Leveraging Advanced Mathematical Methods in Artificial Intelligence to Explore Heterogeneity and Asymmetry in Cross-Border Travel Satisfaction

Abstract

The cross-border port serves as a crucial cross-border travel connecting mainland China with Hong Kong and Macau, directly impacting the overall satisfaction of cross-border travel. While previous studies on neighborhoods, communities, and other areas have thoroughly examined the heterogeneity and asymmetry in satisfaction, research on the satisfaction of cross-border travel at ports remains notably limited. This paper explores the heterogeneity and asymmetry of cross-border travel satisfaction using gradient boosted decision trees (GBDT) and k-means cluster analysis under the framework of three-factor theory, aiming to demonstrate the latest scientific research results on the fundamental theories and applications of artificial intelligence. The results show prevalent asymmetric relationships between factors and cross-border travel satisfaction, with the factor structure exhibiting heterogeneity across different groups. High-income individuals were more likely to prioritize the reliability of cross-border travel, whereas low-income individuals tended to emphasize the convenience of travel. Finally, this paper proposes improvement priorities for different types of passengers, reflecting the practical application of advanced mathematical methods in artificial intelligence to drive intelligent decision-making.

1. Introduction

Cross-border travel occurs across a variety of geographic and geopolitical contexts. Most research focused on cross-border cooperation between EU countries [1,2,3], such as France–Luxembourg [4,5] and Germany–Poland [6]. The dynamics of cross-border travel connecting mainland China with Hong Kong and Macau remain understudied in the academic literature [7,8,9,10].

As a key economic zone in southern China, the Greater Bay Area integrates nine cities from Guangdong Province with the distinct territories of Hong Kong and Macau [11]. As cross-border regional cooperation within the Greater Bay Area intensifies, cross-border travel connecting mainland China with Hong Kong and Macau requires more attention [12,13,14]. However, existing cross-border research from EU countries is inapplicable primarily to the Greater Bay Area, as most EU member states lack border checkpoints [6,15]. Cross-border travel connecting mainland China with Hong Kong and Macau must undergo customs inspection and usually requires intermodal transport at designated ports.

Satisfaction is a vital measure of service quality in intermodal transport services [16]. When passengers’ travel needs are met, they feel satisfied, which enhances their likelihood of using similar services in the future. Conversely, if their travel needs are not addressed, passengers may cease using the service and share their negative experiences with others [17]. Cross-border port connection is the most vulnerable link in intermodal transport, and the quality of connecting transport is a critical correlate in passenger satisfaction [18,19,20]. However, previous intermodal transport studies ignore some unique characteristics of customs inspection, such as customs inspection efficiency and customs flow management in the port inspection hall.

Previous studies have indicated that passenger heterogeneity significantly affects their satisfaction with transportation services [21,22]. Passengers with varying socioeconomic and travel characteristics generally have distinct travel needs and assess the same service differently [23]. Ignoring heterogeneity may result in only some passengers being satisfied with the current service [24]. By examining the heterogeneity in passenger satisfaction, intermodal passengers can be categorized into distinct segments, which is crucial for implementing targeted service quality improvements.

Cluster analysis, as an important unsupervised learning tool in the fields of AI, pattern recognition, and multivariate statistical analysis, has two main advantages over traditional classification methods. On the one hand, there is no need for preset classification criteria, and it can identify segmented groups based on the data itself autonomously and objectively [25,26]. On the other hand, it can handle large amounts of observational data and is compatible with mixed data types [27,28]. In addition, existing studies in the literature use traditional research methods such as dummy variable regression and importance grid analysis [29,30], and while both explore the asymmetric impact of factors on overall satisfaction, GBDT has higher predictive accuracy and more accurately captures the asymmetric nature of the influencing factors. Traditional approaches tend to emphasize the statistical significance of factors, thereby ignoring their importance in practice [31].

This study utilizes the 2023 Hengqin Port cross-border travel satisfaction survey data and explores the heterogeneity and asymmetry of cross-border travel satisfaction using GBDT and k-means cluster analysis. This study aims to address the following research questions: (1) How prevalent are asymmetric associations between factors and cross-border travel satisfaction? (2) What key factors should be the primary focus to optimize the cross-border travel experience for passengers? (3) How do satisfaction outcomes vary across distinct passenger segments?

This study explores the heterogeneity and asymmetry of cross-border satisfaction at ports, broadens the application scenarios of artificial intelligence, and demonstrates the practical use of mathematical methods in AI to facilitate intelligent decision-making. This study has multiple contributions. First, this paper applies classical machine learning tools (k-means cluster analysis + GBDT) to construct a two-stage analysis of “cross-border group classification-factor structure identification”. Second, it reveals a prevalent asymmetric relationship between factors and cross-border travel satisfaction. Finally, it uncovers heterogeneity in the factor structure of different cross-border passengers and suggests targeted strategies for improvement. Combined, these results offer comprehensive empirical evidence regarding cross-border travel satisfaction.

This paper adopts a systematic architecture comprising four integrated components: Section 2 conducts a critical synthesis of extant scholarship, systematically interrogating the multidimensional heterogeneity and spatial-temporal asymmetries inherent in cross-border travel satisfaction paradigms. Section 3 articulates the methodological framework, delineating the multilevel analytic approach and data curation protocols governing the empirical investigation. Section 4 unveils the analytical findings. The culminating section advances theoretical discourse and operational paradigms.

