global bike-sharing market was valued at approximately USD 9 billion, and is projected to nearly double to USD 18.8 billion by 2034, at a compound annual growth rate of about 7.6% [6]. A complementary estimate places the global bicycle sharing market at USD 9.26 billion in 2024 with a projected rise to USD 16.44 billion by 2030, at a CAGR of 10.2% [7]. In Europe alone, ridership of dockless bikes rose by 54% in 2023 and continued to climb 58% in 2024 [8]. In the U.S. District of Columbia, dockless trips reached 8.6 million in 2024, representing a 43% year-on-year increase [9].

China, a major adopter of dockless bike-sharing, has also witnessed rapid expansion. Between 2017 and 2022, the market grew from CNY 13.03 billion to CNY 30.4 billion, reflecting a CAGR of roughly 10%. Over the same period, the user base expanded from 310 million to 460 million, a CAGR of 8.2% [10]. Moreover, about 54% of shared bike users incorporate them into multimodal trips, and 91% of those trips serve as links to public transit [10].

These numbers reflect only a portion of true demand, since many potential users may refrain from using bikes when availability is restrictive. Because of this latent demand, future growth is expected to be many-fold. Governments are prioritising micromobility to meet climate targets, reduce congestion, and enhance last-mile connectivity. The expanding terrain of smart cities, electrified fleets, and bike-friendly infrastructure further strengthens the growth trajectory of shared bike services worldwide.

1.2. Inefficiencies in Bike Allocation

Allocation of shared bikes often suffers from severe mismatches between supply and demand across urban areas. Numerous studies have documented that spatial imbalances arise when bikes accumulate in low-demand locations while shortages occur in high-demand zones, necessitating frequent redistribution operations to maintain service availability [11,12,13]. In many areas, oversupply leads to bikes idling unused, while in other zones demand goes unmet. Because allocation is driven largely by observed trips, it fails to capture hidden unmet demand—rides not taken because no bike is available nearby or within a tolerable walking distance. Recent work shows that when bikes are absent, many users either shift mode, delay travel, or abandon the trip, suggesting that system-recorded usage underestimates true demand by 5–15% in some cities [14].

These inefficiencies directly undermine user satisfaction. Riders who experience shortages are less likely to trust shared-bike services for commuting or time-sensitive trips, and repeated failures can lead to permanent loss of users. Oversupply, on the other hand, generates tangible operational costs. Idle bikes represent underutilised capital, while rebalancing operations require dedicated vehicles, labour resources, and fuel consumption, leading to increased operational expenses and environmental impacts [11,15,16]. Optimisation of redistribution strategies has therefore become a central problem in bike-sharing system management. Studies report that 20–30% of fleets may sit unused during off-peak hours, while poor allocation can inflate redistribution costs by 25–40% [17].

Taken together, oversupply waste, hidden unmet demand, and declining user satisfaction combine to degrade overall system performance. These challenges highlight the necessity for allocation frameworks that explicitly account for latent demand while improving spatial allocation efficiency and reducing costly redistribution operations [12,15].

1.3. Bridging Behavioural Insights and Spatial Optimisation

Existing studies on shared-bike demand prediction generally fall into three streams: clustering-based spatial analysis, user-behaviour modelling, and true-demand estimation. Clustering approaches enhance prediction stability by grouping stations or regions but often assume static spatial boundaries, limiting responsiveness to evolving demand patterns. Behavioural models have begun to account for factors such as walking tolerance and substitution effects, yet most rely on fixed parameters or opaque neural representations, which obscure interpretable behavioural dynamics. Meanwhile, true-demand research emphasises the gap between realised and unmet user intentions but rarely integrates behavioural context or dynamic spatial adaptation.

To address these gaps, this study proposes a user-behaviour based dynamic clustering optimisation algorithm that integrates observed riding behaviour with latent unmet demand. Central to the approach is the concept of Golden Distance—a behaviourally derived and dynamically adaptive service-radius threshold that reflects the distance users are willing to walk to access a bike, varying across districts. Extending our prior IoT-driven demand prediction framework [18], the method first applies density-based clustering, then selectively refines clusters that violate Golden Distance coverage using an elongation-aware adaptive mechanism. This design enables more accurate true demand estimation and significantly enhances forecasting and operational decision-making. The proposed framework is validated on one full year of real operational data from LocoBike’s dockless bike-sharing platform, comprising over 362,000 ride events and 5,700 inferred unmet demand events across three Hong Kong districts.

2. Literature Review

Research on demand prediction in shared-bike systems has evolved significantly over the last decade, with various methodological strands focusing on clustering-based approaches, user-behaviour-informed models, and attempts to capture latent or unmet demand—often termed “true demand.” Each of these research directions has made meaningful contributions, while also leaving gaps that motivate the present study.

2.1. Clustering-Based Demand Prediction

Clustering-based demand prediction has become a widely adopted approach in shared-bike analytics, as it stabilises highly volatile demand signals and reveals latent spatial structures in mobility patterns. Loidl et al. [19] provided an early systematic review of spatial clustering and aggregation techniques used in shared-mobility demand modelling, showing that clustering improves predictive robustness compared with station-level models while enabling scalable demand management across heterogeneous cities.

