The growth of location-tracking technologies has generated large spatiotemporal datasets that require eficient analysis methods. Recent approaches focus on vectorizing the data as a preprocessing step to enable the application of of-the-shelf classical machine learning techniques. To date, such approaches have primarily been evaluated in supervised tasks. This paper presents a benchmark framework for assessing these methods in unsupervised settings, where no target labels are available. We extend and systematically evaluate four families of vectorization techniques: feature-based, shapelet-based, dictionary-based, and matrix-based. The framework assesses both clustering quality and cross-vectorization diversity through quantitative and qualitative analyses. Overall, the ifndings demonstrate that these vectorization approaches ofer a valuable option for unsupervised trajectory analysis. Additionally, our paper provides insight into which vectorization technique is most suitable for the specific characteristics of the task under analysis.
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Spatiotemporal datasets are continually expanding and include videos, social media posts, GPS traces, and other time-series data. Efective analysis of such data can have a significant societal impact, helping to address challenges in environmental and climate change, public s1e]c,uarnidtyh[ealthcare2][.
Several researchers in Mobility Data Science (M3D]Sf)oc[us on understanding and analyzing
this data and producing reports on various observed phenomena. This led to the development of
application- and data-specific procedure4]s, [which reduce the reusability of algorithms. Silva et
al. [
Although these methods achieve state-of-the-art performance in classification tasks, they have not yet been evaluated in an unsupervised setting. We therefore propose a unified benchmarking framework for evaluating trajectory vectorization techniques in such a setting. Within this framework, we formulate the problem as trajectory clustering, which is the task of identifying groups of trajectories that exhibit similar movement patterns. Despite multiple definitions of trajectory similarity, most prior work assumes that trajectories are similar if spatiall7y],cmloaskei n[g clustering based on movement
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ISSN1613-0073
Trajectory clustering consists of partitioning a set of trajectories into grousipms isluarchtrtahjaetctories are assigned to the same cluster, while dissimilar trajectories are placed in diferent clusters. In mobility research, similarity is typically interpreted as spatial proximity between tr7a]j.eIcntocroinetsr[ast, our objective is to examine a more abstract and dataset-dependent notion of similarity. For instance, given a dataset in which certain trajectories exhibit hazardous driving events, such as harsh braking, abrupt turns, or sustained high-speed intervals, we aim to determine whether, and to what extent, diferent vectorizations reveal these behavioral distinctions in the absence of labeled data.
We begin by defining the simplest type of mobility data, namely the position of an object in 2dimensional space over time. Formally: increasing timestam p.
Definition 1
(Trajectory.) A trajectory is a sequence of spatio-temporal poin ts= {(lat0, long0, 0), … , (lat , long , )} ∈ ℝ×3 where the spatial vect o⃗rs= (lat , long ) are sorted by This type of data is typically not sampled at a constant rate, as observations are often recorded irregularly due to sensor limitations, energy-saving policies, communication constraints, or event-driven acquisition processes. Additionally, trajectories into a dataset often have a diferent number of observations, so we denote by ∈ ℝ ××3
a set o f trajectories of lengatthmost . Many mobility analysis tasks can be formulated as a two-phase process: first, the data are transformed into a tabular vector representation, then analyzed using classical machine learning methods. For example, consider the following definition of the trajectory clustering task: Definition 2 (Trajectory Clusteri.ngG)iven a trajectory dat ase,tTrajectory Clustering is the task of defining a function from the space of possible input trajectoriteos an outpu t∈ denoting its cluster identity.
We can define the clustering funct ioans the composition of a vectorization fun c,twiohnich maps each trajectory to a fixed-size feature vec,taonrd a functioℎn, which maps ( ) to one cluster. By changing the vectorization funct,iotnhe definition can accommodate diferent clustering objectives.