2. Literature Review

2.1. Factors of Cross-Border Travel Satisfaction

Most existing research on cross-border travel originates from EU countries [32,33]. The process of European integration has significantly promoted labor mobility within the EU, as most EU member states do not maintain customs inspection, allowing citizens of EU member states to live and work freely in any EU country [1,2,3,4,34,35]. Connecting transport services, clarity of path indication, and convenience of connection are closely related to cross-border travel satisfaction [7,9,33,36]. Gerber et al. [33] focused on cross-border commuters from Luxembourg’s neighboring countries and investigated the relationship between travel attitudes, mode choice, and cross-border travel satisfaction with structural equation modeling (SEM). They found that optimizing intermodal transport quality, such as operating lines and frequency, significantly enhanced cross-border travel satisfaction.

Cross-border travel connecting mainland China with Hong Kong and Macau requires customs inspection and usually requires intermodal transport. However, research on intermodal transport within ports remains relatively limited, let alone studies on passenger satisfaction with intermodal travel [18,19,20,37,38,39,40]. As shown in

Table 1. Overview of studies on intermodal travel.

Authors	Research Area	Influence Factors	Methodology
[42]	Shijiazhuang Zhengding Airport-High Speed Railway	Operating lines, operating frequency, path indication, information service, real-time information	Bayesian network
[41]	Shanghai Hongqiao Comprehensive Transportation Hub	Transfer distance, transfer environment, path indication, information service, multi-language	Analysis of variance
[43]	Nanjing Lukou International Airport	Transfer distance, transfer flow management, path indication, efficiency of security, luggage service, information service	GBDT
[44]	Nanjing South Station Comprehensive Transportation Hub	Operating lines, operating hours, path indication, luggage service	Rasch
[46]	Shijiazhuang Zhengding Airport-High Speed Railway	Operating schedule, operating frequency, operation lines, information service, path indication, transfer efficiency, real-time information	SEM
[45]	Jing-Jin-Ji Urban Agglomeration	Path indication, real-time information, luggage service, operation hours	SEM
[24]		Operation frequency, operating hours, transfer distance, transfer fee	Generalized ordered logistic regression
[20]		Transfer distance, transfer fee	XGBoost

, many scholars have found that the operating lines, operating hours, operating frequency, transfer distance, flow management, and path indication are significant determinants of passenger satisfaction [20,24,41,42,43,44,45]. Yang et al. [42] found that the operating lines and path indication significantly influence passenger satisfaction with air-rail intermodal travel. Since Rasch models are unable to handle complex interaction effects among independent variables and SEM models enforce linear relationships among variables, both types of models suffer from a lack of flexibility [44,45]. In contrast, machine learning techniques can automatically learn complex patterns without the need for predefined structures, which provides an effective way to address the limitations of traditional methods in passenger satisfaction research.

2.2. Heterogeneity in Passenger Satisfaction

Extensive research examines the heterogeneity of passenger satisfaction based on socioeconomic characteristics [21,22,47] and travel characteristics [48], with these findings mainly applied to passenger market segmentation [49]. Abenoza et al. [23] found that passengers with different socioeconomic and travel characteristics evaluate their experiences of the same public transport services differently. Luo et al. [22] investigated passenger satisfaction with Shenzhen metro and bus services and explored the heterogeneity in travel space and time. Results indicated that satisfaction was lower during the morning peak, primarily due to concerns over reliability. Previous studies have examined the heterogeneity of user behavior through market segmentation and developed differentiated strategies for target user groups. While these studies have yielded valuable conclusions [50,51,52], few studies have considered the segmentation of cross-border travel clusters.

2.3. Asymmetric Relationship Between Factors and Satisfaction

The previous literature indicates that factors exhibit different sensitivities to satisfaction depending on whether their performance is good or poor, and the nonlinear effect dynamics between factors and overall satisfaction is prevalent in the field of urban transport systems [29,30,53,54]. Within the framework of the three-factor theory, as illustrated in Figure 1, the factors of passenger satisfaction can be categorized as basic, performance, and excitement factors. Basic factors have significant impacts on satisfaction only when their performance is below passenger expectations; in contrast, excitement factors have significant impacts on satisfaction only when their performance exceeds passenger expectations [55]. The asymmetric relationship indicates a hierarchy of factor importance: basic factors should be satisfied first, and passengers focus only on whether these factors meet basic requirements, not on whether they exceed expectations; excitement factors are at the bottom of the improvement priority scale [56].

Gradient decision boosting belongs to the machine learning methods in the field of artificial intelligence, the principle of which is to optimize the loss function in multiple rounds of iterations by gradient descent, thus reducing the prediction error. Gradient decision boosting is often used in modern finance, intelligent construction, and other practical application scenarios [58,59,60], reflecting the core value of artificial intelligence technology to empower intelligent decision-making through mathematical optimization. Compared to regression models with dummy variables commonly found in the satisfaction research literature [29,30], the GBDT model offers several advantages. First, GBDT outperforms traditional regression models in terms of predictive accuracy. Second, GBDT aids in addressing multicollinearity problems. Given that some factors are interrelated, this correlation may result in multicollinearity within regression models. Decision trees inherently account for interactions between independent variables [57,61]. Third, GBDT can handle various types of independent variables, accommodate missing data, and requires minimal preprocessing [31]. Finally, as an ensemble-based boosting machine learning method, GBDT is highly effective for small samples [55,62].

Existing studies [55,61,63] have introduced machine learning techniques into the study of asymmetric relationships in transportation satisfaction. Dong et al. [61] used the GBDT method to assess the walking satisfaction of community residents in Harbin, China, and found that most factors had a nonlinear effect on comparing satisfaction with the walkability of residents, challenging linear assumptions used in previous research. Fang et al. [55] applied the same methodology to explore the factor structure of different public transport passenger satisfaction in developing countries and found a generally asymmetric relationship between public transport factors and overall satisfaction, which is consistent with other applications in developed countries [62]. Previous studies have demonstrated the widespread existence of asymmetric relationships in transportation satisfaction, and ignoring nonlinearity may misestimate the effects of factors on overall satisfaction, leading to incorrect implications for planning practices [30,54].

