arXiv subjects

Christian S. Jensen

Publications and source records attributed to Christian S. Jensen.

At least 37 records · Page 2Linked to original sources

arXiv2026

VISTA: Knowledge-Driven Vessel Trajectory Imputation with Repair Provenance

Repairing incomplete trajectory data is essential for downstream spatio-temporal applications. Yet, existing repair methods focus solely on reconstruction without documenting the reasoning behind repair decisions, undermining trust in safety-critical applications where repaired trajectories affect operational decisions, such as in maritime anomaly detection and route planning. We introduce repair provenance - structured, queryable metadata that documents the full reasoning chain behind each repair - which transforms imputation from pure data recovery into a task that supports downstream decision-making. We propose VISTA (knowledge-driven interpretable vessel trajectory imputation), a framework that reliably equips repaired trajectories with repair provenance by grounding LLM reasoning in data-verified knowledge. Specifically, we formalize Structured Data-derived Knowledge (SDK), a knowledge model whose data-verifiable components can be validated against real data and used to anchor and constrain LLM-generated explanations. We organize SDK in a Structured Data-derived Knowledge Graph (SD-KG) and establish a data-knowledge-data loop for extraction, validation, and incremental maintenance over large-scale AIS data. A workflow management layer with parallel scheduling, fault tolerance, and redundancy control ensures consistent and efficient end-to-end processing. Experiments on two large-scale AIS datasets show that VISTA achieves state-of-the-art accuracy, improving over baselines by 5-91% and reducing inference time by 51-93%, while producing repair provenance, whose interpretability is further validated through a case study and an interactive demo system.

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arXiv2026

A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective

Multivariate Time Series Forecasting (MTSF) plays a crucial role across diverse fields, ranging from economic, energy, to traffic. In recent years, deep learning has demonstrated outstanding performance in MTSF tasks. In MTSF, modeling the correlations among different channels is critical, as leveraging information from other related channels can significantly improve the prediction accuracy of a specific channel. This study systematically reviews the channel modeling strategies for time series and proposes a taxonomy organized into three hierarchical levels: the strategy perspective, the mechanism perspective, and the characteristic perspective. On this basis, we provide a structured analysis of these methods and conduct an in-depth examination of the advantages and limitations of different channel strategies. Finally, we summarize and discuss some future research directions to provide useful research guidance. Moreover, we maintain an up-to-date Github repository (https://github.com/decisionintelligence/CS4TS) which includes all the papers discussed in the survey.

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arXiv2026

TimeART: Towards Agentic Time Series Reasoning via Tool-Augmentation

Time series data widely exist in real-world cyber-physical systems. Though analyzing and interpreting them contributes to significant values, e.g, disaster prediction and financial risk control, current workflows mainly rely on human data scientists, which requires significant labor costs and lacks automation. To tackle this, we introduce TimeART, a framework fusing the analytical capability of strong out-of-the-box tools and the reasoning capability of Large Language Models (LLMs), which serves as a fully agentic data scientist for Time Series Question Answering (TSQA). To teach the LLM-based Time Series Reasoning Models (TSRMs) strategic tool-use, we also collect a 100k expert trajectory corpus called TimeToolBench. To enhance TSRMs' generalization capability, we then devise a four-stage training strategy, which boosts TSRMs through learning from their own early experiences and self-reflections. Experimentally, we train an 8B TSRM on TimeToolBench and equip it with the TimeART framework, and it achieves consistent state-of-the-art performance on multiple TSQA tasks, which pioneers a novel approach towards agentic time series reasoning.

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arXiv2026

Vector Search for the Future: From Memory-Resident, Static Heterogeneous Storage, to Cloud-Native Architectures

Vector search (VS) has become a fundamental component in multimodal data management, enabling core functionalities such as image, video, and code retrieval. As vector data scales rapidly, VS faces growing challenges in balancing search, latency, scalability, and cost. The evolution of VS has been closely driven by changes in storage architecture. Early VS methods rely on all-in-memory designs for low latency, but scalability is constrained by memory capacity and cost. To address this, recent research has adopted heterogeneous architectures that offload space-intensive vectors and index structures to SSDs, while exploiting block locality and I/O-efficient strategies to maintain high search performance at billion scale. Looking ahead, the increasing demand for trillion-scale vector retrieval and cloud-native elasticity is driving a further shift toward memory-SSD-object storage architectures, which enable cost-efficient data tiering and seamless scalability. In this tutorial, we review the evolution of VS techniques from a storage-architecture perspective. We first review memory-resident methods, covering classical IVF, hash, quantization, and graph-based designs. We then present a systematic overview of heterogeneous storage VS techniques, including their index designs, block-level layouts, query strategies, and update mechanisms. Finally, we examine emerging cloud-native systems and highlight open research opportunities for future large-scale vector retrieval systems.