We organize the related work around our definition of a trajectory clustering
afusntchteioconmposition of a vectorization func tiaonnd a clustering functℎiotnhat assign(s ) to a cluster. Sinℎcecan
be any of-the-shelf algorithm, such a-smeans oroptics, we first review the Mobility Data Science
(MDS) [
Vectorization techniques for MDS To better structure this section, we adopt a time series taxonomy
that categorizes approaches by the core idea underlying data transfo8r].mFaetaitounre-[based
vectorizations compute explicit motion descriptors like speed, acceleration, and heading change and aggregate
them into trajectory-level vectors; they often require the practitioner to select features appropriate to
the specific task and data characteristics, and can be sensitive to preprocessing steps like resampling or
segmentation and aggregation choic9e].sI[n shapelet-based vectorization, trajectories are represented
by their similarity to discriminative sub-trajectories, following the shapelet idea from1t0i]m. e series [
Such approaches are fully data-driven, avoiding the heavy feature engineering often required in
featurebased approaches. In MDS, the most prominent approachesMaorveelets [
Trajectory clustering and similarity objectives.Trajectory clustering groups trajectories
according to a chosen notion of similarity, largely determined by the representation and distance functions.
Existing surveys1[
Positioning of our framework. To the best of our knowledge, there is no existing framework that benchmarkscross-family trajectory vectorizations for an unsupervised clustering objective under a single, fixed evaluation pipeline; most related eforts either standardize mobility primitives (libraries) or benchmark diferent tasks and stages rather than representation families.
In this section, we propose a unified benchmarking framework, summarized in Fig1u,troe evaluate of-the-shelf trajectory vectorization techniques. Rather than asking whether two trajectories are geographically close, our framework allows us to explore how diferent vectorization techniques naturally group trajectories that share behavioral or structural similarities. To make this evaluatio transparent and reproducible, we define a common pipeline and measure both (i) clustering quality within a representation space and (ii) diversity/consistency across representation spaces. The framework is composed of 3 modules: (i) a vectorization fun ct;i(oiin) an optional dimensionality reduction step; (iii) a clustering functiℎo. nFinally, the resulting trajectory clustering is evaluated both in terms of clustering quality within each vectorization and in terms of diversity/consistency across vectorization spaces.
In the following paragraphs, we motivate the inclusion of the three modules and outline the algorithms considered for each in the experimental section. The framework is general and can accommodate a wide range of algorithms per module; the choices made here are preliminary and will be extended in future work.
Vectorization functions. The first step in our framework is selecting a set of vectorization functions
to compare. The scope of this module is to transform complex trajectory data into a tabular-like format
such that a classical of-the-shelf machine learning technique can be applied. Motivated by recent
work in mobility, we select 4 diferent functions. Additionally, inspired by the time series literature,
we divided them into feature-based, shapelet-based, dictionary-based, and matrix-based functions. For
feature-based vectorization, i.e., where explicit descriptors are extracted from the data, we selected the
Trajectory Interval ForTesItF)([
Optional feature reduction. As some vectorization functions may produce very high-dimensional or sparse feature spaces, this step aims to mitigate the curse of dimensionality. Due to their widespread use among practitioners, we selected Principal Component AnaPlCyAs)isa(nd t-distributed Stochastic Neighbor Embedding t(-SNE). We also introduced a pass-through option that allows the clustering algorithm to be executed directly on the full vectors.
Clustering algorithms. The third module applies an of-the-shelf clustering algorithm to the resulting (reduced) vectorized dataset. We consider two widely used methods from diferent fa-meilaines: for centroid-based clusteringoapntdics for density-based clustering. This selection will be expanded in future work.
