A novel ANP-PSO framework for clustering transportation modes from GPS tracking data

The ANP method offers a robust approach for decision-making by considering the complex relationships and feedback effects among decision elements. Figure 1 presents the workflow of the proposed ANP–PSO framework. The figure highlights the integration of feature extraction, ANP-based weighting, and PSO optimization for transportation mode classification.

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By utilizing a network structure and the supermatrix method, ANP overcomes the limitations of the AHP and provides a more comprehensive analysis of interdependencies in decision-making problems. The structure and difference between the AHP and ANP are shown in Fig. 2.

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As can be seen, in the Analytic Network Process, communication between components can be bidirectional, and each component can also have feedback. A classification problem can be considered as a single-part system consisting of n attributes that are interconnected in a network. Figure 1 illustrates a classification problem with three attributes in a compartment. (a) Shows the structure of the Analytic Hierarchy Process (AHP) with one-way communication. (b) Represents the Analytic Network Process (ANP) with bidirectional communication and feedback. (c) is a practical example within the ANP framework, demonstrating its real-world application. The figure shows the distinctions between AHP and ANP, emphasizing ANP’s bidirectional communication and feedback capabilities. This concept is adaptable to more complex scenarios. The arcs represent the interdependence and mutual influence of criteria on each other. Additionally, the loops indicate the feedback effect. The mutual relationships and feedback among the criteria create an impact on the overall decision-making process.

The ANP consists of the following three stages (Moalagh and Ravasan 2013). The first stage is problem modeling and structuring; the problem needs to be clearly articulated and logically organized, for example, by employing a systematic framework such as a decision network. The second stage is pairwise comparisons and priority vectors; the relative importance of each criterion with respect to the control criterion can be obtained from a pairwise comparison matrix. Pairwise comparisons express the relationships between elements within a component. Subsequently, a relative priority vector can be derived from the pairwise comparison matrix. Similarly, all local priority vectors are calculated using a similar method. Furthermore, the relative importance of criteria, and, based on the objective of the decision problem, is calculated from the pairwise comparison matrix. The third stage is the formation of the Super matrix; by substituting the relative priority vectors into the appropriate columns of a super matrix, the global priority weights of each criterion in the decision-making problem can be obtained from the restricted super matrix, which is derived from the multiplication of the super matrix by itself until the column convergence is achieved. The limit supermatrix is obtained by iteratively multiplying the initial supermatrix by itself until the matrix converges to a steady state with identical columns.

In the Analytic Network Process, pairwise comparisons are used to quantify the relative influence of one element on another. Let \(\text{C}=\left\{{\text{c}}_{1},{\text{c}}_{2},\dots ,{\text{c}}_{\text{n}}\right\}\) denote a set of criteria (or features). A pairwise comparison matrix \(\text{A}\in {\mathbb{R}}^{\text{n}\times \text{n}}\) is defined such that each element \({\text{a}}_{\text{ij}}\) represents the relative importance of the criterion \({\text{c}}_{\text{i}}\) with respect to the criterion \({\text{c}}_{\text{j}}\), Eq. (1):where \({\text{a}}_{\text{ij}}>0\) and \({\text{a}}_{\text{ij}}=\frac{1}{{\text{a}}_{\text{ji}}}\). In classical ANP, these values are typically elicited from expert judgment; in this study, they are treated as decision variables optimized through PSO.

Given a pairwise comparison matrix \(\text{A}\), the priority vector \(\text{p}=({\text{p}}_{1},{\text{p}}_{2},\dots ,{\text{p}}_{\text{n}}{)}^{\text{T}}\) represents the relative weights of the criteria and is obtained as the normalized principal eigenvector of \(\text{A}\), Eq. (2):where \({\uplambda }_{\text{max}}\) is the maximum eigenvalue of \(\text{A}\), and the elements of \(\text{p}\) satisfy \(\sum\nolimits_{{{\text{i}} = 1}}^{{\text{n}}} {{\text{p}}_{{\text{i}}} } = 1\). These priority vectors populate the corresponding columns of the ANP supermatrix.