Building on this idea, Chen et al. [20] proposed a dynamic cluster-based over-demand prediction framework that combines correlation-based grouping with contextual features to identify areas with high stockout risk. Hierarchical clustering strategies have also been explored to support scalable prediction. For example, Feng et al. [21] introduced a station-clustering-based hierarchical demand prediction method, while Liu et al. [22] proposed a functional-zone-based hierarchical framework for bike-sharing demand estimation and system expansion.

More recent studies integrate clustering with machine-learning-based prediction models. Mehdizadeh Dastjerdi and Morency [23] used community detection to construct spatial prediction units before deep-learning forecasting, demonstrating improved prediction accuracy under dynamic demand patterns. Similarly, Yang et al. [24] showed that graph-based representations of inter-station flows can enhance short-term bike demand prediction by capturing relational spatial structures. Wang et al. [25] further proposed a demand-driven clustering approach that dynamically groups stations according to spatiotemporal usage patterns to support system-level operations.

Despite these advances, most existing clustering frameworks rely on spatial partitions optimised primarily for prediction stability rather than user accessibility behaviour. As a result, cluster structures often remain insensitive to users’ effective walking tolerance and may fail to reflect realistic service-radius constraints. This limitation motivates the development of behaviour-aware clustering mechanisms that adapt cluster structures based on user accessibility characteristics and latent demand signals.

2.2. User-Behaviour-Aware Approaches

Recent research has increasingly emphasised the behavioural foundations of shared-bike demand, recognising that user decision-making—shaped by walking tolerance, substitution choices, and trip migration—plays a central role in demand formation. Rather than treating demand as a static spatiotemporal process, these studies explicitly model how users adapt when availability or accessibility changes.

User accessibility and travel behaviour have also been shown to strongly influence bike-sharing demand realisation. Fishman et al. [26] synthesised evidence across bike-share systems and highlighted that access convenience, user experience, and system design are central determinants of ridership formation. Zhang et al. [27] analysed dockless bike-sharing behaviour in Singapore and showed that trip generation, attraction, and spatial clustering are closely associated with the built environment and access conditions, with a large share of trips linked to metro stations. Mix et al. [28] further demonstrated that accessibility-based variables are important in explaining bike-sharing trip generation and station demand, underscoring that user access constraints should be incorporated into planning and demand modelling.

These findings suggest that demand should not be interpreted purely as a spatiotemporal count process. Instead, it is partly shaped by how easily users can access bicycles within their surrounding urban context. This behavioural accessibility perspective provides an important foundation for the Golden Distance concept proposed in this study.

Li et al. [29] made an early breakthrough by integrating behavioural similarity into spatial modelling through the IrConv+LSTM framework. Their concept of “semantic neighbours” allowed demand correlations to be captured beyond geographic distance, thereby improving generalisation across heterogeneous urban layouts. Liang et al. [30] further advanced this direction by constructing the B-MRGNN model, which jointly modelled bike-sharing, ride-hailing, and transit data to learn multimodal relationships, quantifying behavioural substitution and complementarity.

Building on these foundations, Ren et al. [31] proposed the Demand Truncation and Migration Process (DTMP), a process-based behavioural model that explicitly estimates how users reallocate trips when preferred bikes are unavailable. Unlike prior black-box models, DTMP quantified the hidden portion of “unrealised” demand, offering an interpretable mechanism for unmet-demand estimation.

2.3. True Demand and Unmet Demand Estimation

A third strand of research seeks to correct the bias inherent in modelling only realised trips by estimating true demand—the sum of observed and unmet demand when users fail to locate an available bike. This line of inquiry reframes demand prediction as a problem of censored observation rather than simple data sparsity.

Ren et al. [31] made a major conceptual advance by introducing DTMP, which explicitly modelled how user intentions are truncated by system constraints and subsequently migrate to nearby substitutes. Zhu et al. [32] extended this notion empirically, showing that revealing unmet demand enables operators to better align fleet allocation with actual user needs, especially under spatially uneven supply conditions.

Negahban [33] pioneered a simulation-based approach to infer hidden demand from censored bike-sharing observations, showing that observed pickups and drop-offs may systematically understate the underlying demand distribution when resource availability is constrained. Cui et al. [34] further deepened behavioural understanding by documenting mode-shift phenomena when bikes were absent, offering empirical evidence that unmet demand often manifests as substitution to other modes rather than complete trip disappearance.

Beyond bike-sharing, the broader operations-research literature has long treated unmet demand as a censored-demand or lost-sales estimation problem. Nahmias [35] established an early analytical foundation for estimating demand in lost-sales systems where stockouts conceal the true level of customer demand. Jain et al. [36] later showed that stock-out timing itself can provide highly informative signals for recovering demand under censoring.

Collectively, these studies establish the analytical foundation for true-demand estimation and prove its relevance for both behavioural modelling and operational optimisation. However, simulation-based approaches remain computationally intensive, while empirical approaches often depend on auxiliary data sources that are not always available. Most importantly, these models are rarely integrated with adaptive clustering or behaviour-driven spatial optimisation, leaving true-demand estimation disconnected from the spatial decision structures needed for deployment and rebalancing.