This section extendGseolet to unsupervised taskGs.eolet is composed of four steps: (i) trajectory segmentation into a set of candidate discriminative sub-trajectories, (ii) sub-trajectory normalization, (iii) sub-trajectory filtering to select the most discriminative candidates, and (iv) transformation of the dataset into a dissimilarity matrix between each trajectory and the selected discriminative candidates SinceGeolet was originally proposed for supervised tasks, the filtering step relies on dataset labels to identify, through statistical tests, the most relevant discriminative sub-trajectories. We therefore focu on replacing this step with a more general approach suitable for unsupervised settings. Inspired by time series literature, we build upon the conceupntsuopfervised shapelets (u-shapelets)2[0], which extends the original notion of time series shapelets to scenarios where class labels are unavailable. The underlying intuition of the proposed work is that, even in unlabeled data, certain short subsequences tend to recur within groups of instances while remaining dissimilar to the rest of the dataset. Accordingly, a u-shapelet can be identified by assessing how efectively a candidate subsequence separates the dataset into two partitions: trajectories that contain a close match to the subsequence and those that do not. W incorporate the following iterative proceduGreeoinletto. Candidate subsequences are first extracted from a reference trajectory using spatial, temporal, or spatio-temporal sliding windows. For each candidate, a distance measure is used to compute a dissimilarity vector for all trajectories in the dataset The distance measure is defined as the minimal distance over all possible alignments of the subsequence within each trajectory. Sorting this vector produocrdeesraline, over which all possible split points are evaluated. For each split, a gap score measures the separation between the two induced groups by balancing the diference in their mean distances against their respective variances. Given a subsequence that partitions the dataset into two trajector y garnodup,sthe gap score is formally defined as: gap = − − ( + ) (1) Where and are the means of the best fitting oifn all trajectorie s inand in respectively, while and represent the standard deviations. The subsequence that maximizes this separation is selected as a discriminative subsequence. Trajectories that are well explained by the selected u-shapelet are then removed from the dataset. The process is repeated on the remaining instances to extract additional u-shapelets, until the desired number of u-shapelets has been extracted or no further splits of the remaining instances are possible.
This section lays the groundwork for shifting from continuous to discrete representations of trajectories.
We introduce a set of algorithms designed to transform trajectory data into sequences of symbols.
This discretization provides several important benefits: it enables the use of highly eficient data
structures; it simplifies storage and indexing by reducing continuous data into compact symbolic
forms; and it facilitates faster similarity searches and pattern discovery. We formally define the
problem of trajectory discretization as the composition of a normalization function and a discretization
function, i.ed.,iscretize ∘ normalize. The discretize ∶ ℝ ′×3 → Σ ′ function maps each observation
in the normalized trajectory to a symbol from an alpΣh, apbreotducing a symbolic sequence. The
normalize ∶ ℝ×3 → ℝ ′×3 function transforms the original trajectory into a normalized version.
This step serves two purposes: first, it acts as an approximation function simpialarintsoax [
Normalization We present three possible normalization strategies suited for trajectory data. The first involves resampling trajectories at constant time intervals, ensuring that observations are uniforml spaced in time. The second normalizes by constant travel distance, where a new observation is sampled each time the moving object covers a fixed spatial distance. However, due to positional noise, this method may produce redundant samples when the object is stationary. To address this, we introduce a third variant that generates a new observation only after the object has moved a minimum distance from the last sampled point, rather than after a fixed cumulative distance. In all three strategies, missing observations are interpolated, and excess ones are subsampled to preserve temporal or spatial regularity. Discretization We present several strategies for assigning a sequence of symbols to a trajectory. A ifrst, straightforward approach relies on tessellation techniques already established in the literature Figure2 (left) illustrates a conceptual example using Geoh2a2s]h, w[here each geohash region crossed by the trajectory generates a corresponding s1y.mTbhoelsame idea can be extended to other spatial partitioning methods. However, since our goal is to analyze multiple aspects of trajectories beyond mere origin–destination movement, we aim to design a discretization strategy that yields comparable symbolic vectorizations across diferent geographic contexts. One possible approach is to leverage the hierarchical structure of some tessellation encodings, such as Geohash. Leveraging this property, we can design discretization techniques based on sufix relationships among GeoHash sequences, enabling vectorizations that remain structurally consistent even when trajectories span diferent geographic areas. Figure2 (center-left) illustrates such an example. The main limitation of this approach is its reliance on a fixed spatial grid: two similar movements are represented by similar subsequences only if they occur within the same subregion. For instance, consider two right-turn events–oneCfBr”om cell “ to “AD” and another fromBC“” to “BD”. Despite being similar, the discretized subsequences difeCrB”(“ vs. “CD”) solely due to their geographic position. This spatial dependence limits the generalization of symbolic vectorizations across regions. To overcome this, we introduce two alternative discretization strategies that are independent of geographic location and instead rely on the intrinsic dynamics of motion. Specifically, thetraveling direction and theturning angle. The first computes the direction between consecutive observations and assigns symbols based on predefined angular intervals, as shown in Figure2 (center-right). The second focuses on the turning angle, i.e., the change in direction between successive segments. Revisiting the right-turn example, this vectorization consistently captures both events as the same symbolic pattern, generating the symG”btowli“ce. The resulting longest common subsequence, “AG”, efectively captures a straight movement followed by a right turn, ofering a locationand orientation-independent yet behaviorally meaningful vectorization. Additionally, to account fo stationary behavior, we introduce a dedicated symbol that indicates when the object is not moving.