The ANP supermatrix aggregates all local priority vectors into a single matrix that captures the interdependencies among criteria. By arranging the priority vectors into their appropriate columns, a weighted supermatrix is formed. The global priority weights of the criteria are then obtained by computing the limit supermatrix, which is derived by iteratively multiplying the weighted supermatrix by itself until convergence is achieved. Under standard ANP assumptions that the supermatrix is column-stochastic, irreducible, this iterative process converges to a steady-state matrix in which all columns are identical, in accordance with the Perron–Frobenius theorem.

The control criterion defines the context under which pairwise comparisons are performed and determines the dependency structure of the ANP network. In the present study, the control criterion is the transportation mode classification objective, under which all GPS-derived features are assumed to be mutually interdependent and evaluated with respect to their contribution to distinguishing transportation modes. Unlike traditional ANP applications that rely on subjective expert assessments, this study adopts a data-driven formulation in which the pairwise comparison matrices and resulting priority vectors are parameterized and optimized automatically within the PSO framework.

This section describes how the Analytic Network Process (ANP) is operationalized for transportation mode classification. In the proposed framework, each GPS trip is represented by an n-dimensional feature vector, and ANP is used to assign relative importance weights to these features. These weights are then used to compute a weighted classification score, which forms the basis for transportation mode detection.

Let x = (x₁,x₂,…,x_n) denote the feature vector corresponding to a single GPS trip (i.e., one GPS trajectory), where each component xi represents the value of the i-th GPS-derived feature, where each element corresponds to one extracted mobility feature (e.g., speed, distance, acceleration). The corresponding ANP-derived weight vector is denoted by w = (w₁,w₂,…,w_n), where each weight reflects the relative importance of a feature as determined by the ANP supermatrix.

In the classification problem based on the ANP, the goal is to determine the appropriate class for each n-dimensional input pattern in the form of x. Each input pattern is treated as an option in ANP, its value is calculated using Eq. (3):

In this equation, the values of X are normalized between zero and one. It should be noted that the X values correspond to different features of a sample and are measured on different scales. The utility value u(x) represents a weighted aggregation of trip characteristics and serves as a one-dimensional score summarizing the mobility pattern of a trip. Higher values of u(x) indicate greater similarity to faster or longer-distance transportation modes, while lower values correspond to slower modes such as walking. To ensure compatibility of judgments, Eq. (5) is used to normalize the data instead of the parameter X in Eqs. (2–3):

This normalization ensures that all features contribute comparably to the weighted aggregation, preventing variables with larger numerical ranges from dominating the classification score. In Eq. (4), x_i’ represents the normalized value, x_i, ma_i is the maximum value of the i-th and mi_i feature is the minimum value of the i-th feature, which are determined based on the available training and testing data. By considering x_i^’ according to Eq. (4), which results in \(0\le {x}_{i}`\le 1\), and also considering the equation \(\sum {w}_{i}=1\) it is easily ensured that \(0\le \text{u}(\text{x})\le 1\), where represents x = (x₁^’, x₂^’, …, x_n^’).

Different thresholds can be set to determine the classes according to the desired criterion and utilized in the representation of solutions in the metaheuristic algorithm. For example, by determining the thresholds of u(x)with a two-class problem, if the value of option u(x) is less than the threshold, the pattern belongs to class 1; otherwise, it belongs to class 2. Therefore, to generalize this principle to an m-class problem, m-1 thresholds are defined:

In the proposed framework, these thresholds are not predefined heuristically but are treated as decision parameters. Their values are optimized using the Particle Swarm Optimization algorithm described in “Particle swarm optimization algorithm”, jointly with the ANP feature weights, to minimize classification error. The next section will explain how the PSO algorithm can be used to determine the parameters of a classification problem using the ANP method based on the pattern data. These data include the parameters related to the elements of the super matrix and the thresholds. Thus, the ANP-based weighting scheme provides a structured feature aggregation mechanism, while PSO is responsible for identifying the optimal combination of feature weights and classification thresholds.

The Particle swarm optimization algorithm is an algorithm is a stochastic optimization technique based on swarm, which was proposed by (Eberhart and Kennedy 1995). It is inspired by the behavior of fish and birds, and in a way, it can be considered as a combination of collective group experiences and individual experiences that individuals use in their decision-making processes. (Richardson and Boyd 1985) examined the human decision-making process and developed the concept of individual learning and cultural transmission, which humans use two important types of information in their decision-making process: first, their own experiences and experiments and second experiences and experiments of other individuals.