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arXiv2026

DeXOR: Enabling XOR in Decimal Space for Streaming Lossless Compression of Floating-point Data

With streaming floating-point numbers being increasingly prevalent, effective and efficient compression of such data is critical. Compression schemes must be able to exploit the similarity, or smoothness, of consecutive numbers and must be able to contend with extreme conditions, such as high-precision values or the absence of smoothness. We present DeXOR, a novel framework that enables decimal XOR procedure to encode decimal-space longest common prefixes and suffixes, achieving optimal prefix reuse and effective redundancy elimination. To ensure accurate and low-cost decompression even with binary-decimal conversion errors, DeXOR incorporates 1) scaled truncation with error-tolerant rounding and 2) different bit management strategies optimized for decimal XOR. Additionally, a robust exception handler enhances stability by managing floating-point exponents, maintaining high compression ratios under extreme conditions. In evaluations across 22 datasets, DeXOR surpasses state-of-the-art schemes, achieving a 15% higher compression ratio and a 20% faster decompression speed while maintaining a competitive compression speed. DeXOR also offers scalability under varying conditions and exhibits robustness in extreme scenarios where other schemes fail.

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arXiv2025

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

Trajectory similarity computation is fundamental functionality that is used for, e.g., clustering, prediction, and anomaly detection. However, existing learning-based methods exhibit three key limitations: (1) insufficient modeling of trajectory semantics and hierarchy, lacking both movement dynamics extraction and multi-scale structural representation; (2) high computational costs due to point-wise encoding; and (3) use of physically implausible augmentations that distort trajectory semantics. To address these issues, we propose MovSemCL, a movement-semantics contrastive learning framework for trajectory similarity computation. MovSemCL first transforms raw GPS trajectories into movement-semantics features and then segments them into patches. Next, MovSemCL employs intra- and inter-patch attentions to encode local as well as global trajectory patterns, enabling efficient hierarchical representation and reducing computational costs. Moreover, MovSemCL includes a curvature-guided augmentation strategy that preserves informative segments (e.g., turns and intersections) and masks redundant ones, generating physically plausible augmented views. Experiments on real-world datasets show that MovSemCL is capable of outperforming state-of-the-art methods, achieving mean ranks close to the ideal value of 1 at similarity search tasks and improvements by up to 20.3% at heuristic approximation, while reducing inference latency by up to 43.4%.

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arXiv2025

Beyond Relational: Semantic-Aware Multi-Modal Analytics with LLM-Native Query Optimization

Multi-modal analytical processing has the potential to transform applications in e-commerce, healthcare, entertainment, and beyond. However, real-world adoption remains elusive due to the limited ability of traditional relational query operators to capture query semantics. The emergence of foundation models, particularly the large language models (LLMs), opens up new opportunities to develop flexible, semantic-aware data analytics systems that transcend the relational paradigm. We present Nirvana, a multi-modal data analytics framework that incorporates programmable semantic operators while leveraging both logical and physical query optimization strategies, tailored for LLM-driven semantic query processing. Nirvana addresses two key challenges. First, it features an agentic logical optimizer that uses natural language-specified transformation rules and random-walk-based search to explore vast spaces of semantically equivalent query plans -- far beyond the capabilities of conventional optimizers. Second, it introduces a cost-aware physical optimizer that selects the most effective LLM backend for each operator using a novel improvement-score metric. To further enhance efficiency, Nirvana incorporates computation reuse and evaluation pushdown techniques guided by model capability hypotheses. Experimental evaluations on three real-world benchmarks demonstrate that Nirvana is able to reduce end-to-end runtime by 10%--85% and reduces system processing costs by 76% on average, outperforming state-of-the-art systems at both efficiency and scalability.