This section describes the hyperparameters for vectorization, feature reduction, and clustering evaluated in our experiments. Due to limited prior knowledge of the efectiveness of these vectorization techniques for unsupervised tasks, we designed the experiments to evaluate all possible combinations of the three components. Consequently, each vectorization hyperparameter setting was evaluated with every feature reduction hyperparameter configuration, and each of those combinations was in turn evaluated with every clustering hyperparameter configuration. As the total number of experiments increases exponentially with the number of hyperparameters across modules, we prioritize extensive exploration of the vectorization hyperparameters while restricting the feature reduction and clustering stages to smaller set of representative methods and settings. 1For clarity, the figure shows the full trajectory, though after normalization each cell (symbol) correspond to a single point.
Vectorization method hyperparameters. Fortif, we explored intervals defined by the number of observations, time, or distance-based intervals. The number of intervals ranged from 2 to 20, with diferent constraints on minimum and maximum lengths. We disabled the use of latitude and longitude to avoid making position-based tasks trivialG. eFoolret, we tested diferent numbers of subsequences, from 5 up to 100, using a Geohash-based partitioning with precision levels between 3 and 7. To select the most discriminative shapelets, we experimented with the algorithm described in4.S1e.cFtoiron the distance computation between trajectories and shapelets, we tested standard Euclidean, timeinterpolated Euclidean, and space-interpolated Euclidean distaRnocSesIT.aF,owre used a time-based sliding window ranging from 10 seconds to 1 hour. For the Hough Transform, the angle resolution varied between 1° and 10°, and the image size ranged fro×m505t0o 1080×1080 pixels. Consequently, the Hough accumulator had dimensions ranging f7r0o×m18 to1527 × 180. We tested clustering using the full accumulator, its vertically summed-squared version, and its FFT transf2o3r]m.F,oasr itnh[e dictionary-based approach described4.2in,we evaluated all discretization and resampling strategies. Time-based resampling was tested every 1, 50, or 300 seconds, and distance-based resampling was tested every 3, 50, or 300 meters. For tessellation-based discretization, we used Geohash with precision levels 3 to 7 and sufix variants, ignoring the first 1 to 3 charactLeorws.er precision values help to capture movement patterns of objects traversing wide aDrieraesc.tion-based discretization employed alphabets of 4 to 16 symbols, plus one for stationarity. We then tbuf-iildtfamatrix over words extracted with sliding windows of 3 to 20 symbols.
Feature reduction hyperparameters. Regarding the feature reduction step, we evaluated several approaches commonly adopted in machine learning. In particular, we experimented with Principal Component AnalysisP(CA) and t-distributed Stochastic Neighbor Embedtd-iSnNgE(). For both methods, we tested output dimensionalities of 5, 10, 50, and 100 componentts-.SFNoEr, we additionally varied the perplexity parameter over 5-100. All remaining hyperparameters foPrCAboatnhdt-SNE were left unchanged and set to their default values as defined in the scikit-learn implem2e.nWteatdieonnote the output dimension using the symbo.l Clustering methods hyperparameters. Finally, regarding the clustering step, we limited our experiments t o-means andOPTICS. For -means, we evaluated values oefqual to 2, 3, 4, 6, and 10. ForOPTICS, we tested two values for the minimum number of samples required in the neighborhood of a point for it to be considered a core point: 5 and 10% of the trajectories in the dataset. All remaining hyperparameters were left at their default v2a.lPulesase note that clustering quality metrics were computed on the non-reduced vectorized representations. This choice was made to enable a fair comparison of clustering scores across diferent vectorization methods sharing the same hyperparameter configurations. Otherwise, such metrics would also be conditioned by the output of the feature reduction step, thereby confounding the evaluation of the vectorization methods themselves.