In summary, although previous studies have thoroughly discussed the heterogeneity and asymmetric relationships in passenger satisfaction, studies on the satisfaction of cross-border groups at ports are scarce, with a lack of consideration for the various stages of cross-border travel at ports and limited discussion on the heterogeneity of different types of groups. To fill these gaps, this paper employs k-means clustering analysis and GBDT in the field of artificial intelligence to explore the heterogeneity and asymmetry of cross-border travel satisfaction at Hengqin Port, aiming to demonstrate the latest scientific research results on the fundamental theories and applications of artificial intelligence and machine learning techniques.

3. Study Method

3.1. Data and Variables

This study utilizes structured questionnaire surveys administered at Hengqin Port, located within the Guangdong-Macao In-Depth Cooperation Zone in Hengqin, with data collection spanning from October to November 2023. Located at Zhuhai’s southern periphery in Guangdong Province, the Guangdong-Macao In-Depth Cooperation Zone in Hengqin occupies a 106 km² area bordering Macau’s maritime boundary, with its closest point separated by merely 200 m of waterways, as shown in Figure 2. Hengqin Port began operations in 2020 and implemented a 24/7 Joint Inspection-One Time Release (JI-OTR) mechanism, allowing passengers to enjoy the one-stop clearance experience. In 2023, the number of passenger customs clearances exceeded 16.7 million.

The survey was pretested by 50 cross-border passengers and revised based on their feedback. After receiving a 2-h questionnaire training, 20 surveyors conducted face-to-face interviews to recruit respondents at the passenger inspection hall of Hengqin Port. No incentives were used for respondent recruitment, and the response rate exceeded 70%. Researchers established perpendicular virtual demarcation lines at the passenger inspection hall, implementing a k = 15 interval selection protocol where every fifteenth consecutive passenger crossing the lines was enrolled. Responses were recorded using tablet computers, and the data was transmitted wirelessly to the server. This study obtained 2067 valid responses. The sample demonstrated near-equilibrium in cross-border flow directions: Macau-to-Hengqin passengers constituted 49.3% of participants (N = 1020), while Hengqin-to-Macau passengers comprised the remaining 50.7% (N = 1047).

The dependent variable in this study is overall satisfaction with cross-border travel, and the independent variables fall into three groups: satisfaction with factors, travel characteristics, and socioeconomic characteristics. The survey used a five-point Likert scale, asking respondents to rate their overall satisfaction as well as eight factors where “1” represents “unacceptable” and “5” represents “excellent”. The selection of factors was based on the previous literature on intermodal transport satisfaction and other relevant factors [20,41,42,45], encompassing the entire process of cross-border travel. This process includes connecting transportation to the port inspection hall and the customs inspection stage at the inspection hall. The factors include path indication, operating lines, operating hours, operating frequency, and transfer distance for connecting transportation, as well as path indication, customs inspection efficiency, and customs flow management in the port inspection hall. Travel-related factors in this study are defined by main travel purpose and travel frequency in the previous year. Socioeconomic characteristics include gender, age, education, annual income, and occupation.

Table 2. Profile of socioeconomic and travel characteristics of survey respondents.

Category	Description	Percentage
		Passengers from Macau to Hengqin	Passengers from Hengqin to Macau
Socioeconomic characteristics
Gender	Male	50.20%	49.95%
	Female	49.80%	50.05%
Age	24 years or lower	16.47%	17.86%
	25–29 years	19.22%	20.15%
	30–34 years	19.41%	21.01%
	35–39 years	19.51%	19.87%
	40–49 years	11.76%	11.17%
	50 years or higher	13.63%	9.93%
Education	High school or lower	11.08%	7.16%
	High school	12.94%	9.07%
	Associate degree	10.29%	12.99%
	Bachelor degree	48.24%	48.23%
	Graduate degree	17.45%	22.54%
Annual income (CNY)	<50,000	30.49%	30.37%
	50,000–100,000	12.94%	15.66%
	100,000–150,000	23.92%	20.82%
	150,000–200,000	16.96%	14.80%
	200,000–300,000	9.02%	11.56%
	>300,000	6.67%	6.78%
Occupation	Self-employees	5.00%	8.98%
	Worker	5.98%	3.53%
	Enterprise staff	48.43%	46.42%
	Public institution Staff	4.61%	5.92%
	Student	23.63%	24.83%
	Retiree	10.00%	7.55%
	Other	2.35%	2.77%
Travel characteristics
Main travel purpose	Business	1.96%	3.15%
	Reside	8.73%	2.01%
	Commute	24.90%	19.39%
	Study	19.80%	20.44%
	Visit	4.02%	4.97%
	Leisure	40.59%	50.05%
Travel frequency	≤2 times per year	26.37%	33.91%
	1–3 times per month	12.84%	9.74%
	1 time per week	10.20%	9.07%
	2–3 times per week	10.39%	12.32%
	≥4 times per week	40.20%	34.96%

and

Table 3. Profile of overall satisfaction and factors of survey respondents.