This theory later became the basis for the development of the PSO algorithm by (Eberhart and Kennedy 1995). This algorithm utilizes a set of particles that form a swarm and move in the solution space in search of the best solution. Each particle determines its own movement path in the search space based on its individual experiences and the experiences of other particles. Each particle keeps track of its best position (Pbest) and its value, as well as the best overall position of the swarm (gbest) and its value that has been found so far, and then updates its movement path based on this information.

If we assume that each particle moves in an n-dimensional space, we represent the position vector of particle i as x_i = (x_i,1, x_i,2, …, x_{i, n}) ∈ ℜⁿ, and the velocity vector as v_i = (v_i,1, v_i,2, …, v_{i, n}) ∈ ℜⁿ. After each iteration of the algorithm, we update the particle's velocity and position using Eqs. (5) and (6)

In Eq. (5), "ω" represents the inertia component, "c₁" represents the cognitive component, and "c₂" represents the social learning component. Additionally, "r₁" and "r₂" are random numbers between 0 and 1. pbest_i is the personal best (the best solution found by particle i), and gbest_i is the best solution found by particle i’s neighbours. The inertia component is a memory that retains the previous movement direction. This memory component can be seen as inertia that prevents sudden changes in movement direction. In Eq. (6) x_i (k + 1) is the updated position of particle i at time k + 1, and x_i (k) is the current position of particle i at time t, and v_i (k + 1) is the updated velocity as calculated in the previous step.

c₁ and c₂ are used in the Particle Swarm Optimization (PSO) algorithm to control the velocity and position updates of particles within the swarm. Specifically, c₁ reflects a particle’s self-confidence, while c₂ represents its confidence in other particles. If c₂ > 0 and c₁ = 0, the entire swarm converges towards a single point, transforming all particles into random explorers. Conversely, if c₁ > 0 and c₂ = 0, particles become independent explorers, performing local search. Excessive growth of these components leads to oscillatory particle movement, whereas smaller values create smoother paths. Typically, suitable values for c₁ and c₂ are empirically determined. In a 1998 article, Kennedy demonstrated that the sum of c₁ and c₂ should be less than 4 to ensure network convergence; otherwise, velocities and positions tend towards infinity.

The cognitive component evaluates the efficiency of the particle relative to its previous performances. Similar to memory, the cognitive component keeps track of the position where the particle performed better. The effect of this component is to encourage the particle to return to its previous best position, similar to individuals’ tendency to return to a location or situation that satisfied them more in the past.

The social learning component evaluates the efficiency of the particle relative to a group of particles or the entire swarm. Conceptually, the social component acts as a criterion that particles strive to achieve. The effect of this component is to attract each particle towards the best position found by its neighbours or the whole swarm. Figure 3. schematically illustrates the change in the particle’s trajectory in the PSO algorithm.

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During each iteration, it is essential to assess the fitness of individual particles to align with the intended optimization objective. The evaluation process involves quantifying the performance of neural networks using the root-mean-square-error (RMSE) metric. This RMSE metric gauges the average detection error and can be computed using the subsequent Eq. (7):

In Eq. (7), nTr represents the count of training samples, nOut signifies the number of network outputs, and t_i,j and y_i,jstand for the derived and reported outputs, respectively, corresponding to the ith training sample and jth network output. For instance, when the reported travel mode for the ith training sample is “walk,” y_i,1 equals 1. Similarly, if the derived travel mode for the ith training sample is “bus,” t_i,1 and t_i,3 are set to 0 and 1, respectively. The fitness function is defined as follows Eq. (8):

This fitness value serves as a metric to gauge the performance of the proposed algorithm. After assessing the initial swarm, the individual best performance for each particle (referred to as “personal best”) and the best performance among neighbouring particles (referred to as “local best”) are retained.

If the fitness of a particle surpasses its personal best, the local best is updated with that particle’s position. Likewise, if a particle’s fitness outperforms the local best, the local best is updated to match the particle’s current position. This iterative process continues until the user-defined criterion is met, which could involve reaching a specific RMSE threshold or completing a designated number of iterations. In this algorithm, the most important parameters are the particle count, velocity components, and inertia weight.