2.4. Toward an Integrated Framework for Demand Prediction

In summary, clustering methods provide stability but overlook dynamic behavioural changes and latent demand. Behaviour-aware approaches introduce valuable user-centric modelling but often lack interpretability and dynamic adaptability. True-demand estimation offers a conceptual advance by recognising unmet demand but is typically constrained by computational cost and weak integration with other approaches.

These observations highlight the need for an integrated framework that unifies clustering, behavioural modelling, and latent demand estimation. In particular, the notion of a dynamic walking threshold—what we define as the “Golden Distance”—remains underexplored. Most prior work assumes static tolerance levels, while real-world willingness to walk varies by context. By combining density-based clustering with dynamic, behaviour-informed thresholds and explicit latent-demand estimation, this study aims to address these limitations and provide a more accurate and actionable representation of shared-bike demand.

3. Proposed Method

This study extends our previously published demand-prediction framework [18] by introducing a behaviour-grounded spatial optimisation layer designed to align clustering structures with real user accessibility constraints. The central design principle of the proposed framework is the concept of Golden Distance (GD), a behaviour-derived service-radius threshold representing the distance users are willing to walk to access a shared bike. Unlike traditional clustering parameters that are purely geometric or density-driven, Golden Distance is estimated from observed user behaviour and reflects realistic accessibility constraints in dockless bike-sharing systems. By embedding this behavioural constraint into the clustering process, the proposed algorithm generates spatial partitions that are both data-driven and operationally meaningful.

Figure 1 illustrates the overall system framework of the proposed method. The framework extends the baseline demand-prediction pipeline in [18] by integrating Golden Distance-guided clustering optimisation into the demand forecasting workflow. The system consists of five major phases: (1) ride records, inferred unmet demand events, and contextual information are integrated to construct the true-demand dataset; (2) district-level demand prediction is performed using an XGBoost [37] model trained on temporal and environmental features; (3) the Golden Distance is estimated from behavioural observations and used to guide spatial clustering through HDBSCAN [38] topology discovery followed by adaptive k-medoids refinement; (4) district-level predictions are downscaled to cluster-level demand based on historical activity shares; and (5) the proposed framework is evaluated and compared with a baseline DBSCAN-based [39] clustering approach under an identical prediction pipeline.

Overall pipeline of the proposed User-Behaviour Based Dynamic Clustering Optimisation Algorithm.

3.1. Behavioural Modelling via Golden Distance

A central contribution of this work is the introduction of Golden Distance, a behaviour-adaptive spatial threshold that represents users’ effective willingness to walk in order to access a shared bike. Unlike conventional clustering radii that are geometrically or statistically defined, Golden Distance is derived directly from observed user behaviour, bridging the gap between realised demand and latent unmet demand.

When a user opens a bike-sharing application, two types of behavioural events may occur: a successful rental event or an unsuccessful attempt where no bike is rented. Both outcomes reveal information about users’ walking tolerance. Figure 2 illustrates the behavioural interpretation of these two cases.

Behavioural interpretation of a successful rental event and an unsuccessful attempt where no bike is rented.

In a successful ride event, two distances are defined:

• Line-of-sight distance of ride event ${\mathrm{L}\mathrm{O}\mathrm{S}}_{\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{e}}$: the straight-line distance between the user’s app-open location and the rented bike location.
• Walking distance of ride event ${\mathrm{W}\mathrm{D}}_{\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{e}}$: the actual walking path distance from the user to the rented bike.

In an unmet demand event, two distances are defined analogously:

• Line-of-sight distance of unmet-demand event ${\mathrm{L}\mathrm{O}\mathrm{S}}_{\mathrm{u}\mathrm{n}\mathrm{m}\mathrm{e}\mathrm{t}}$: the straight-line distance between the user location and the nearest available bike.
• Walking distance of unmet-demand event ${\mathrm{W}\mathrm{D}}_{\mathrm{u}\mathrm{n}\mathrm{m}\mathrm{e}\mathrm{t}}$: the estimated walking path distance from the user to the nearest available bike.

The unmet-demand case reflects situations where the nearest bike is beyond the user’s acceptable walking tolerance. Therefore, combining ride events and unmet-demand events allows the estimation of a behavioural threshold that captures realistic walking willingness.

For each district $d$, let ${\overline{\mathrm{L}\mathrm{O}\mathrm{S}}}_d^{\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{e}}$ denote the average line-of-sight distance of successful ride events and ${\overline{\mathrm{L}\mathrm{O}\mathrm{S}}}_d^{\mathrm{u}\mathrm{n}\mathrm{m}\mathrm{e}\mathrm{t}}$ the average line-of-sight distance of unmet demand events. Golden Distance is then defined as

$${\mathrm{G}\mathrm{D}}_d\left(\alpha \right)=\alpha \cdot \left({\overline{\mathrm{L}\mathrm{O}\mathrm{S}}}_d^{\mathrm{u}\mathrm{n}\mathrm{m}\mathrm{e}\mathrm{t}}-{\overline{\mathrm{L}\mathrm{O}\mathrm{S}}}_d^{\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{e}}\right)+{\overline{\mathrm{L}\mathrm{O}\mathrm{S}}}_d^{\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{e}},$$

where $\alpha \in [0,1]$ is a behavioural scaling parameter capturing elasticity in walking tolerance. Smaller values emphasise conservative access preferences, while larger values reflect persistence observed in unmet-demand events. Golden Distance thus represents a behavioural service-radius constraint, rather than an area-packing or density threshold, and provides a principled way to align spatial clustering with realistic user accessibility.