Category		Code	Description	Mean	Std
Passengers from Macau to Hengqin	Overall Satisfaction			4.45	0.69
	Macau side connecting transport	M1	Path indication	4.25	0.80
		M2	Operating lines	4.14	0.88
		M3	Operating hours	4.13	0.87
		M4	Operating frequency	4.10	0.87
		M5	Transfer distance	4.17	0.82
	In the inspection hall	T1	Path indication	4.38	0.71
		T2	Customs inspection efficiency	4.40	0.72
		T3	Customs flow management	4.24	0.82
Passengers from Hengqin to Macau	Overall Satisfaction			4.58	0.64
	Hengqin side connecting transport	H1	Path indication	4.28	0.81
		H2	Operating lines	4.31	0.82
		H3	Operating hours	4.32	0.79
		H4	Operating frequency	4.26	0.84
		H5	Transfer distance	4.28	0.79
	In the inspection hall	T1	Path indication	4.45	0.68
		T2	Customs inspection efficiency	4.51	0.68
		T3	Customs flow management	4.37	0.78

present the descriptive statistics of the survey respondents. The majority of respondents hold bachelor’s degrees and are enterprise staff, with most traveling across borders for leisure purposes and having a relatively high frequency of travel. In general, the average overall satisfaction with cross-border travel and satisfaction with factors for the group of passengers from Hengqin to Macau is 4.37, which exceeds the 4.25 reported for the group of passengers from Macau to Hengqin.

3.2. Analysis Approaches

3.2.1. Cluster Analysis

In this study, we apply the k-means clustering algorithm to categorize passenger groups according to their socioeconomic and travel characteristics [27,28]. The k-means clustering method is an advanced mathematical method of artificial intelligence technology, which has an important position in the field of unsupervised learning, and despite its relatively simple algorithm, it still widely supports the construction of artificial intelligence systems in practical applications such as data processing. The k-means clustering divides all samples into k mutually exclusive clusters, where samples within each cluster are as close as possible while being as far as possible from those in other clusters [25].

The silhouette coefficient is a commonly used metric for evaluating clustering performance, as it considers both cohesion within clusters and separation between clusters. The procedure for calculating the silhouette coefficient is illustrated in Equations (1) and (2):

$$\mathrm{s}\left(i\right)={\displaystyle \frac{B\left(i\right)-A\left(i\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left\{B\left(i\right),A\left(i\right)\right\}}}$$

(1)

$$B\left(i\right)=\underset{k}{\min }\left\{B\left(i,k\right)\right\}$$

(2)

where $\mathrm{s}\left(i\right)$ is the silhouette coefficient of sample i, $A\left(i\right)$ represents the average distance from sample i to other samples in the same cluster, and $B\left(i\right)$ represents the minimum distance from sample i to any sample in another cluster. The closer $\mathrm{s}\left(i\right)$ is to 1, the more appropriate the clustering of sample i [26,64]. $\overline{\mathrm{s}}\left(k\right)$ is the mean of all the individual silhouettes, referred to as the silhouette coefficient for clustering result k. The procedure for calculating $\overline{\mathrm{s}}\left(k\right)$ is illustrated in Equation (3):

$$\overline{\mathrm{s}}\left(k\right)={\displaystyle \frac{{\sum }_{i=1}^{m }\mathrm{s}\left(i\right)}{m}}$$

(3)

where m represents the number of samples in the cluster. A higher silhouette coefficient implies better clustering quality [25].

Referring to similar studies [26,64], the selection of the optimal number of clusters, k, in k-means clustering analysis is mainly determined by the silhouette coefficient method, and the closer the silhouette coefficient is to 1, it means that the clustering result of the sample is more reasonable.

3.2.2. Impact-Asymmetry Analysis Cluster Analysis

Penalty-reward contrast analysis is a commonly used method for identifying asymmetric relationships between factors and overall satisfaction [55,57,61]. This study consists of three steps: recoding satisfaction variables, estimating the penalty and reward indices for factors, and classifying them. First, factors are recoded into three categorical variables. Given the average ratings for overall satisfaction and specific factors are around 4.3, a score of 4 is labeled as “0,” indicating the standard category (i.e., meeting expectations). Scores from 1 to 3 are categorized as “−1,” representing penalties (i.e., performance below expectations), while a score of 5 is assigned a “1,” signifying rewards (i.e., performance exceeding expectations) [30,61]. Second, machine learning models are utilized to calculate the penalty and reward index for various factors. Finally, the impact-asymmetry index is calculated based on the relative sizes of the penalties and rewards [55,57]. Detailed steps are provided in Section 4.2. Gradient decision boosting is a machine learning method that belongs to the advanced mathematical methods in the field of artificial intelligence. A systematic comparison of the three indexes of R², RMSE, and MAPE reveals that the prediction performance of GBDT in this study is significantly better than that of XGBoost and SVM (the comparison results are shown in

Table 4. Comparison results of GBDT, XGBoost, and SVM.

Category	Indicator	R2	RMSE	MAPE
Passengers from Macau to Hengqin	GBDT	0.483	0.506	0.089
	XGBoost	0.166	0.642	0.104
	SVM	0.442	0.524	0.094
Passengers from Hengqin to Macau	GBDT	0.413	0.470	0.076
	XGBoost	0.123	0.577	0.083
	SVM	0.381	0.475	0.078

). This is shown by the fact that the GBDT model obtained higher R² values, as well as lower RMSE and MAPE values for both populations. This result suggests that GBDT can effectively support the asymmetric impact analysis in this study despite the limited sample size.

GBDT employs decision trees to approximate the observed values in the sample, with the goal of iteratively minimizing the prediction error until the loss function reaches convergence, thus reducing the overall loss [57].

This section introduces the GBDT algorithm using mathematical symbols. It assumes that the variable x represents the independent variables (which include socioeconomic and travel characteristics and factor satisfaction in this study), while F(x) serves to estimate the dependent variable y (overall cross-border travel satisfaction). The algorithm models the function as an additive series of the basis function $h\left(x;a_m\right)$, with each decision tree contributing incrementally. The procedure for calculating F(x) is illustrated in Equation (4):

$$F\left(x\right)=\sum _{m=1}^M{f}_m\left(x\right)=\sum _{m=1}^M{\beta }_{m}h\left(x;a_m\right)$$

(4)

In this model, $a_m$ denotes the average of the split locations and the terminal nodes for each variable involved in the splits of the decision tree $h\left(x;a_m\right)$. Additionally, ${\beta }_m$ is refined through the minimization of the loss function $L\left(y,F\left(x\right)\right)={\left(y-F\left(x\right)\right)}^2$. For the parameter estimation, Ding et al. [65] proposed the gradient boosting framework. The optimization technique can be summarized in the following way (Algorithm 1):

Algorithm 1. The optimization algorithm of GBDT.