A higher inertia weight accompanies a broader search space with sudden changes, while a lower inertia weight focuses the search in a narrower and more concentrated region. The optimal value of inertia weight depends on the problem and the dependent velocity components. In fact, these three parameters are selected simultaneously. In the past, the inertia weight was considered a constant value for all iterations. However, nowadays, these parameters are defined as variables. These methods typically start with higher initial inertia weight values, gradually reducing them over time. As a result, particles engage in exploration during the initial stages and gradually shift towards exploitation of desired regions. The adjusted inertia weight for each iteration can be determined using Eq. (9).

In the above equation ω_min, ω_max, there are maximum and minimum inertia weight values, which are input parameters of the algorithm and should be determined by the user. ’iter ’ represents the current iteration of the algorithm, while iter_max indicates the maximum number of iterations.

Furthermore, the initial conditions and termination criteria of the algorithm should be specified. The particle positions vector can be randomly generated or initialized using heuristic methods, and the initial particles must be assigned values that ensure sufficient diversity. The initial velocity vector is commonly set to zero, but if it is randomly initialized, the values should be very small.

The dataset used in this study is drawn from the MOBIS:COVID-19 research project conducted by ETH Zürich (Molloy et al. 2023). This dataset was collected across Switzerland during the COVID-19 pandemic to monitor and analyze how individual travel behavior and transportation choices changed in response to public health interventions and societal restrictions. The data was acquired through a smartphone application called Catch-my-Day, which passively recorded GPS trajectories and sensor data from thousands of volunteer participants over an extended period. Each participant’s device continuously captured time-stamped geolocation information, allowing for the reconstruction of detailed daily mobility patterns and the inference of transportation modes.

The original dataset comprised a total of 1,230,196 trips, distributed across multiple transportation modes: Car (606,770), Walk (566,812), Bus (21,334), LightRail (16,400), Bicycle (13,718), Train (2,996), RegionalTrain (928), Tram (846), Subway (199), Plane (134), and Ebicycle (59). Although the MOBIS dataset also contains a substantial number of light rail, tram, subway/metro, and regional rail trips, these modes were not combined into the “Train” category and were excluded from the present analysis. This decision was made because different rail-based public transport modes often exhibit highly overlapping speed, acceleration, and distance profiles at the trip level, which increases classification ambiguity when relying solely on GPS-derived features. For this study, we focused on the five primary transportation modes Car, Walk, Bus, Bicycle, and Train as they represent the most common and relevant categories for analysis. This filtering resulted in a refined dataset comprising 1,211,630 trips, which provided a more focused and meaningful basis for evaluating transportation mode detection methodologies.

The MOBIS dataset contains both validated and non-validated trip records, as documented by Molloy et al. (2023). In this study, GPS trajectory data and derived movement features (e.g., speed, distance, acceleration, and bearing) were used as the sole inputs for the K-means clustering stage. This step was entirely unsupervised and did not rely on transportation mode labels generated by the MotionTag system or user validation. For the subsequent ANP–PSO hybrid classification, transportation mode labels were used only for calibration, balancing, and performance evaluation. Specifically, a balanced subset was constructed using trips for which transportation mode had been validated by users at least once, following MOBIS documentation that approximately 85% of participants provided validation. This strategy was adopted to mitigate known reliability issues of automated mode detection, particularly for bus trips, while preserving the unsupervised nature of the clustering process. MotionTag-inferred modes were not used as ground truth for clustering or optimization, but only as a reference for evaluating classification performance.

To prepare the data for transport mode classification, several preprocessing steps were applied. First, entries from users with invalid GPS recordings, such as those trips with a maximum speed of zero, were removed to ensure the dataset’s reliability. Further cleaning was performed by filtering out trips with an average speed of trips below one meter per second, as these typically represented stationary behavior or sensor noise. The GPS trajectory data was then aligned with the labeled transport legs provided in the dataset to ensure consistency between inferred and reported modes.