3.2. District-Level Demand Topology Discovery via HDBSCAN

3.2.1. Motivation for Density-Based Topology Discovery

Urban bike demand exhibits strong heterogeneity across districts, influenced by land-use patterns, transport infrastructure, and population density. Prior clustering approaches that rely on a single global distance parameter tend to perform poorly across such heterogeneous environments, either over-fragmenting dense areas or collapsing sparse regions into excessively large clusters. To address this issue, the proposed algorithm employs HDBSCAN [38] as a topology-discovery mechanism at the district level.

3.2.2. Why HDBSCAN Instead of DBSCAN

HDBSCAN is preferred over DBSCAN for three fundamental reasons. First, HDBSCAN relaxes the assumption of a single global density scale by constructing a hierarchy of clusters across multiple density levels, enabling the simultaneous identification of dense commercial zones and sparse residential areas—an ability that DBSCAN lacks due to its reliance on a fixed $\epsilon$ parameter. Second, HDBSCAN provides explicit noise modelling based on cluster stability, whereby demand points that fail to form persistent density structures are treated as noise, reducing spurious clusters arising from sporadic or exploratory user behaviour. Third, clusters are selected based on their persistence across density thresholds, yielding spatial partitions that are robust to sampling variability and small perturbations in the underlying demand distribution.

3.2.3. Single-Run (Non-Recursive) Design

HDBSCAN is executed once per district and is not applied recursively. This design choice is deliberate: HDBSCAN’s role in the proposed framework is to uncover the natural density structure of demand, not to enforce cluster compactness. Recursive application tends to fragment clusters along marginal density variations, which often reflect sampling noise rather than meaningful behavioural distinctions. Empirically, repeated HDBSCAN runs rarely yield additional stable sub-clusters, while systematically increasing fragmentation and reducing interpretability. Therefore, HDBSCAN is used strictly as a first-stage topology extractor, producing a small number of stable, behaviour-agnostic demand regions.

3.3. Golden-Distance-Constrained Refinement via Adaptive k-Medoids

Although HDBSCAN effectively reveals the intrinsic density structure of demand points, the resulting clusters are not guaranteed to satisfy the Golden Distance service-radius constraint. In practice, density connectivity may group geographically extended demand regions into a single cluster whose spatial extent exceeds users’ walking tolerance. When this occurs, a single centroid cannot adequately represent the service coverage of the cluster. Figure 3 illustrates a representative example of such a situation.

Example of an oversized cluster that violates the Golden Distance constraint. Left: a demand cluster discovered by HDBSCAN whose spatial extent significantly exceeds the Golden Distance service radius (only 23 out of 5813 demand points are covered, a coverage of approximately 0.4%). Right: the same cluster after refinement using adaptive k-medoids, where multiple sub-clusters collectively cover nearly all demand points.

3.3.1. Cluster Geometry and Elongation Measurement

Consider a demand cluster $c$ identified by HDBSCAN, containing $N$ demand points with projected spatial coordinates ${\mathit{x}}_i=(x_i,y_i)$, $i=1,\dots ,N$. Let ${\mathsf{\Sigma }}_c\in {\mathbb{R}}^{2\times 2}$ denote the sample covariance matrix of these coordinates:

$${\mathsf{\Sigma }}_c=\mathrm{C}\mathrm{o}\mathrm{v}({\mathit{x}}_1,\dots ,{\mathit{x}}_N).$$

Let ${\lambda }_1\ge {\lambda }_2>0$ be the eigenvalues of ${\mathsf{\Sigma }}_c$, representing the principal variances along the major and minor spatial axes of the cluster, respectively. To quantify the degree of anisotropy, we define a cluster elongation index:

$$E_c=1-{\displaystyle \frac{{\lambda }_2}{{\lambda }_1}}, E_c\in [0,1).$$

$E_c\approx 0$ indicates a near-isotropic (approximately circular) cluster, while $E_c\to 1$ indicates a highly elongated, corridor-like cluster. This elongation index captures whether spatial growth occurs uniformly in two dimensions or primarily along a single dominant axis.

3.3.2. Shape-Aware Scaling Exponent

Let $L_c$ denote the characteristic spatial extent of cluster $c$, computed as the maximum pairwise distance or the cluster diameter derived from its convex hull. To avoid systematic over-fragmentation of elongated clusters, the number of sub-clusters is not scaled quadratically with area. Instead, we define a shape-adaptive scaling exponent:

$${\alpha }_c=\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{p}(2-E_c,\hspace{0.33em}1,\hspace{0.33em}2),$$

where $\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{p}(\cdot )$ bounds the exponent within $[1,2]$. This formulation yields ${\alpha }_c\approx 2$ for compact, isotropic clusters and ${\alpha }_c\approx 1$ for highly elongated clusters. Figure 4 illustrates the relationship between cluster morphology and the adaptive scaling exponent.