$\mathrm{Initialize} F_0\left(x\right)$$\mathrm{to} \mathrm{be} \mathrm{a} \mathrm{constant}, F_0\left(x\right)={\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{\beta }\sum _{i=1}^{N}L\left(y_i,\beta \right)$ For m = 1 to M: For i = 1, 2, …, N compute the negative gradient            ${\tilde{y}}_{im}=-{\left[{\displaystyle \frac{\partial L(y_i,F(x_i\left)\right)}{\partial F\left(x_i\right)}}\right]}_{F\left(x\right)=F_{m-1}\left(x\right)}$ $\mathrm{Fit} \mathrm{a} \mathrm{regression} \mathrm{tree} h\left(x;a_m\right)$$\mathrm{to} \mathrm{the} \mathrm{targets} {\tilde{y}}_{im}$  $\mathrm{Compute} \mathrm{a} \mathrm{gradient} \mathrm{descent} \mathrm{step} \mathrm{size} \mathrm{as} {\beta }_m={\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{\beta }\sum _{i=1}^{N}L\left(y_i,F_{m-1}\left(x_i\right)+\beta h\left(x;a_m\right)\right)$ $\mathrm{Update} \mathrm{the} \mathrm{model} \mathrm{as} F_m\left(x\right)=F_{m-1}\left(x\right)+{\beta }_{m}h\left(x;a_m\right)$ $\mathrm{Output} \mathrm{the} \mathrm{final} \mathrm{model} F\left(x\right)=F_M\left(x\right)$

This study uses the learning rate to prevent the issue of model over-fitting by introducing a factor $\nu \left(0< \nu \le 1\right)$, which scales the contribution of each basis function $h\left(x;a_m\right)$[66], as shown in Equation (5):

$$F_m\left(x\right)=F_{m-1}\left(x\right)+\nu {\beta }_{m}h\left(x;a_m\right),where 0<\nu \le 1$$

(5)

Smaller learning rate values are more effective at minimizing the loss function, but this necessitates adding more trees to the model, presenting a balance between the number of trees and the learning rate [31]. Tree complexity, or the number of nodes within each tree, is another crucial factor for the GBDT method. To properly capture complex interactions among variables, increasing the complexity of the trees is essential. Ultimately, the effectiveness of the GBDT model is influenced by the interplay of the number of trees, the learning rate, and the complexity of the trees [66]. Referring to similar studies [31], this study uses the R “gbm” package to construct a GBDT model and determines the optimal parameter through 3-fold cross-validation. The final model parameters are the number of trees = 500, the learning rate = 0.015, and the complexity of trees = 4.

4. Results

4.1. Cluster Analysis

This study employs the k-means clustering algorithm to categorize passenger groups according to their socioeconomic and travel characteristics. For each group, this study conducted continuous clustering, and the silhouette coefficient was calculated for consecutive numbers ranging from k = 2 to k = 8 clusters. To make the clustering results more stable, we repeat the clustering calculation 10 times for each possible number of classifications k and record the silhouette coefficients each time. Finally, the average of these 10 results is taken as the final silhouette coefficients for this k value [26]. The results were displayed in a line chart, as shown in Figure 3. When k reaches 4, the silhouette coefficient for both travel groups reaches its maximum value. Based on this observation, this study considered that the four clusters appear to be optimal clustering results. The distribution of the sample from the clustering analysis is detailed in

Table 5. Distribution of samples from the clustering result.

Cluster	Passengers from Macau to Hengqin	Passengers from Hengqin to Macau
Group 1	23.80%	25.50%
Group 2	32.70%	39.54%
Group 3	11.70%	8.22%
Group 4	31.80%	26.74%
Total Respondents	1020	1047

, while

Table 6. Comparison of socioeconomic and travel characteristics of the clustering result.