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arXiv2025

AutoHFormer: Efficient Hierarchical Autoregressive Transformer for Time Series Prediction

Time series forecasting requires architectures that simultaneously achieve three competing objectives: (1) strict temporal causality for reliable predictions, (2) sub-quadratic complexity for practical scalability, and (3) multi-scale pattern recognition for accurate long-horizon forecasting. We introduce AutoHFormer, a hierarchical autoregressive transformer that addresses these challenges through three key innovations: 1) Hierarchical Temporal Modeling: Our architecture decomposes predictions into segment-level blocks processed in parallel, followed by intra-segment sequential refinement. This dual-scale approach maintains temporal coherence while enabling efficient computation. 2) Dynamic Windowed Attention: The attention mechanism employs learnable causal windows with exponential decay, reducing complexity while preserving precise temporal relationships. This design avoids both the anti-causal violations of standard transformers and the sequential bottlenecks of RNN hybrids. 3) Adaptive Temporal Encoding: a novel position encoding system is adopted to capture time patterns at multiple scales. It combines fixed oscillating patterns for short-term variations with learnable decay rates for long-term trends. Comprehensive experiments demonstrate that AutoHFormer 10.76X faster training and 6.06X memory reduction compared to PatchTST on PEMS08, while maintaining consistent accuracy across 96-720 step horizons in most of cases. These breakthroughs establish new benchmarks for efficient and precise time series modeling. Implementations of our method and all baselines in hierarchical autoregressive mechanism are available at https://github.com/lizzyhku/Autotime.

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arXiv2025

ACTIVE: Continuous Similarity Search for Vessel Trajectories

Publicly available vessel trajectory data is emitted continuously from the global AIS system. Continuous trajectory similarity search on this data has applications in, e.g., maritime navigation and safety. Existing proposals typically assume an offline setting and focus on finding similarities between complete trajectories. Such proposals are less effective when applied to online scenarios, where similarity comparisons must be performed continuously as new trajectory data arrives and trajectories evolve. We therefore propose a real-time continuous trajectory similarity search method for vessels (ACTIVE). We introduce a novel similarity measure, object-trajectory real-time distance, that emphasizes the anticipated future movement trends of vessels, enabling more predictive and forward-looking comparisons. Next, we propose an efficient continuous similar trajectory search (CSTS) algorithm together with a segment-based vessel trajectory index and a variety of search space pruning strategies that reduce unnecessary computations during the continuous similarity search, thereby further improving efficiency. Extensive experiments on two large real-world AIS datasets offer evidence that ACTIVE is capable of outperforming state-of-the-art methods considerably. ACTIVE significantly reduces index construction costs and index size while achieving a 70% reduction in terms of query time and a 60% increase in terms of hit rate.

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arXiv2025

MH-GIN: Multi-scale Heterogeneous Graph-based Imputation Network for AIS Data (Extended Version)

Location-tracking data from the Automatic Identification System, much of which is publicly available, plays a key role in a range of maritime safety and monitoring applications. However, the data suffers from missing values that hamper downstream applications. Imputing the missing values is challenging because the values of different heterogeneous attributes are updated at diverse rates, resulting in the occurrence of multi-scale dependencies among attributes. Existing imputation methods that assume similar update rates across attributes are unable to capture and exploit such dependencies, limiting their imputation accuracy. We propose MH-GIN, a Multi-scale Heterogeneous Graph-based Imputation Network that aims improve imputation accuracy by capturing multi-scale dependencies. Specifically, MH-GIN first extracts multi-scale temporal features for each attribute while preserving their intrinsic heterogeneous characteristics. Then, it constructs a multi-scale heterogeneous graph to explicitly model dependencies between heterogeneous attributes to enable more accurate imputation of missing values through graph propagation. Experimental results on two real-world datasets find that MH-GIN is capable of an average 57% reduction in imputation errors compared to state-of-the-art methods, while maintaining computational efficiency. The source code and implementation details of MH-GIN are publicly available https://github.com/hyLiu1994/MH-GIN.

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arXiv2025

An Encode-then-Decompose Approach to Unsupervised Time Series Anomaly Detection on Contaminated Training Data--Extended Version

Time series anomaly detection is important in modern large-scale systems and is applied in a variety of domains to analyze and monitor the operation of diverse systems. Unsupervised approaches have received widespread interest, as they do not require anomaly labels during training, thus avoiding potentially high costs and having wider applications. Among these, autoencoders have received extensive attention. They use reconstruction errors from compressed representations to define anomaly scores. However, representations learned by autoencoders are sensitive to anomalies in training time series, causing reduced accuracy. We propose a novel encode-then-decompose paradigm, where we decompose the encoded representation into stable and auxiliary representations, thereby enhancing the robustness when training with contaminated time series. In addition, we propose a novel mutual information based metric to replace the reconstruction errors for identifying anomalies. Our proposal demonstrates competitive or state-of-the-art performance on eight commonly used multi- and univariate time series benchmarks and exhibits robustness to time series with different contamination ratios.