Illustration of cluster morphology and its effect on the adaptive scaling exponent ${\alpha }_c$. For compact clusters ($E_c\approx 0$) the exponent approaches 2, resulting in quadratic scaling; for highly elongated corridor-like clusters ($E_c\to 1$) it approaches 1, resulting in approximately linear scaling.

3.3.3. Adaptive k Formula

Given Golden Distance ${\mathrm{G}\mathrm{D}}_d$ for district $d$, the number of sub-clusters for cluster $c$ is determined as:

$$k_c=⌈{\left({\displaystyle \frac{L_c}{{\mathrm{G}\mathrm{D}}_d}}\right)}^{{\alpha }_c}⌉.$$

This expression generates the minimum number of medoids required to ensure that each resulting sub-cluster has an effective spatial radius on the order of Golden Distance. Once $k_c$ is determined, k-medoids clustering [40] is applied independently within each oversized cluster $c$, yielding sub-clusters whose medoids correspond to actual demand points. This ensures spatial robustness, interpretability, and direct operational relevance.

The adaptive $k$ formulation is designed to address a fundamental mismatch between geometric clustering assumptions and real-world demand morphology. Conventional approaches implicitly assume two-dimensional isotropic growth, leading to quadratic scaling of $k$ with spatial extent. However, in shared-bike systems, demand clusters are often constrained by road networks, coastlines, pedestrian corridors, and linear transit interchanges. In such cases, cluster expansion occurs predominantly along one dimension. Applying area-based scaling in these scenarios results in excessive fragmentation and artificial micro-clusters that do not reflect behavioural accessibility.

3.4. True-Demand Prediction via XGBoost

Once clustering is finalised, demand prediction follows the same methodology as in the baseline framework [18]. An XGBoost [37] regression model is trained using temporal, weather, and historical demand features to predict district-level true demand. Predicted district-level demand is subsequently downscaled to the cluster level based on each cluster’s historical activity share. This hierarchical strategy preserves temporal coherence at the district scale while capturing spatial heterogeneity at the cluster scale, without introducing data sparsity issues.

3.5. Algorithmic Summary

Algorithm [alg:main] presents the pseudocode for the complete User-Behaviour Based Dynamic Clustering Optimisation Algorithm.

Algorithm 1: User-Behaviour Based Dynamic Clustering Optimisation Algorithm

1: 1: for$\mathrm{each} \mathrm{district} d$ do 2: 2:        $\mathrm{Compute} \mathrm{Golden} \mathrm{Distance} {\mathrm{G}\mathrm{D}}_d$ from successful and failed user search behaviour – (Equation [eq:golden_distance]) 3: 3:    Run HDBSCAN once on demand points to extract initial demand clusters 4: 4:    $\mathbf{for} \mathrm{each} \mathrm{cluster} c$ do 5: 5:       $\mathrm{Compute} \mathrm{cluster} \mathrm{extent} L_c$ 6: 6:       $\mathbf{if} L_c\le {\mathrm{G}\mathrm{D}}_d$ then 7: 7:            $\mathrm{Keep} \mathrm{cluster} c$ unchanged 8: 8:            else 9: 9:            $\mathrm{Compute} \mathrm{covariance} \mathrm{matrix} {\mathsf{\Sigma }}_c$$\mathrm{of} \mathrm{coordinates} \mathrm{in} c$ 10: 10:            $\mathrm{Compute} \mathrm{eigenvalues} {\lambda }_1\ge {\lambda }_2$ 11: 11:            $\mathrm{Compute} \mathrm{elongation} E_c=1-{\lambda }_2/{\lambda }_1$          (Equation [eq:elongation]) 12: 12:            $\mathrm{Compute} \mathrm{adaptive} \mathrm{exponent} {\alpha }_c=\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{p}(2-E_c,1,2)$          (Equation [eq:exponent]) 13: 13:             $\mathrm{Compute} \mathrm{adaptive} \mathrm{cluster} \mathrm{count} k_c=\lceil (L_c/{\mathrm{G}\mathrm{D}}_d{)}^{{\alpha }_c}\rceil$          (Equation [eq:adaptive_k]) 14: 14:             $\mathrm{Apply} \mathrm{k-medoids} \mathrm{to} \mathrm{split} \mathrm{cluster} c$$\mathrm{into} k_c$ sub-clusters 15: 15:       end if 16: 16:     end for 17: 17:     Train XGBoost model to predict district-level true demand 18: 18:     $\mathrm{Predict} \mathrm{district}-\mathrm{level} \mathrm{demand} {\widehat{y}}_d$ 19: 19:     $\mathbf{for} \mathrm{each} \mathrm{final} \mathrm{cluster} c$  do 20: 20:       $\mathrm{Compute} \mathrm{historical} \mathrm{activity} \mathrm{share} w_c$ 21: 21:       $\mathrm{Downscale}: {\widehat{y}}_c=w_c\cdot {\widehat{y}}_d$ 22: 22:     end for 23: 23: end for

By explicitly separating density discovery from behavioural constraint enforcement, the proposed algorithm produces spatial clusters that reflect how users actually access bikes, rather than how demand points merely co-locate. This design constitutes a substantive methodological advance over existing clustering-based demand prediction frameworks.

