Trajectory Anomaly Detection with Language Models (2409.15366v1)

Abstract: This paper presents a novel approach for trajectory anomaly detection using an autoregressive causal-attention model, termed LM-TAD. This method leverages the similarities between language statements and trajectories, both of which consist of ordered elements requiring coherence through external rules and contextual variations. By treating trajectories as sequences of tokens, our model learns the probability distributions over trajectories, enabling the identification of anomalous locations with high precision. We incorporate user-specific tokens to account for individual behavior patterns, enhancing anomaly detection tailored to user context. Our experiments demonstrate the effectiveness of LM-TAD on both synthetic and real-world datasets. In particular, the model outperforms existing methods on the Pattern of Life (PoL) dataset by detecting user-contextual anomalies and achieves competitive results on the Porto taxi dataset, highlighting its adaptability and robustness. Additionally, we introduce the use of perplexity and surprisal rate metrics for detecting outliers and pinpointing specific anomalous locations within trajectories. The LM-TAD framework supports various trajectory representations, including GPS coordinates, staypoints, and activity types, proving its versatility in handling diverse trajectory data. Moreover, our approach is well-suited for online trajectory anomaly detection, significantly reducing computational latency by caching key-value states of the attention mechanism, thereby avoiding repeated computations.

• The paper introduces LM-TAD, which models movement trajectories as language sequences to detect anomalies via perplexity and surprisal rates.
• The methodology leverages a transformer architecture with user-specific tokens, enabling precise, context-aware anomaly localization.
• Experimental results indicate LM-TAD outperforms autoencoder baselines on agent-specific metrics and supports real-time detection with efficient caching.

Trajectory Anomaly Detection with LLMs: LM-TAD

Introduction and Motivation

The paper "Trajectory Anomaly Detection with LLMs" (2409.15366) introduces LM-TAD, an autoregressive causal-attention model for unsupervised trajectory anomaly detection. The central premise is the analogy between natural language statements and movement trajectories: both are ordered sequences of discrete elements governed by external rules and contextual dependencies. This conceptualization enables the application of LLMing techniques to trajectory data, facilitating the identification of anomalous patterns at both the trajectory and location levels.

Figure 1: Conceptual visualization of trajectories as natural language statements, highlighting the analogy between ordered elements and contextual rules in both domains.

Model Architecture and Methodology

LM-TAD leverages a transformer-based architecture, employing token and positional embeddings, multi-head causal self-attention, and a final linear-softmax output layer. The model is trained to maximize the likelihood of observed trajectories, predicting the next location conditioned on historical context. User-specific tokens are incorporated to capture individual behavioral patterns, enabling context-aware anomaly detection.

Figure 2: Architecture of LM-TAD, illustrating the embedding layers, transformer blocks, and output prediction mechanism.

The model supports various trajectory representations, including discretized GPS coordinates, staypoints, and activity types. This flexibility is achieved by abstracting locations as tokens, allowing the model to operate on heterogeneous trajectory modalities.

Figure 3: Example of discretized GPS coordinates as input tokens for LM-TAD.

Anomaly Scoring: Perplexity and Surprisal Rate

Anomaly detection is performed using perplexity, a standard metric in LLMing, which quantifies the uncertainty in predicting the next location. High perplexity indicates low-probability (anomalous) trajectories. For localization of anomalies within trajectories, the surprisal rate is introduced, measuring the unexpectedness of individual locations given their context.

Figure 4: Surprisal rate through trajectories on the Pattern of Life dataset, demonstrating the identification of anomalous locations via elevated surprisal scores.

Thresholds for anomaly detection are computed as the mean plus standard deviation of perplexity scores, either globally or per-user, enabling both global and user-specific outlier identification.

Experimental Evaluation

Datasets

Experiments are conducted on two datasets:

• Pattern-of-Life (PoL): Simulated agent trajectories with labeled anomalies, supporting user-contextual anomaly detection.
• Porto Taxi: Real-world taxi GPS traces, with synthetic anomalies (random shift and detour) injected for evaluation.

Baselines

LM-TAD is compared against deep autoencoder (SAE), variational autoencoder (VSAE), and Gaussian mixture VSAE (GM-VSAE) baselines. All baselines use reconstruction error as the anomaly score.

Results

On the PoL dataset, LM-TAD consistently outperforms all baselines in F1 and PR-AUC for agent-specific anomaly detection. Autoencoder-based methods fail to distinguish anomalies due to overfitting and lack of user-context modeling. LM-TAD's use of user tokens and conditional likelihood estimation enables robust identification of context-dependent anomalies.

On the Porto dataset, LM-TAD achieves competitive performance with GM-VSAE for global anomaly detection, particularly excelling in random shift scenarios. For detour anomalies affecting small trajectory segments, GM-VSAE shows marginally higher sensitivity, attributed to the averaging effect in perplexity-based scoring.

Figure 5: Visualization of random shift anomalies in the Porto dataset, illustrating the perturbation of trajectory segments.

Figure 6: SAE baseline performance, highlighting its limitations in distinguishing anomalous trajectories.

Figure 7: F1 scores for random shift anomalies, demonstrating LM-TAD's competitive accuracy across anomaly types.

Ablation and Online Detection

An ablation paper confirms LM-TAD's adaptability to different location modalities (staypoints, GPS, dwell time), with staypoint labels yielding the highest anomaly detection accuracy in PoL. LM-TAD supports online anomaly detection by caching key-value states in the attention mechanism, enabling low-latency scoring of partial trajectories without recomputation.

Theoretical and Practical Implications

The LM-TAD framework advances trajectory anomaly detection by:

• Contextual Modeling: Conditioning on user and temporal tokens enables fine-grained, context-aware anomaly detection, addressing the heterogeneity of normal behavior across individuals.
• Localization: Surprisal rate facilitates precise identification of anomalous locations within trajectories, overcoming the limitations of aggregate anomaly scores.
• Modality Flexibility: The token-based approach generalizes across spatial, semantic, and temporal trajectory representations.
• Online Efficiency: KV cache utilization in transformer inference supports real-time anomaly detection, critical for applications in transportation, surveillance, and healthcare.

Future Directions

Potential avenues for further research include:

• Integration with External Knowledge: Incorporating road network constraints, POI semantics, or multimodal sensor data to enhance anomaly characterization.
• Adaptive Thresholding: Developing dynamic, context-sensitive thresholding mechanisms for anomaly scores.
• Scalability: Extending LM-TAD to large-scale, multi-agent environments with federated or distributed training.
• Explainability: Augmenting the model with interpretable attention mechanisms to elucidate the rationale behind anomaly detection decisions.

Conclusion

LM-TAD represents a significant methodological advancement in trajectory anomaly detection, leveraging LLMing paradigms to capture sequential dependencies and contextual variability in movement data. Its superior performance in user-contextual anomaly detection, competitive results in global outlier identification, and support for diverse trajectory modalities and online inference position it as a robust solution for real-world spatiotemporal anomaly detection tasks. The approach opens new possibilities for user-centric, scalable, and explainable anomaly detection in mobility analytics and related domains.