Characteristics	Passengers from Macau to Hengqin				Passengers from Hengqin to Macau
	Group 1	Group 2	Group 3	Group 4	Group 1	Group 2	Group 3	Group 4
Gender
Male	55.56%	46.71%	34.45%	55.56%	47.57%	50.48%	31.40%	57.14%
Female	44.44%	53.29%	65.55%	44.44%	52.43%	49.52%	68.60%	42.86%
Age
24 years or lower	65.02%	1.50%		1.54%	62.55%	3.62%		1.79%
25–29 years	25.93%	23.05%	0.84%	16.98%	29.59%	21.01%		16.07%
30–34 years	8.23%	23.65%	0.84%	30.25%	6.74%	29.95%		27.86%
35–39 years	0.82%	31.44%	3.36%	27.16%	1.12%	28.74%	5.81%	28.93%
40–49 years		14.07%	12.61%	17.90%		13.04%	12.79%	18.57%
50 years or higher		6.29%	82.35%	6.17%		3.62%	81.40%	6.79%
Education
High school or lower	1.23%	4.19%	56.30%	8.95%	0.37%	3.14%	54.65%	5.00%
High school	1.65%	12.28%	28.57%	16.36%	2.62%	7.49%	25.58%	12.50%
Associate degree	0.82%	16.17%	7.56%	12.35%	0.75%	19.81%	10.47%	15.36%
Bachelor degree	58.85%	58.38%	7.56%	44.75%	48.31%	58.94%	9.30%	44.29%
Graduate degree	37.45%	8.98%		17.59%	47.94%	10.63%		22.86%
Annual Income (CNY)
<50,000	80.66%	7.78%	59.66%	5.56%	82.02%	5.56%	72.09%	5.00%
50,000–100,000	11.93%	11.98%	19.33%	12.35%	11.24%	20.29%	15.12%	13.21%
100,000–150,000	4.94%	33.53%	9.24%	33.64%	4.49%	28.99%	9.30%	27.86%
150,000–200,000	0.82%	25.75%	5.04%	24.38%	1.87%	18.60%	2.33%	25.36%
200,000–300,000	1.65%	12.57%	2.52%	13.27%		16.91%	1.16%	17.86%
>300,000		8.38%	4.20%	10.80%	0.37%	9.66%		10.71%
Occupation
Worker		5.39%	0.84%	12.96%		3.38%	3.49%	7.14%
Enterprise staff		73.65%	9.24%	73.15%		64.25%	6.98%	76.43%
Public institution staff		7.78%	4.20%	4.94%	0.37%	7.49%	1.16%	10.36%
Student	98.77%	0.30%			97.00%			0.36%
Retiree	0.41%	0.30%	82.35%	0.62%	1.12%	0.97%	82.56%	0.36%
Self-employees		11.98%		3.40%		19.81%	1.16%	3.93%
Other	0.82%	0.60%	3.36%	4.94%	1.50%	4.11%	4.65%	1.43%
Main Travel Purpose
Business	1.23%			5.25%	1.87%		3.49%	8.93%
Reside			33.61%	15.12%			11.63%	3.93%
Commute	0.82%	0.30%		77.47%	1.50%		1.16%	71.01%
School	81.89%			0.93%	74.16%	0.24%		5.36%
Visit	2.47%	7.19%	5.88%	1.23%	2.25%	6.52%	10.47%	3.57%
Recreation	13.58%	92.51%	60.50%		20.22%	93.24%	73.26%	7.50%
Travel Frequency
≤2 times per year	2.06%	47.01%	63.87%	9.57%	5.62%	64.73%	62.79%	6.43%
1–3 times per month	4.53%	20.96%	24.37%	6.48%	5.24%	15.70%	16.28%	3.21%
1 time per week	9.47%	19.16%	2.52%	4.32%	7.49%	12.32%	11.63%	5.00%
2–3 times per week	16.87%	8.38%	5.88%	9.26%	23.60%	7.25%	2.33%	12.14%
≥4 times per week	67.00%	4.49%	3.36%	70.37%	58.05%		6.98%	73.21%

displays the descriptive statistics for the socioeconomic and travel characteristics.

Among the passengers from Macau to Hengqin, the first group consists almost entirely of students (99.00%) who have the least income (81.00% with an annual income below 50,000 CNY). Their main cross-border travel purpose is commuting to school (82.00%), and they demonstrate a relatively high travel frequency (67.00% traveling more than four times per week). This group can be described as “low-income students with high-frequency cross-border travel”. This group generally has distinctive price-sensitive characteristics and tends to prioritize economic modes such as buses and shared bikes in their choice of connecting transportation while paying extra attention to the convenience of transferring. They have a high degree of travel flexibility, often take advantage of carpooling services or exclusive student discounts, and tend to avoid holiday rush hours. In customs clearance, they favor electronic methods such as self-service gates to enhance the efficiency of passage during off-peak hours.

The second group primarily comprises enterprise staff (74.00%) with higher incomes (72.00% earning 100,000–300,000 CNY annually). Their main travel purpose is recreation (93.00%), and nearly two-thirds of them only travel 1–3 times per month or less. This group can be described as “high-income tourists with low-frequency cross-border travel”. This group shows a strong pursuit of a comfortable experience, usually choosing direct transportation such as private cars or cabs, and is willing to pay extra for quality services. They have high requirements for the smoothness of transportation connections and port connections and are especially concerned about the convenience of customs clearance when carrying duty-free goods. In addition, this group generally wants to obtain clear customs clearance guidelines in advance, including the requirements for the preparation of documents, such as health declarations, to ensure a smooth trip.

The third group has the highest percentage of older individuals, with 82.00% aged 50 and above, and the lowest educational attainment, as 85.00% have no more than a high school education. Most individuals in this group are retired (82.00%), with recreation as their main travel purpose (61.00%). They have the lowest travel frequency (88.00% traveling 1–3 times per month or less) and can be described as “low-income retirees with low-frequency cross-border travel”. This group’s travel preferences are centered on safety and convenience, and they tend to choose simple modes of transportation, such as direct buses or transfers by relatives. Their demand for barrier-free facilities is more prominent, such as handrails, wheelchair access, and other supporting equipment. In the process of customs clearance, this group of people relies more on the services of traditional manual windows, and although they have a higher tolerance for waiting in line, they still need clear guidance signs or facilitation measures such as priority lanes.

The last group mainly consists of middle-aged and young adults, with 92% of them aged between 25 and 50 years. Their main travel purpose for cross-border travel is commuting (77.00%), and they display the highest travel frequency (70.00% traveling more than four times per week). This group can be described as “high-income commuters with high-frequency cross-border travel”. This group regards time efficiency as a primary consideration, usually chooses efficient connecting modes such as rail transportation or priority dispatching of online vehicles, and expects transportation to be equipped with office support functions such as charging and Wi-Fi. This group generally takes the initiative to use biometrics and other fast clearance technologies and, at the same time, is highly sensitive to changes in cross-border policies, often adjusting their travel arrangements in accordance with tax exemptions, visa rules, and so on.

A similar grouping pattern is observed among passengers from Hengqin to Macau.