From each trajectory, a set of numerical features was derived to support mode detection. These include average speed, mean speed, total distance traveled, total trip duration, average acceleration, mean directional bearing, maximum speed, and maximum acceleration. These variables were normalized and used as input for the Analytic Network Process (ANP) combined with Particle Swarm Optimization (PSO). The ANP framework was used to model the interrelationships and relative importance of the extracted features, while PSO served as a heuristic optimization technique to identify the most effective feature weights and classification thresholds. Unlike other studies that rely heavily on manual labeling or unsupervised clustering such as k-means, this approach benefits from the semi-labeled nature of the MOBIS dataset, enabling more robust model training and evaluation. In this study, the MOBIS dataset is referred to as semi-labelled in the sense that transportation mode labels are available but are not uniformly validated at the trip level. Mode labels are primarily inferred automatically by the MotionTag system, and only a subset of trips are explicitly validated by users. While approximately 85% of participants validated at least one trip, not all individual trip records are confirmed, and the reliability of automatic mode detection varies across modes. For this reason, the dataset is not treated as fully labelled ground truth in the present analysis. The combination of rich sensor data, rigorous cleaning procedures, and a hybrid classification methodology provides a comprehensive and scalable solution for detecting transportation modes in real-world mobility datasets.

In order to classify and identify transportation modes accurately, the K-means algorithm was employed as a clustering technique using selected features from the data. The features considered for clustering included average speed, mean speed, total distance, total time, average acceleration, mean bearing, maximum speed, and maximum acceleration. These features were selected based on common practice in the transportation mode detection literature, where GPS-derived variables such as speed, distance, time, acceleration, and bearing are consistently shown to be discriminative for distinguishing between walking, cycling, and motorized modes (Dabiri et al. 2020; Sadeghian et al. 2024a). Such features have been widely used in both supervised and unsupervised mode detection approaches and are considered robust indicators of travel behavior.

Before applying the K-means algorithm, the data underwent preprocessing and sorting procedures. Additionally, new records such as maximum speed and acceleration were extracted from the data to enhance the clustering process. The K-means algorithm was then applied using Python, iteratively clustering the data for a total of 10,000 iterations.

The resulting output of Table 1 presents the cluster centers obtained from the K-means clustering method. Each cluster is associated with specific transportation modes. Cluster 1 is identified as the walking cluster, Cluster 2 as the bike cluster, Cluster 3 as the buses cluster, Cluster 4 as the cars cluster, and Cluster 5 as the trains cluster. These assignments were made based on the characteristic features and patterns exhibited by the data points within each cluster.

While it is possible to determine the transportation mode of a new trip by calculating the distance between its features and the cluster centers, further accuracy improvement is desired. To achieve this, the classification method described in “Methodology” section is employed. By utilizing this classification method, new data points can be assigned to their respective clusters, ensuring a more precise classification of transportation modes.

The classification method works by leveraging the information gathered during the clustering process. The new data points are evaluated based on their feature values, and their distances to the cluster centers are calculated. The cluster with the minimum distance to the new data point is then selected as the likely transportation mode for that trip. By incorporating the classification method alongside the clustering approach, the accuracy of the data mining method for transportation mode detection is significantly enhanced.

Some extreme values observed in Table 1, particularly for maximum speed and maximum acceleration, reflect the inherent noise and positional uncertainty associated with raw GPS measurements. Although preliminary data cleaning was performed by removing trips with invalid recordings (e.g., zero maximum speed and unrealistically low average speed), no trajectory-level smoothing or point-wise outlier filtering was applied prior to feature extraction. As a result, maximum speed and acceleration values represent upper-bound GPS-derived estimates rather than continuous physical motion and should be interpreted accordingly.

In conclusion, the combination of the K-means algorithm for initial clustering and the classification method described in “Methodology” section provides an effective approach for accurately detecting transportation modes. The K-Means clustering algorithm achieved an accuracy of approximately 50% on the full dataset. Although this number may appear low, it is important to note that the dataset is both large and imbalanced. Most of the trips are labeled as Car (606,770) and Walk (566,812), while other modes such as Bus (21,334), Bicycle (13,718), and Train (2,996) have much fewer instances. Given this imbalance and the unsupervised nature of K-Means, the 50% accuracy indicates that the algorithm was able to identify meaningful structure in the data. Furthermore, the algorithm demonstrated computational efficiency, completing its execution in 128.12 s. This result provides a useful baseline and demonstrates the effectiveness of clustering as a first step in transportation mode classification. The K-means algorithm helps to identify distinct patterns in the data and supports the classification process by grouping similar trips. Additionally, the clustering results are used to generate initial threshold values for the ANP-PSO algorithm, helping to improve the accuracy of feature weighting and classification. This combined approach offers a reliable method for detecting transportation modes and can support applications in transport planning, urban mobility studies, and intelligent transport systems.