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arXiv2025

Comprehending Spatio-temporal Data via Cinematic Storytelling using Large Language Models

Spatio-temporal data captures complex dynamics across both space and time, yet traditional visualizations are complex, require domain expertise and often fail to resonate with broader audiences. Here, we propose MapMuse, a storytelling-based framework for interpreting spatio-temporal datasets, transforming them into compelling, narrative-driven experiences. We utilize large language models and employ retrieval augmented generation (RAG) and agent-based techniques to generate comprehensive stories. Drawing on principles common in cinematic storytelling, we emphasize clarity, emotional connection, and audience-centric design. As a case study, we analyze a dataset of taxi trajectories. Two perspectives are presented: a captivating story based on a heat map that visualizes millions of taxi trip endpoints to uncover urban mobility patterns; and a detailed narrative following a single long taxi journey, enriched with city landmarks and temporal shifts. By portraying locations as characters and movement as plot, we argue that data storytelling drives insight, engagement, and action from spatio-temporal information. The case study illustrates how MapMuse can bridge the gap between data complexity and human understanding. The aim of this short paper is to provide a glimpse to the potential of the cinematic storytelling technique as an effective communication tool for spatio-temporal data, as well as to describe open problems and opportunities for future research.

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arXiv2025

Advancing Knowledge Tracing by Exploring Follow-up Performance Trends

Intelligent Tutoring Systems (ITS), such as Massive Open Online Courses, offer new opportunities for human learning. At the core of such systems, knowledge tracing (KT) predicts students' future performance by analyzing their historical learning activities, enabling an accurate evaluation of students' knowledge states over time. We show that existing KT methods often encounter correlation conflicts when analyzing the relationships between historical learning sequences and future performance. To address such conflicts, we propose to extract so-called Follow-up Performance Trends (FPTs) from historical ITS data and to incorporate them into KT. We propose a method called Forward-Looking Knowledge Tracing (FINER) that combines historical learning sequences with FPTs to enhance student performance prediction accuracy. FINER constructs learning patterns that facilitate the retrieval of FPTs from historical ITS data in linear time; FINER includes a novel similarity-aware attention mechanism that aggregates FPTs based on both frequency and contextual similarity; and FINER offers means of combining FPTs and historical learning sequences to enable more accurate prediction of student future performance. Experiments on six real-world datasets show that FINER can outperform ten state-of-the-art KT methods, increasing accuracy by 8.74% to 84.85%.

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arXiv2025

TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods

Time series are generated in diverse domains such as economic, traffic, health, and energy, where forecasting of future values has numerous important applications. Not surprisingly, many forecasting methods are being proposed. To ensure progress, it is essential to be able to study and compare such methods empirically in a comprehensive and reliable manner. To achieve this, we propose TFB, an automated benchmark for Time Series Forecasting (TSF) methods. TFB advances the state-of-the-art by addressing shortcomings related to datasets, comparison methods, and evaluation pipelines: 1) insufficient coverage of data domains, 2) stereotype bias against traditional methods, and 3) inconsistent and inflexible pipelines. To achieve better domain coverage, we include datasets from 10 different domains: traffic, electricity, energy, the environment, nature, economic, stock markets, banking, health, and the web. We also provide a time series characterization to ensure that the selected datasets are comprehensive. To remove biases against some methods, we include a diverse range of methods, including statistical learning, machine learning, and deep learning methods, and we also support a variety of evaluation strategies and metrics to ensure a more comprehensive evaluations of different methods. To support the integration of different methods into the benchmark and enable fair comparisons, TFB features a flexible and scalable pipeline that eliminates biases. Next, we employ TFB to perform a thorough evaluation of 21 Univariate Time Series Forecasting (UTSF) methods on 8,068 univariate time series and 14 Multivariate Time Series Forecasting (MTSF) methods on 25 datasets. The benchmark code and data are available at https://github.com/decisionintelligence/TFB. We have also launched an online time series leaderboard: https://decisionintelligence.github.io/OpenTS/OpenTS-Bench/.