4.2. Impact-Asymmetry Analysis

Following the studies [55,57,61], we carry out an analysis of impact asymmetry. The GBDT model generates predictions of overall satisfaction (POS) for each factor. This satisfaction is categorized into three levels: below expectation, meet expectation, and exceed expectation, which are denoted as POSb, POSm, and POSe, respectively. The impact asymmetry index is calculated as follows:

The Reward Index (RI) is defined as RI = POSe − POSm. It quantifies the increase in overall satisfaction when a factor’s performance shifts from “meeting expectation” to “exceeding expectation”.

The Penalty Index (PI) is calculated as PI = POSm − POSb. It assesses the decline in overall satisfaction when a factor’s performance drops from “meeting expectation” to “below expectation”.

The Range of Impact on Overall Satisfaction (RIOS) is represented by RIOS = PI + RI = POSe − POSb. The Satisfaction-Generating Potential (SGP) is expressed as SGP = RI/RIOS; The Dissatisfaction-Generating Potential (DGP) is calculated as DGP = PI/RIOS.

The impact-asymmetry index (IA Index) is IA = SGP − DGP. Based on the IA Index thresholds presented by [43], as shown in

Table 7. Factor classification based on IA Index.

Factor Classification	IA Index
Excitement factor	0.2 ≤ IA ≤ 1
Performance factor	−0.2 < IA < −0.2
Basic factor	−0.2 ≤ IA ≤ −1

, we categorize the factor into one of three groups.

In this study, the stability test of feature importance ranking is conducted through 3-fold cross-validation, and, combined with the noise resistance capability of the GBDT algorithm itself and the high consistency of feature importance shown in different data subsets, it can be considered that the model output results have good reliability [31]. The factor structures of factors are shown in

Table 8. Factor classification of factors.

Category	Group	Factor	IA Index	Factor Classification	Mean Performance
Passengers from Macau to Hengqin	Student group	M1	−0.65	Basic	4.32
		M2	0.76	Excitement	4.17
		M3	0.45	Excitement	4.16
		M4	0.93	Excitement	4.09
		M5	0.27	Excitement	4.20
		T1	0.58	Excitement	4.50
		T2	0.40	Excitement	4.49
		T3	−0.13	Performance	4.26
	Tourist group	M1	−0.18	Performance	4.36
		M2	0.72	Excitement	4.30
		M3	0.31	Excitement	4.29
		M4	−0.06	Performance	4.29
		M5	0.18	Performance	4.34
		T1	−0.18	Performance	4.45
		T2	−0.44	Basic	4.49
		T3	−0.96	Basic	4.39
	Retiree group	M1	−0.39	Basic	3.88
		M2	−0.42	Basic	3.82
		M3	−0.99	Basic	3.79
		M4	0.12	Performance	3.83
		M5	0.63	Excitement	3.86
		T1	0.33	Excitement	4.05
		T2	0.75	Excitement	4.20
		T3	0.99	Excitement	4.13
	Commuter group	M1	0.95	Excitement	4.22
		M2	0.01	Performance	4.07
		M3	−0.44	Basic	4.05
		M4	0.42	Excitement	4.01
		M5	−0.98	Basic	4.10
		T1	0.69	Excitement	4.33
		T2	0.19	Performance	4.30
		T3	−0.78	Basic	4.11
Passengers from Hengqin to Macau	Student group	H1	0.00	Performance	3.87
		H2	0.96	Excitement	3.92
		H3	−0.91	Basic	3.72
		H4	−0.98	Basic	3.76
		H5	0.17	Performance	3.81
		T1	−0.49	Basic	4.13
		T2	0.98	Excitement	4.22
		T3	−0.56	Basic	4.09
	Tourist group	H1	−0.84	Basic	4.37
		H2	0.81	Excitement	4.38
		H3	0.95	Excitement	4.42
		H4	0.52	Excitement	4.34
		H5	−0.07	Performance	4.38
		T1	−0.52	Basic	4.58
		T2	0.93	Excitement	4.63
		T3	0.84	Excitement	4.37
	Retiree group	H1	−0.03	Performance	4.15
		H2	0.11	Performance	4.21
		H3	0.24	Excitement	4.22
		H4	0.60	Excitement	4.14
		H5	0.70	Excitement	4.20
		T1	−0.27	Basic	4.33
		T2	0.16	Performance	4.39
		T3	−0.72	Basic	4.26
	Commuter group	H1	−0.67	Basic	4.40
		H2	0.58	Excitement	4.42
		H3	−0.53	Basic	4.44
		H4	0.59	Excitement	4.38
		H5	−0.97	Basic	4.35
		T1	0.45	Excitement	4.52
		T2	0.70	Excitement	4.57
		T3	−0.01	Performance	4.51

, indicating that asymmetric relationships between factors and cross-border overall satisfaction are prevalent. Among passengers from Macau to Hengqin, only one factor is categorized as a performance factor for the student and retiree groups, while performance factors account for four out of eight and two out of eight factors for the tourist and commuter groups, respectively. For passengers from Hengqin to Macau, only one factor is classified as a performance factor for the tourist and commuter groups, while performance factors account for two out of eight and three out of eight factors for the student and retiree groups, respectively.

The factor classifications for passengers from Macau to Hengqin are illustrated in Figure 4, Figure 5, Figure 6 and Figure 7, while factor classifications for passengers from Hengqin to Macau are illustrated in Figure 8, Figure 9, Figure 10 and Figure 11. The horizontal axis represents the average performance of each factor, while the vertical axis displays the IA Index for the corresponding factor.