Since the original dataset was imbalanced, with a disproportionate number of trips across different transportation modes, a balanced subset was created to ensure fair and effective training. Specifically, 2,996 trips were randomly selected for each mode, resulting in a balanced dataset that was used as input for the ANP-PSO algorithm. This approach helped to prevent bias toward overrepresented classes and improved the reliability of the classification results.

The hybrid ANP-PSO algorithm, as detailed in “Methodology” section, was applied through Phyton programming to classify transportation modes based on the designated variables. Within this approach, updating the solution vector ‘x’ is essential to explore potential solutions more comprehensively. The iterative update of travel features aims to enhance the transport mode detection process by optimizing the weightings assigned to distinctive features and refining the classification thresholds. This dynamic adaptation of ‘x’ permits the algorithm to fine-tune its parameters for each cluster, ensuring a more accurate and tailored outcome.

The implementation unfolds as follows: commencing with the application of the K-means algorithm to cluster GPS data into distinct transportation modes, the ANP-PSO hybrid algorithm is subsequently employed on each cluster individually. This segment-wise application of ANP-PSO is geared towards determining specific weights for selected features and individualized classification thresholds corresponding to each transportation mode. The algorithm encompasses a configuration of 64 elements intertwined with the ANP super matrix, encapsulating 8 variables (average speed, mean speed, total distance, total time, average acceleration, average bearing, maximum speed, and maximum acceleration), in connection with 5 variables linked to classification thresholds. The algorithm’s parameters, employed during the initial analysis, are delineated in Table 2, offering a comprehensive insight into the algorithm’s functioning and configuration.

Table 2 shows the values assigned to the parameters used in the combined ANP and PSO algorithm. The parameter ω_max represents the maximum inertia weight, ω_min represents the minimum inertia weight, c1 and c2 represent the cognitive and social learning factors, respectively. The number of iterations represents the maximum number of iterations allowed for the algorithm, and the maximum number of particles represents the number of particles in the PSO process.

Figure 4 shows the convergence behavior of the PSO algorithm over 300 iterations. The fitness function value steadily increases, indicating that the algorithm is successfully improving its solution quality with each iteration. This upward trend reflects PSO’s ability to effectively explore the solution space and optimize model parameters for transportation mode detection. The consistent improvement in fitness values supports the final classification accuracy of over 92.4%, demonstrating the robustness of the algorithm and the relevance of the selected features.

In this context, a higher fitness function value indicates better convergence and more accurate classification. As shown in Fig. 5, the fitness value rises steadily throughout the iterations, confirming that the algorithm is approaching optimal parameter settings. The increasing fitness trend is a strong indicator of the algorithm’s learning progress and its ability to generalize to accurate results. The classification variables of the algorithm include the weights assigned to each characteristic and the threshold values used in the classification process. These weights and thresholds can be utilized for classifying new data, enabling accurate transportation mode detection. Furthermore, the execution details of the algorithm, such as the solving time, are presented. The results indicate that the execution time of the algorithm was 336,635 s, reflecting the good performance but lacking efficiency in terms of time due to using a large dataset.

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To further explore the performance of the hybrid-algorithm, the confusion matrix was calculated. Recall and precision are used to measure the evaluation of the classifier's classification capability hinges on the utilization of recall and precision metrics, whose definitions are elucidated in detail by (Forman 2003). As is demonstrated in Table 3, the most elevated recall is attained for modes corresponding to walk, registering at 93.68%. This outcome was anticipated, considering the conspicuous discrepancies in various features, such as average speed and travel distance, between walk and other modes. Notably, the recall for points associated with bus and bike modes is comparably lower amongst the four modes. Regarding precision, the lowest value is observed for bus segments at 88.47%, likely due to the intermediate nature of bus-related speed features, which overlap with those of both slower modes (e.g., bicycling) and faster modes like car, leading to greater classification ambiguity.

The model leverages a two-step process, combining K-means clustering with the ANP-PSO hybrid method. The K-means clustering step effectively forms initial clusters of transportation modes without relying on labelled data, using only raw GPS data. Subsequently, the ANP-PSO hybrid method refines these clusters to achieve a high level of classification accuracy. Through this approach, we have indeed enhanced the model's performance compared to traditional methods. The results show an accurate rate of over 92.4%, surpassing previous studies using alternative techniques. This enhancement is attributed to the integration of unsupervised clustering and a hybrid approach that leverages multi-criteria decision-making and meta-heuristic optimization. It demonstrates the feasibility of accurately classifying transportation modes while minimizing dependence on labelled data.