4. Experimental Setup

4.1. Experimental Objective and Validation Strategy

The experimental design is constructed to rigorously evaluate whether the user-behaviour based dynamic clustering optimisation algorithm provides measurable advantages over conventional density-based clustering in true-demand prediction. Specifically, the experiments are designed to test three core hypotheses:

Predictive Accuracy Hypothesis. Clusters aligned with Golden Distance constraints reduce cluster-level demand variance and therefore improve prediction accuracy (lower RMSE) compared with DBSCAN-based clustering.

Spatial Validity Hypothesis. Enforcing centroid-based service-radius constraints produces spatial partitions that better reflect real service accessibility, resulting in improved demand-point retention and structurally coherent clusters.

Morphological Robustness Hypothesis. The proposed algorithm generalises across heterogeneous urban morphologies without district-specific tuning, demonstrating scalability and adaptability.

To isolate the causal impact of clustering design, all downstream forecasting components are held constant across experiments. The clustering module is the only component replaced, ensuring that any observed differences in performance are attributable to spatial partitioning strategy rather than predictive model variation.

4.2. Study Areas and Datasets

To comprehensively evaluate the robustness and adaptability of the proposed Golden Distance (GD) framework, three representative districts in Hong Kong were selected: Tseung Kwan O, Sha Tin, and Tuen Mun. These districts exhibit distinct urban morphologies, population densities, and mobility characteristics, thereby forming a heterogeneous testbed for algorithm validation.

Tseung Kwan O. Tseung Kwan O (TKO) is a planned new town characterised by high-density residential clusters, waterfront promenades, and structured cycling infrastructure. Demand patterns are relatively concentrated, with clear residential-to-commercial commuting flows. The spatial distribution of trips tends to form compact, high-density clusters.

Sha Tin. Sha Tin exhibits a mixed land-use pattern, combining residential estates, riverside cycling corridors, and commercial centres. The district features elongated spatial structures along the Shing Mun River, resulting in corridor-shaped demand clusters. This morphology is particularly suitable for testing the adaptive $k$ mechanism of Golden Distance.

Tuen Mun. Tuen Mun represents a relatively lower-density and more spatially dispersed district. Demand hotspots are scattered and often separated by industrial or coastal zones, producing irregular cluster shapes and higher noise proportions.

The dataset consists of one full year of operational records (January–December 2024) collected from LocoBike’s dockless bike-sharing platform, comprising 362,086 ride events and 5,744 inferred unmet demand events in total. The data include trip start/end timestamps, GPS coordinates (projected to metric space), anonymised user IDs, bike IDs, and trip status logs (ride success, unlock failure, timeout, etc.). Using a full-year dataset mitigates seasonal bias and ensures stability across varying weather, weekday/weekend, and holiday conditions. All spatial coordinates were transformed into a projected coordinate system (metres) to allow precise Golden Distance computation.

4.3. Feature Engineering

The core objective of feature engineering is to estimate True Demand, defined as the sum of ride events and statistically inferred unmet demand events.

A ride event is defined as a successfully unlocked and completed trip with valid GPS origin and destination coordinates. Records with missing timestamps, abnormal duration ($<$1 minute or $>$24 hours), or invalid geolocation were removed.

Unmet demand refers to user attempts that did not result in successful rides due to insufficient bike availability or operational constraints. Since dockless systems do not explicitly record “failed demand,” heuristic rules were applied to infer unmet demand events from system logs. Table 1 summarises the filtering criteria applied.

Filtering criteria for inferring unmet demand events from system logs.

Criterion	Description
Unlock timeout	App unlock initiated but no ride started within threshold duration
Repeated attempts	Multiple unlock attempts by same user within short time window
No nearby bikes	App session with zero bikes within search radius at time of query
Short session	App session closed within seconds of opening without ride

Criterion	Description
Unlock timeout	App unlock initiated but no ride started within threshold duration
Repeated attempts	Multiple unlock attempts by same user within short time window
No nearby bikes	App session with zero bikes within search radius at time of query
Short session	App session closed within seconds of opening without ride

4.4. Baseline Clustering Method and Prediction Model

To ensure a fair and controlled comparison, the experimental framework follows the methodology established in our previously published study [18]. The baseline system adopts a two-stage pipeline consisting of spatial clustering and district-level demand prediction with subsequent downscaling.

To isolate the impact of clustering strategy, all downstream processes remain identical across experiments: the same feature engineering pipeline, the same XGBoost [37] architecture and hyperparameters, the same district-level prediction procedure, the same downscaling mechanism, and the same training–testing split and evaluation metrics. The only component replaced is the clustering module:

• Baseline: DBSCAN [39] clustering $\to$ district-level XGBoost prediction $\to$ downscaling to clusters.
• Proposed method: User-Behaviour Based Dynamic Clustering Optimisation Algorithm $\to$ district-level XGBoost prediction $\to$ downscaling to clusters.

4.5. Evaluation Metrics

To evaluate the effectiveness of the proposed method against the DBSCAN baseline, three core metrics are adopted.