Basic factors are regarded as “must be” factors. If they do not perform well, they have a detrimental effect on overall satisfaction. Basic factors with performance below passengers’ expectations (i.e., the average satisfaction of all factors) should be the highest priority improvements. However, once they meet passengers’ expectations, their impact on overall satisfaction becomes limited. Planners should only improve basic factors when their performance is poor, and the improvement is only made to align with passengers’ expectations to minimize overinvestment. Among passengers from Macau to Hengqin, all basic factors for the student and tourist groups exceed their expectations and therefore do not require further improvement. For the retiree group, factors such as path indication, operating lines, and operating hours for connecting transportation are below passengers’ expectations and must be prioritized for improvement. For the commuter group, operating hours and transfer distance for connecting transportation and customs flow management are below expectations and require urgent attention. For passengers from Hengqin to Macau, factors such as path indication and customs flow management in the port inspection hall are below passengers’ expectations for both the retiree and commuter groups and must be prioritized for improvement. Additionally, for the retiree group, operating hours and operating frequency for connecting transportation are below passengers’ expectations and require immediate attention.

Performance factors have a lower priority compared to basic factors. Although any improvement in performance factors can enhance overall satisfaction, there is a diminishing return once they meet passengers’ expectations. Among passengers from Macau to Hengqin, connecting transportation operating frequency for the retiree group and operating lines for the commuter group fall below passengers’ expectations and should be enhanced. For passengers from Hengqin to Macau, the performance of connecting transportation path indication and transfer distance for the retiree group falls below passengers’ expectations. Similarly, the performance of connecting transportation path indication and operating lines for the commuter group falls below passengers’ expectations, and improvement should also be made.

Excitement factors refer to factors that do not cause dissatisfaction even if they do not meet passengers’ expectations. Planners should improve excitement factors to a level beyond passengers’ expectations. Among the passengers from Macau to Hengqin, the excitement factors that exceed passengers’ expectations include path indication and customs inspection efficiency in the port inspection hall for the student group, connecting transportation operating lines and operating hours for the tourist group, and path indication in the port inspection hall for the commuter group. For the passengers from Hengqin to Macau, the excitement factors that exceed passengers’ expectations include connecting transportation operating lines and operating hours, customs inspection efficiency, and customs flow management for the student group; Operating lines and operating frequency for connecting transportation, as well as path indication and customs inspection efficiency in the port inspection hall for the tourist group.

The analyses of basic factors reveal that high-income groups are more likely to prioritize the reliability of cross-border travel, whereas low-income groups are more likely to value its convenience. For high-income commuters and tourist travel groups, basic factors include customs flow management, customs inspection efficiency, operating hours, and transfer distance. These factors are closely related to travel efficiency and reliability. In contrast, for low-income students and retirees travel groups, basic factors include path indication, operating lines, and operating hours, which are more associated with travel guidance and convenience.

This divergence is plausible. High-income people often have tighter time constraints for cross-border travel and thus prioritize the efficiency of customs inspections and the connections between transportation modes to ensure their travel time remains manageable.

5. Conclusions

Applying the two-stage analysis approach in artificial intelligence, this study explores the heterogeneity and asymmetry of cross-border satisfaction at ports, providing actionable insights for cross-border transportation planning and policy-making. This study broadens the application scenarios of artificial intelligence and demonstrates the practical use of mathematical methods in AI to facilitate intelligent decision-making. The contributions, key findings, recommendations, and limitations are summarized as follows:

• The innovation of this study is the application of classical machine learning tools (k-mean cluster analysis + GBDT) to construct a two-stage analysis of “cross-border group classification - factor structure identification”, which broadens the application scenarios of artificial intelligence, thus providing a methodological tool to study the heterogeneity and asymmetry of cross-border satisfaction of ports. Specifically, this study firstly adopts the k-means clustering algorithm to identify four types of typical cross-border groups, then applies the GBDT to identify the factor structure of service attributes, and finally proposes the priorities for improving the service quality of different groups. Combined, these results offer comprehensive empirical evidence regarding cross-border travel satisfaction.
• This study reveals prevalent asymmetric relationships between factors and cross-border overall travel satisfaction. The result aligns with the use of asymmetric research in studying passenger satisfaction in other urban planning investigations [55,57,61]. Furthermore, heterogeneity was observed among different types of cross-border passengers: high-income individuals were more likely to prioritize the reliability of cross-border travel, whereas low-income individuals tended to emphasize the convenience of travel.

This study proposes prioritized options for improving cross-border factors for typical population groups. Suggestions for the retiree group include: (1) Conducting further interviews to optimize the operating lines and operating hours of connecting transportation on the Macau side based on the specific needs of this group. For example, appropriately extend the operating hours of line 50 to 23:00 while optimizing line 701X to cover the downtown area of Coloane; (2) Proactively encouraging demand-responsive transit services to accommodate the flexible travel requirements of this group, thereby decreasing their dependence on fixed schedules. Suggestions for commuters include the following: (1) Optimizing transfer pathways to shorten the walking distance for passengers during transfers. For example, the opening of an accompanying vehicle inspection hall at the Hengqin Port. (2) Providing “frequent passenger” fast-track clearance channels for commuters with good credit records to enhance inspection efficiency for this group.

In addition, this study recommends that the port administration should include the student groups in the “frequent passenger” fast-track clearance channel. Finally, this study suggests that the transport administration should optimize the routes of connecting transportation to cover the main tourist and cultural attractions in Macao and Hengqin in order to target this group of tourists.

This study has notable limitations. First, the whole process conceptual framework does not incorporate cost considerations, which are critical for evaluating the financial feasibility and scalability of proposed improvements. This omission limits its direct applicability to real-world decision-making. Future studies should build upon this foundational framework by integrating economic evaluations. Second, the sample data for this study had limitations of self-reported data, as well as seasonal fluctuations in data, which could be mitigated in future studies by setting up reverse questions and comparative analyses of data from different seasons. Finally, this study mainly followed the generally accepted IA threshold criteria in the field to ensure comparable results [57,61], and future studies can optimize the threshold division with specific data.