We compared the ANP-PSO hybrid method with the Convolutional AutoEncoder (Markos and Yu 2020), Modetect algorithm (Lin et al. 2013), Expectation Maximization algorithm (Patterson et al., 2003) and masked autoregressive flow (MAF) (Dutta and Patra 2023). These methods were selected due to their relevance in transportation mode detection and their use of fully raw GPS dataset. By addressing both accuracy and execution time, the ANP-PSO hybrid method achieved outperformed results, with an accuracy of 92.4%, showcasing its effectiveness and practicality over these established approaches (Table 4).

As is shown in Table 4 below, model used by Patterson et al. (2003) obtained 58% accuracy with the Expectation Maximization algorithm, considering Velocity and standard deviation of velocity for Walk, Car, and Bus modes. Model applied by Lin et al. (2013) achieved 74% accuracy by incorporating diverse GPS input variables to classify Walk, Car, Bus, and Bike modes. Our study surpassed the others with an accuracy of 92.4% by combining clustering with multi-criteria decision-making. Markos and Yu (2020) proposes an unsupervised deep learning approach to identify transportation modes from unlabeled GPS trajectory data using a Convolutional AutoEncoder with an integrated clustering layer. The method achieves 80.5% clustering accuracy on the Geolife dataset, demonstrating the potential of unsupervised learning for transportation mode detection without relying on labeled data. In the recent study done by Dutta and Patra (2023), proposes an unsupervised learning approach for transportation mode detection that addresses the limitations of supervised methods, such as the reliance on scarce labeled data. By using point-level features and masked autoregressive flow (MAF) to estimate probability densities, followed by K-means clustering, the method effectively identifies transportation modes and outperforms traditional techniques.(Dutta and Patra 2023).

The ANP-PSO hybrid method classified Walk, bike, Car, Bus, and Train modes using GPS input variables such as average speed, mean speed, total distance, total time, average acceleration, mean bearing, maximum speed, and maximum acceleration. The comparison highlights the efficiency of diverse approaches and the potential of our clustering-based method for accurate transportation mode prediction from GPS trajectories. Our study's utilization of transportation-specific input variables and multi-criteria decision-making provided a distinct advantage in achieving higher accuracy. The results showcase promising avenues for future research in GPS trajectory analysis and transportation mode classification. The comparison presented in Table 4 is based on performance figures reported in the respective original studies and is intended to provide contextual insight rather than a direct, controlled benchmark. The listed methods were evaluated on different datasets with varying sizes, sampling frequencies, preprocessing pipelines, and parameter settings. The reported accuracies of approaches such as convolutional autoencoders and expectation–maximization models depend strongly on how GPS trajectories are segmented, how model parameters are tuned, and how labels are defined or inferred in each study. The present study did not re-implement these baseline methods on the MOBIS dataset; therefore, differences in accuracy should not be interpreted as arising solely from algorithmic superiority, but also from dataset characteristics and experimental configurations.

This study is one of the first to mention and evaluate the execution time of a transportation mode classification algorithm alongside its accuracy. The proposed hybrid ANP-PSO algorithm achieved an accuracy of over 92% in the final iteration, demonstrating strong performance in classifying transportation modes based on GPS trajectory data. The total execution time of the algorithm was approximately 336,652 s, corresponding to about 93.5 h (nearly four days) of computing time. This runtime reflects the execution of the K-means clustering and ANP–PSO optimization stages on trip-level feature representations and does not include preliminary data cleaning or raw GPS filtering. As the framework operates on aggregated trip-level features, the computational cost is primarily influenced by the number of trips and feature dimensionality, while the GPS sampling frequency affects runtime indirectly through feature extraction. This extended runtime is largely due to the algorithm’s complexity and the use of a significantly larger dataset compared to previous studies. By including execution time in the evaluation, this study offers a more comprehensive analysis of the algorithm’s practical applicability, particularly in scenarios where real-time or time-sensitive processing is required.

Comparing this with other algorithms that mainly focus on accuracy highlights the unique strength of our approach in balancing both computational efficiency and classification accuracy. The results showed that the proposed algorithm is well-suited for real-world scenarios, where rapid and reliable transportation mode detection is important.