This section describes the datasets used in our experiments and the preprocessing steps applied. We consider both real-world and synthetic datasets. This distinction allows us to capture diferent levels of similarity to real data. Synthetic datasets are fully controlled and used to test specific, isolated aspect of the vectorization functions.
Real-world datasets. We selected five real datase3tfsor GPS trajectory classification with different sizes, semantics, and classification objectives,ani.iem.,als, vehicles, seabirds, geolife. The vehicles andgeolife datasets mainly represent road-constrained vehicle movements, whereas 2Specific default hyperparameters are available in sk-leta.lryn/r(lINN)and in the project GitHub repositotr.lyy(/oSmLh). 3animals andvehicles: t.ly/klP5 M,seabirds: t.ly/LpMx3,geolife: t.ly/FbqVa. animals andseabirds capture unconstrained animal movements on the ground and in tThaeblaei1r. (top five rows) reports descriptive statistics for the datasets, including the number of trajectories, the total number of observations, the average and standard deviation of observations per trajectory, th average sampling rate, and the number and proportion of target classesa.nFiomraltshedataset, the classification task is to recognize three species.vFeohricles, the objective is to distinguish between buses and trucks. Fosreabirds, the objective is to recognize the flying trajectories of three species of seabirds. For thgeeolife dataset, we set the classification problem to recognize trajectories of public versus private means of transport a6s]i.n [ Synthetic Datasets For synthetic datasets, we use an extended version of those introd2u4c],ed in [ consisting of a larger number of trajectories per dataset. The synthetic datasets are deliberately simple to isolate the hypothesis under analysis, minimizing confounding variables such as trafic, trafic lights, and road priorities.
To measure the extent to which diferent vectorization techniques capture the movement’s geometry, we generated two synthetic datasets shown in F3i.guTrhee first datasetS,traight-Right (SR), consists of objects that either move in a straight line or make a 90-degree right turn. Each object in this dataset travels at a constant speed for precisely 100 seconds. The secondYadoa,tisaisnestp, ired by the dataset introduced by Yao et al2.5i]n. I[t includes three distinct movement patterns: straight, circling, and bending. Unlike thSeR dataset, this dataset introduces additional complexity to the analysis task, as each object travels in a diferent direction with a variable sampling rate for a varying number of seconds between 70 and 130. We generated 100 trajectories per class, resulting in 20S0Rfdoarttahset and 300 for thYeao dataset.
Kinematic-related synthetic datasets.We generated a simple synthetic dataFseatst– Slow (FS)– of moving objects turning 90 degrees right and traveling at two diferent speeds. By isolating a specific structural movement pattern while varying the travel speed, we aim to assess the efectiveness of vectorization techniques in capturing movement dynamics without confounding efects from other variables. The target labels associated with the trajectories could be either moving “slow” or “fast”.