Root Mean Square Error (RMSE). RMSE measures the accuracy of cluster-level demand prediction after district-level forecasting and downscaling:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}(D_i-{\widehat{D}}_i{)}^2},$$

where $D_i$ and ${\widehat{D}}_i$ denote the actual and predicted demand for cluster $i$, respectively. Lower RMSE indicates higher prediction accuracy and better operational reliability.

Noise Ratio. Noise ratio quantifies the proportion of demand points labelled as noise during clustering:

$$\mathrm{Noise} \mathrm{Ratio}={\displaystyle \frac{\mathrm{Number} \mathrm{of} \mathrm{noise} \mathrm{points}}{\mathrm{Total} \mathrm{demand} \mathrm{points}}}.$$

A lower noise ratio reflects better spatial coverage and fewer discarded demand events.

Number of Clusters. The total number of generated clusters reflects the degree of spatial segmentation. Excessively large values may indicate over-fragmentation; too few clusters may imply insufficient spatial resolution. This metric is used to assess clustering granularity and structural stability across districts.

5. Results and Discussion

5.1. Clustering Quality Analysis

Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 present a visual comparison between the baseline DBSCAN-based clustering and the proposed Golden Distance-guided HDBSCAN with adaptive k-medoids method across the three representative districts. In all figures, the dotted circular boundary centred at each cluster centroid represents the Golden Distance service radius, providing a direct visual benchmark for evaluating whether the spatial extent of each cluster complies with the intended service constraint.

Tseung Kwan O—resulting cluster map of baseline DBSCAN.

Tseung Kwan O—resulting cluster map of proposed HDBSCAN + adaptive k-medoids.

Sha Tin—resulting cluster map of baseline DBSCAN.

Sha Tin—resulting cluster map of proposed HDBSCAN + adaptive k-medoids.

Tuen Mun—resulting cluster map of baseline DBSCAN.

Tuen Mun—resulting cluster map of proposed HDBSCAN + adaptive k-medoids.

Under the baseline method, clusters exhibit substantial variability in both size and geometry. Many clusters expand well beyond the Golden Distance circle, particularly in dense or spatially continuous regions (Figure 5 and Figure 7, and 9). These oversized clusters frequently span multiple functional zones, indicating that density connectivity alone is insufficient to enforce service feasibility. At the same time, smaller fragmented clusters and isolated noise points appear in lower-density or irregular areas, reflecting DBSCAN’s sensitivity to local density fluctuations.

By contrast, the proposed method produces clusters that are visibly aligned with the Golden Distance constraint (Figure 6 and Figure 8, and 10). Cluster extents are largely contained within, or tightly bounded by, the Golden Distance circle, even when demand distributions are elongated or constrained by urban structures such as road corridors or waterfronts. When clusters exceed the Golden Distance, controlled subdivision is triggered along the dominant spatial axis, yielding geometrically coherent sub-clusters rather than arbitrary fragmentation.

These visual results confirm that the proposed method enforces Golden Distance as an explicit centroid-based service constraint, rather than an indirect outcome of density assumptions. As a result, the generated clusters are more interpretable, operationally meaningful, and better aligned with real-world service coverage requirements.

5.2. Quantitative Performance Comparison

Table 2, Table 3 and Table 4 report the RMSE, noise ratio, and number of clusters for each district under the baseline and proposed methods.

Prediction performance and clustering statistics for Tseung Kwan O.

Algorithm	RMSE	Noise Ratio	No. of Clusters
Baseline (DBSCAN)	0.6020	0.12	65
Proposed	0.3737	0.20	154

Algorithm	RMSE	Noise Ratio	No. of Clusters
Baseline (DBSCAN)	0.6020	0.12	65
Proposed	0.3737	0.20	154

Prediction performance and clustering statistics for Sha Tin.

Algorithm	RMSE	Noise Ratio	No. of Clusters
Baseline (DBSCAN)	0.4304	0.38	73
Proposed	0.2546	0.24	245

Algorithm	RMSE	Noise Ratio	No. of Clusters
Baseline (DBSCAN)	0.4304	0.38	73
Proposed	0.2546	0.24	245

Prediction performance and clustering statistics for Tuen Mun.

Algorithm	RMSE	Noise Ratio	No. of Clusters
Baseline (DBSCAN)	0.3027	0.48	39
Proposed	0.1529	0.28	195

Algorithm	RMSE	Noise Ratio	No. of Clusters
Baseline (DBSCAN)	0.3027	0.48	39
Proposed	0.1529	0.28	195

Across all three districts, the proposed method consistently achieves substantial RMSE reductions compared with the baseline: Tseung Kwan O: RMSE decreases from 0.6020 to 0.3737 ($\approx$37.92% reduction); Sha Tin: RMSE decreases from 0.4304 to 0.2546 ($\approx$40.85% reduction); Tuen Mun: RMSE decreases from 0.3027 to 0.1529 ($\approx$49.49% reduction). These results demonstrate that clustering aligned with the Golden Distance constraint leads to significantly more accurate cluster-level demand prediction. By limiting intra-cluster spatial heterogeneity, the proposed method reduces demand variance within each cluster, thereby improving predictive stability.

