Skip to content

MovSemCL: Movement-Semantics Contrastive Learning for Trajectory Similarity (Extension)

Conference: AAAI 2026 arXiv: 2511.12061 Code: https://github.com/ryanlaics/MovSemCL Area: Self-Supervised Learning / Trajectory Analysis Keywords: trajectory similarity, contrastive learning, movement semantics, hierarchical encoding, curvature-guided augmentation

TL;DR

This paper proposes MovSemCL, a framework that transforms GPS trajectories into movement-semantic features (displacement vectors + heading angles + Node2Vec spatial graph embeddings), achieves hierarchical encoding via patch-level two-stage attention (reducing complexity from \(O(L^2)\) to near-linear), and designs Curvature-Guided Augmentation (CGA) to preserve behaviorally critical segments such as turns and intersections. The framework achieves a mean rank approaching the ideal value of 1 on trajectory retrieval tasks while reducing inference latency by 43.4%.

Background & Motivation

Background: Trajectory similarity computation is a fundamental function for ride-sharing, logistics optimization, and urban analytics. Traditional methods (Hausdorff, Fréchet distance) are computationally expensive and semantics-agnostic; learning-based methods (RNN/CNN/Transformer) embed trajectories into vector spaces for efficient cosine-similarity retrieval.

Three Core Limitations: - (L1) Insufficient semantic and hierarchical modeling: Existing methods treat trajectories as flat coordinate sequences, neither extracting movement dynamics (velocity changes, direction shifts) nor modeling the hierarchical structure of points → maneuvers → trips. - (L2) Poor computational efficiency: Real-world trajectories often contain hundreds of points. RNNs cannot be parallelized, and the \(O(L^2)\) attention of Transformers forces lossy downsampling, degrading motion fidelity. - (L3) Semantics-agnostic augmentation: Random masking in contrastive learning causes spatial discontinuities, while uniform sampling discards turn/intersection information, producing physically implausible trajectory views.

Key Insight: The three limitations are addressed by dedicated designs—movement-semantics encoding (L1), patch-based hierarchical encoding (L1+L2), and curvature-guided augmentation (L3)—which together constitute a unified framework.

Method

Overall Architecture

MovSemCL consists of three stages: (1) Movement-Semantics Encoding, which converts raw GPS into movement-semantic features; (2) Hierarchical Semantics Encoding, which applies two-stage attention over patches; and (3) Semantics-Aware Contrastive Learning, which trains with CGA augmentation and a MoCo-style contrastive loss.

Stage 1: Movement-Semantics Encoding

  • Coordinate normalization: WGS84 latitude/longitude is first projected to a planar coordinate system via Mercator projection, then normalized to \([0,1]\) by region width and height.
  • Movement dynamics features: Displacement vectors \((dx_i, dy_i)\) and heading angles \(\theta_i = \arctan2(dy_i, dx_i)/\pi\) are computed between consecutive points to capture directional flow and instantaneous changes.
  • Trajectory-induced spatial graph: The map is partitioned into an \(N_x \times N_y\) grid; a directed weighted graph is constructed from transition frequencies between adjacent cells in historical trajectories, and Node2Vec is applied to learn structural embeddings \(\mathbf{ST}_i \in \mathbb{R}^{d_{se}}\) per cell.
  • Feature concatenation: The final representation of each point is \(\mathbf{f}_i = [dx_i, dy_i, \theta_i, \mathbf{ST}_i] \in \mathbb{R}^{d_{in}}\), where the first three dimensions encode local motion and the spatial embedding encodes global context.

Stage 2: Hierarchical Semantics Encoding

  • Patch construction: A sequence of length \(L\) is divided into \(M = \lceil L/P \rceil\) patches (\(P=4\)), each representing a locally coherent motion unit.
  • Intra-Patch Attention: Self-attention is applied within each patch to capture local motion patterns, followed by masked average pooling to compress each patch into a fixed-length vector \(\mathbf{h}_j\).
  • Inter-Patch Attention: Self-attention over the sequence of patch embeddings captures global long-range dependencies and overall trajectory intent.
  • Complexity advantage: Complexity is reduced from \(O(L^2)\) to \(O(L \cdot P + M^2)\); since \(M \ll L\) for typical trajectory lengths, this achieves near-linear scaling.

Stage 3: Semantics-Aware Contrastive Learning

  • Curvature-Guided Augmentation (CGA): The local turning angle is computed at each trajectory point; points with large angles (turns/intersections) receive high retention weights, while points with small angles (straight-line redundancy) are more likely to be masked. Start and end points are always retained. A multinomial sampling procedure selects the mask set using weights proportional to \((1 - p_i)\).
  • Distinction from naive augmentation: Random masking produces spatial discontinuities; uniform sampling loses critical turn information; block masking may remove entire key maneuvers. CGA retains segments with the highest behavioral information density.
  • Contrastive objective: The MoCo framework is adopted. Two CGA-augmented views of each trajectory serve as a positive pair, with embeddings of other trajectories as negatives. Temperature \(\tau = 0.05\); the query encoder is updated via backpropagation and the key encoder via exponential moving average.