In this section, we analyze how distinct vectorization captures structural patterns in the data unde an unsupervised setting. Standard clustering practice often relies on the knee method or selects hyperparameters that maximize the silhouette (SIL) score. However, both heuristics depend on pairwise distances; hence, they are afected by the shape of the clusters. Additionally, clustering is applied in the vectorized space; therefore, these metrics can be used only when comparing clustering outcomes derived from the same vectorization type and configuration. In our framework, we compute the SIL score in the non-reduced vectorization spaces, enabling the use of this metric to compare clustering results across various feature reduction techniques. Additionally, since our datasets include class labels, we use them #trj #obs #obs per trj AvgΔtime (s)
Classes Animals 102 15k as a proxy for ground truth and select, for each component of the pipeline, the hyperparameters that maximize the Fowlkes–Mallows (FM) score. Alternative heuristics to select the best clustering results without any prior knowledge are left as future work. SIL and FM scores alone do not characterize diferences between feature spaces; they only quantify cluster separation and agreement with the labeled structure. To evaluate how the relative positions of instances vary across vectorizations o diferent dimensionality, we exploit the Triplet Loss introduc2e6d],ian w[idely used one-shot learning loss function that encourages embeddings in which similar instances are close together, and dissimilar instances are far apart. In our framework, we adopt a variant called Random TripletrtAac)c,uracy ( proposed in [27], to measure the impact of feature reduction techniques. This measure operates by randomly sampling triplets of instances from two feature spaces and evaluating the proportion of triplets in which the relative distance ordering between instances is preserved across both spaces. A score near 1 indicates that both spaces encode instance relationships consistently, while a score near 0 suggests that they reverse these relationships, placing samples that are close in one space farther apart in the other. Figur4eillustrates three scenarios. In the first, 90 instances are randomly projected into two unrelated feature spaces. Srintcaesamples triplets at random, we repeat the evaluation 100 times and obtain an average score≈o0f.50, indicating that an ordering sucehda(,s) ≤ ed(, ) in one space fails to hold in the other in roughly half of the cases. In the second scenario, both vectorizations yield the same three clusters; however, the points are randomly arranged within each cluster, and the orange cluster is closer to diferent neighbors across the two spaces. Under the same experimental conditions, the resulting score is approximately 0.70. Please note that such a scenario would have the same FM score and approximately the same SIL score. Finally, in the third scenario, the vectorizations difer only by scale, leading to a score close to 1.
Tables2 and3 present the experimental results on vectorization diversity, reported thrrtoaugh the score, and clustering quality, reported through the SIL and FM scores. The optimal pipeline for each vectorization and dataset is selected using the FM score2. aTdadbilteionally reports the SIL score associated with the pipeline that maximizes the FM score, as well as the FM and SIL scores of the pipeline that performs best with respect to the SIL score, thereby simulating a selection process that relies solely on internal clustering criteria.
We begin by examining the upper part of Tab2l,ewhich reports the FM and SIL scores of the pipeline achieving the highest FM. To facilitate interpretation, FM and SIL scores are averaged across datasets with the same characteristics: shape-based, kinematic-based, and real-world trajectories. By selecting the pipeline that maximizes FtMif, achieves the overall best performance across all datasets. NotablyR,oSITa performs particularly well on geometry-based datasets, which aligns with its design. MoreoverG,eolet consistently attains the overall best SIL scores, indicating an average higher degree of cluster separation w.r.t. other vectorization techniques, which can be attributed to its sub-trajector ifltering strategy based on tghaep score. For the other vectorizations, we do not observe any interesting patter4n. Instead, selecting the best pipeline that maximizes SIL yields slightly lower FM scores across all vectorization methods and dataset categories. On the other side, SIL scores are extremely high for most datasets and vectorization techniques. Our interpretation is as follows: we found pipelines with high FM or SIL scores, which means that, for some vectorization hyperparameters, each vectorization is able to discover clusters similar to the ground truth or produce vectorization spaces with well-separated clusters, but with lower similarity to the ground truth. While this highlights the flexibility of such vectorization in capturing higher-level mobility patterns beyond mere spatial proximity, it also makes it dificult for practitioners to determine the optimal hyperparameters without additional information about the data.
Despite that, several consistent trends emerge from the results2i.nTThaebtleif vectorization 4We would like to recall the dependencies between SIL scores and vectorization spaces. As a result, we can only consider the single SIL score, comparison between vectorization methods or diferent datasets may be misleading y tif etr Geolet eom RoSITa G tf-idf ic tif ta Geolet m in RoSITa e K tf-idf lrd tif ow Geolet ea RoSITa l R tf-idf
tif demonstrates the highest overall FM values across almost all dataset categories. This indicates that the handcrafted feature extraction pipeline efectively captures both spatial and temporal properties of movement, producing clusters that closely correspond to the actual labeled classes. GCeoonlveetrsely, achieves superior performance on real-world datasets, where data are more complex, irregular, and noisy. This suggests that shapelet-based vectorizations are especially well-suited to capture localized movement variations or subpatterns (e.g., turns, stops, or loops) that often define behavior in natural or human mobility. The relatively lower SIL values, combined with high FM scores, indicate that, whileGeolet clusters may be less compact geometrically, they still align closely with the semantic ground truth. ThReoSITa vectorization performs best on geometry-related datasets, as expected due to its design for rotation- and scale-invariant shape encoding. This confirms that geometric alignment is particularly important when trajectories exhibit clear structural regularitiReos.SIHTao’wsever, performance drops slightly on datasets dominated by dynamic diferences, suggesting its invariance properties may suppress meaningful kinematic variation. Fitnfa–lildyf, (dictionary-based) achieves competitive results on real-world datasets, suggesting significant potential for this technique.