The noise ratio exhibits a more nuanced pattern. In Tseung Kwan O, the proposed method results in a modest increase in noise ratio, reflecting stricter enforcement of service feasibility in extremely dense environments. In contrast, both Sha Tin and Tuen Mun experience substantial noise reduction, indicating improved retention of structurally meaningful demand points that DBSCAN misclassifies as noise. Importantly, the proposed framework does not seek to minimise noise ratio as an isolated objective, but rather balances coverage against spatial validity.

The number of clusters increases significantly under the proposed method across all districts. This increase is expected and intentional, as clusters violating the Golden Distance constraint are subdivided to preserve centroid-based service coverage. In the context of dockless bike-sharing operations, these smaller clusters can be directly interpreted as candidate bike deployment or rebalancing spots, enabling finer-grained and more accurate bike placement. The improved RMSE results indicate that such operationally aligned spatial units provide more reliable demand estimation than coarse, density-driven clusters.

5.3. District-Level Adaptability

The results further demonstrate that the proposed method generalises effectively across districts with diverse spatial densities and urban morphologies.

In Tseung Kwan O, a high-density district characterised by concentrated residential demand, the baseline method aggregates large contiguous regions into oversized clusters. The proposed method automatically increases cluster granularity to satisfy Golden Distance constraints, resulting in significant RMSE improvement despite a moderate increase in noise ratio. This highlights the prioritisation of service feasibility over maximal point inclusion.

In Sha Tin, where demand exhibits mixed density and elongated spatial patterns along riverbanks and transport corridors, the proposed method achieves both lower noise ratio and lower RMSE. This indicates that adaptive subdivision along dominant spatial axes preserves meaningful demand structure while maintaining centroid-based coverage.

In Tuen Mun, a lower-density and more spatially dispersed district, the baseline method produces few large clusters with high noise ratio. The proposed method substantially increases cluster resolution while simultaneously reducing noise and halving RMSE, demonstrating strong adaptability even in sparse environments.

Across all districts, the same algorithmic framework and parameterisation are applied without district-specific tuning. The observed variations in cluster granularity and geometry arise naturally from local spatial structure rather than manual adjustment, confirming the robustness and scalability of the proposed Golden Distance-guided clustering approach.

5.4. Behavioural Insights and Generalisability

Beyond the improvement in prediction accuracy, the results also provide several behavioural insights. First, users’ effective willingness to walk to access a shared bike is not spatially uniform. The variation in Golden Distance across districts suggests that accessibility tolerance is influenced by local urban context, so a single static service radius is insufficient for representing true user behaviour.

Second, unmet-demand events contain meaningful behavioural information rather than simply representing missing observations. Even when a rental is not completed, the event still reveals a boundary between acceptable and unacceptable access distance. By combining successful ride events with unmet-demand events, the proposed framework captures this behavioural threshold more effectively and therefore provides a better representation of true demand.

Third, the results show that user behaviour should influence not only demand estimation but also the design of spatial demand units. Density-based clustering alone may produce clusters that are not behaviourally feasible from the perspective of user access. By enforcing Golden Distance as a service constraint and selectively refining oversized clusters, the proposed method generates clusters that are more aligned with realistic service coverage and operational deployment needs.

Although the experiments are conducted in Hong Kong, the framework itself is not location-specific. Its core components—Golden Distance estimation, HDBSCAN-based topology discovery, and adaptive k-medoids refinement—can be applied to other cities using commonly available operational data. The exact value of Golden Distance is expected to vary across cities due to differences in urban form, walking culture, climate, and transport integration. Therefore, the method is generalisable at the framework level, while remaining locally adaptive through behaviour-based recalibration.

6. Conclusions

Key Findings. This study demonstrates that incorporating user walking tolerance into spatial clustering significantly improves true demand prediction in dockless shared-bike systems. By dynamically adapting cluster structures according to Golden Distance constraints, the proposed method produces behaviour-consistent service zones across heterogeneous districts. Empirical results from multiple Hong Kong study areas show substantial predictive improvements, with up to 49.49% RMSE reduction in the best-performing district compared with the prior DBSCAN-based framework, and an average RMSE reduction of 42.75% across districts. These findings confirm that demand estimation accuracy is highly sensitive to how spatial units are constructed.

Core Innovations. The core innovation lies in introducing Golden Distance as a dynamic, behaviour-driven service-radius constraint and embedding it into a user-behaviour based dynamic clustering optimisation algorithm. Unlike static geometric partitioning, the method selectively refines only clusters that violate accessibility constraints and incorporates elongation-aware adaptive scaling. This design bridges behavioural modelling and spatial optimisation within a unified clustering framework.

Practical Implications. Operationally, the proposed method enables more precise bike allocation, reduced oversupply, and better mitigation of unmet demand. By aligning clustering structures with real service accessibility, operators can deploy resources more efficiently, design better rebalancing strategies, and improve overall system responsiveness.

Future Directions. This work extends our prior IoT-driven demand prediction framework [18] by embedding adaptive, behaviour-aware spatial optimisation. Future research may explore temporal adaptation of Golden Distance, integration with dynamic pricing mechanisms, and validation across other shared-mobility modes and cities.