CGA Algorithm Details

  1. Compute the turning angle \(\alpha_i\) at each interior point (arccos of the angle between adjacent displacement vectors).
  2. Normalize to \([0,1]\) and assign retention weights: endpoints receive \(w_{\text{endpoint}}\); interior points receive \(w_{\text{base}} + \hat{\alpha}_i \cdot w_{\text{direction}}\).
  3. After normalization to a probability distribution, sample \(\lfloor L \cdot r_{\text{mask}} \rfloor\) points for masking via multinomial sampling with weights \((1-p_i)\).
  4. Time complexity is \(O(L)\); controllable parameters include the mask ratio and the weight triple.

Key Experimental Results

Datasets

Dataset Source Avg. Points Avg. Length Characteristics
Porto Portuguese taxi trajectories (2013–2014) 48 6.37 km Dense urban short trips
Germany Cross-city German trajectories (2006–2013) 72 252.49 km Sparse long-distance routes

Main Results

Trajectory Retrieval (RQ1)

On a 100K database, MovSemCL achieves a mean rank of 1.005 (Porto) and 1.008 (Germany), approaching the ideal value of 1. TrajCL achieves 1.010 and 1.045, respectively, while the traditional method EDR reaches as high as 28.75 and 1370.

Robustness (RQ2)

  • Downsampling: At a mask probability of 0.5, TrajCL degrades to a mean rank of 36.35 on Porto, while MovSemCL reaches only 9.95.
  • Coordinate distortion: At a distortion rate of 0.5, MovSemCL maintains a mean rank of approximately 1.004 (Porto), demonstrating strong noise robustness.

Heuristic Distance Approximation (RQ3)

After fine-tuning to approximate traditional distances (EDR, Hausdorff, Fréchet), MovSemCL achieves the best average rank across all metrics. HR@5 for EDR improves by 20.3% over TrajCL (0.172 → 0.207).

Efficiency (RQ4)

Metric TrajCL MovSemCL Gain
FLOPs (M) 158.69 93.34 41.2%
Latency (ms) 6.08 3.44 43.4%
Throughput (samples/s) 164.46 290.41 76.6%

Ablation Study (RQ5)

On Porto 100K: removing Movement-Semantics Encoding (MSE) degrades mean rank from 1.005 to 3.045 (largest impact); removing CGA degrades it to 1.098; removing Hierarchical Semantics Encoding (HSE) degrades it to 1.012. MSE is the most critical component.

Hyperparameter Analysis (RQ6)

  • Convergence is achieved within 10 epochs; training stabilizes at 20 epochs without overfitting.
  • As few as 20K training trajectories suffice for convergence under standard conditions.
  • Embedding dimension 256 is optimal; further increases yield no significant gain.
  • Patch size \(P=4\) is optimal—smaller patches lack local context, while larger patches dilute movement semantics.

Highlights & Insights

  • Curvature-Guided Augmentation (CGA) is the most creative design in this work: rather than random masking, it selectively retains critical segments based on motion complexity, balancing physical plausibility with semantic richness.
  • Movement-semantic features (displacement + heading angle + spatial graph embeddings) carry far greater information density than raw coordinates; ablation studies confirm they are the primary performance driver.
  • Patch-based hierarchical encoding elegantly reduces \(O(L^2)\) attention to \(O(L \cdot P + M^2)\), balancing efficiency and expressiveness for long trajectories.
  • The paper is exceptionally well-structured: three identified limitations correspond one-to-one to three design components, forming a clear logical chain.
  • The MoCo contrastive framework with a dynamic negative queue ensures training stability.

Limitations & Future Work

  • Node2Vec embeddings for the spatial graph depend on trajectory coverage in the training set—effective embeddings may not be obtainable for new or data-sparse regions.
  • Patch size \(P\) is a fixed hyperparameter; different scenarios (urban vs. highway) may require different settings.
  • Evaluation is conducted on only two datasets; non-vehicular trajectories (pedestrian, cycling) are not assessed.
  • The CGA weight triple \((w_{\text{endpoint}}, w_{\text{base}}, w_{\text{direction}})\) requires manual tuning.
  • Traditional methods: EDR (edit distance with spatial threshold), Hausdorff (maximum nearest-neighbor distance), Fréchet (order-aware spatiotemporal distance) → computationally expensive and semantics-agnostic.
  • RNN-based methods: t2vec (seq2seq autoencoder) → TrjSR / E2DTC (recurrent + attention) → non-parallelizable with weak long-range dependency modeling.
  • Transformer + contrastive learning: TrajCL (trajectory augmentation + dual-feature attention), CLEAR (multi-positive contrastive learning) → \(O(L^2)\) complexity with semantics-agnostic augmentation.
  • Positioning of MovSemCL: The first work to unify movement-semantic feature extraction, hierarchical patch encoding, and semantics-aware augmentation within a contrastive learning framework.

Rating

  • Novelty: ⭐⭐⭐⭐ — CGA is novel and practical; the combination of movement semantics and hierarchical encoding reflects thoughtful design.
  • Experimental Thoroughness: ⭐⭐⭐⭐ — Six research questions, multi-dataset evaluation, efficiency analysis, complete ablation and hyperparameter studies.
  • Writing Quality: ⭐⭐⭐⭐ — Three limitations mapped to three design components; clear and coherent structure.
  • Value: ⭐⭐⭐⭐ — Provides an efficient and semantically rich complete solution for trajectory representation learning.