Table3 reports threta scores between pairs of vectorizations across all dataset categories. Vectorization hyperparameters follow the configuration that yielded the highest FM score. Overall, the scores obtained by comparing diferent transformation spaces average a0r.o54u3n,dwith values reaching up to0.714 for specific dataset–vectorization combinations. As illustrated in4, Feingtuirreely unrelated vectorizations typically yield a score of about 0.500, while points that fall into the same clusters but difer in their cluster-wise positioning tend to produce scores near 0.700. Interpreting these results benefits from revisiting Tabl2e, particularly the FM values. Since the FM score, defined as the geometric mean of precision and recall, ranges f0rotmo1 and reflects cluster similarity, its generally high values here suggest that morstta scores correspond to cases where clusters are similar but difer in their internal positioning.
The highestrta values ≈( 0.714) occur betweenGeolet andRoSITa for geometry-based datasets, suggesting that although the methods rely on diferent principles, they capture similar global structure. In contrast, the lowerstta values ≈( 0.500) appear betweenGeolet andtf–idf in real-world datasets, reflecting a fundamental diference between local shapelet patterns and symbolic discretization. These relationships highlight the complementarity among vectorization families. From a practical perspective, the reporterdta scores suggest promising research avenues for ensemble or hybrid vectorizations.
To qualitatively observe such complementarity, we now examine representative embedding spaces for the selected datasets. Fig5uprreesents 2D PCA projections ftoirf, Geolet, andRoSITa (left to right). For thSeR dataset (top row), all three embedding spaces clearly separate instances by their true clusters. FoFSr (bottom row), where classes difer only in movement speteidf, yields a clean separation, whereas the 2D projection ofRtohSeITa space collapses the instances into a single point. Nonetheless, its FM score is nearly optimal, indicating that the collapse is a visual artefact of PCA. The Geolet projection also appears scattered randomly. However, its FM score of 0.705 suggests that, despite the imperfect visualization, meaningful separation persists in this balanced binary setting.
We introduced a benchmark framework for evaluating alternative trajectory vectorizations for unsu pervised clustering. By comparing representative vectorization families on real-world and synthetic datasets, we analyzed how sub-trajectory dynamics and geometry are reflected in diferent vector spaces. The results show that vectorization choice substantially afects clustering, that methods performing well under controlled conditions may not generalize to noisy real-world data, and that diferent vectorizations capture complementary (not redundant) information, as indicated by mrotdaevraaltuees. We also observe that relying on a single metric (e.g., SIL or FM) can be misleading, whereas combining internal and external criteria supports more robust model selection. At a finer level, feature-based methods are efective for motion dynamics, shapelet-based methods capture local geometric variatRiooSnI,Taand performs strongly on geometry-dominated datasets. These findings motivate future work on multivectorization ensembles, fusion strategies, and broader evaluation across more datasets, vectorizations, and clustering algorithms.
During the preparation of this work, the author(s) used ChatGPT-4 and Grammarly to perform grammar and spelling checks. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content.
This work has been partly supported by the University of Piraeus Research Center.
GeoInformatica 29 (2025) 999–1032. [25] D. Yao, C. Zhang, Z. Zhu, J. Huang, J. Bi, Trajectory clustering via deep representation learning, in: IEEE IJCNN, 2017, pp. 3880–3887. [26] F. Schrof, D. Kalenichenko, J. Philbin, Facenet: A unified embedding for face recognition and clustering, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2015, pp. 815–823. [27] Y. Wang, H. Huang, C. Rudin, Y. Shaposhnik, Understanding how dimension reduction tools work: An empirical approach to deciphering t-sne, umap, trimap, and pacmap for data visualization, J. Mach. Learn. Res. 22 (2021) 201:1–201:73.