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arXiv2025

Skeleton-Guided Learning for Shortest Path Search

Shortest path search is a core operation in graph-based applications, yet existing methods face important limitations. Classical algorithms such as Dijkstra's and A* become inefficient as graphs grow more complex, while index-based techniques often require substantial preprocessing and storage. Recent learning-based approaches typically focus on spatial graphs and rely on context-specific features like geographic coordinates, limiting their general applicability. We propose a versatile learning-based framework for shortest path search on generic graphs, without requiring domain-specific features. At the core of our approach is the construction of a skeleton graph that captures multi-level distance and hop information in a compact form. A Skeleton Graph Neural Network (SGNN) operates on this structure to learn node embeddings and predict distances and hop lengths between node pairs. These predictions support LSearch, a guided search algorithm that uses model-driven pruning to reduce the search space while preserving accuracy. To handle larger graphs, we introduce a hierarchical training strategy that partitions the graph into subgraphs with individually trained SGNNs. This structure enables HLSearch, an extension of our method for efficient path search across graph partitions. Experiments on five diverse real-world graphs demonstrate that our framework achieves strong performance across graph types, offering a flexible and effective solution for learning-based shortest path search.

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arXiv2025

TAB: Unified Benchmarking of Time Series Anomaly Detection Methods

Time series anomaly detection (TSAD) plays an important role in many domains such as finance, transportation, and healthcare. With the ongoing instrumentation of reality, more time series data will be available, leading also to growing demands for TSAD. While many TSAD methods already exist, new and better methods are still desirable. However, effective progress hinges on the availability of reliable means of evaluating new methods and comparing them with existing methods. We address deficiencies in current evaluation procedures related to datasets and experimental settings and protocols. Specifically, we propose a new time series anomaly detection benchmark, called TAB. First, TAB encompasses 29 public multivariate datasets and 1,635 univariate time series from different domains to facilitate more comprehensive evaluations on diverse datasets. Second, TAB covers a variety of TSAD methods, including Non-learning, Machine learning, Deep learning, LLM-based, and Time-series pre-trained methods. Third, TAB features a unified and automated evaluation pipeline that enables fair and easy evaluation of TSAD methods. Finally, we employ TAB to evaluate existing TSAD methods and report on the outcomes, thereby offering a deeper insight into the performance of these methods. Besides, all datasets and code are available at https://github.com/decisionintelligence/TAB.

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arXiv2025

OneDB: A Distributed Multi-Metric Data Similarity Search System

Increasingly massive volumes of multi-modal data are being accumulated in many {real world} settings, including in health care and e-commerce. This development calls for effective general-purpose data management solutions for multi-modal data. Such a solution must facilitate user-friendly and accurate retrieval of any multi-modal data according to diverse application requirements. Further, such a solution must be capable of efficient and scalable retrieval. To address this need, we present OneDB, a distributed multi-metric data similarity retrieval system. This system exploits the fact that data of diverse modalities, such as text, images, and video, can be represented as metric data. The system thus affords each data modality its own metric space with its own distance function and then uses a multi-metric model to unify multi-modal data. The system features several innovations: (i) an extended Spart SQL query interface; (ii) lightweight means of learning appropriate weights of different modalities when retrieving multi-modal data to enable accurate retrieval; (iii) smart search-space pruning strategies that improve efficiency; (iv) two-layered indexing of data to ensure load-balancing during distributed processing; and (v) end-to-end system parameter autotuning. Experiments on three real-life datasets and two synthetic datasets offer evidence that the system is capable of state-of-the-art performance: (i) efficient and effective weight learning; (ii) retrieval accuracy improvements of 12.63\%--30.75\% over the state-of-the-art vector similarity search system at comparable efficiency; (iii) accelerated search by 2.5--5.75x over state-of-the-art single- or multi-metric solutions; (iv) demonstrated high scalability; and (v) parameter tuning that enables performance improvements of 15+%.

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arXiv2025

Gaussian Process Latent Variable Modeling for Few-shot Time Series Forecasting

Accurate time series forecasting is crucial for optimizing resource allocation, industrial production, and urban management, particularly with the growth of cyber-physical and IoT systems. However, limited training sample availability in fields like physics and biology poses significant challenges. Existing models struggle to capture long-term dependencies and to model diverse meta-knowledge explicitly in few-shot scenarios. To address these issues, we propose MetaGP, a meta-learning-based Gaussian process latent variable model that uses a Gaussian process kernel function to capture long-term dependencies and to maintain strong correlations in time series. We also introduce Kernel Association Search (KAS) as a novel meta-learning component to explicitly model meta-knowledge, thereby enhancing both interpretability and prediction accuracy. We study MetaGP on simulated and real-world few-shot datasets, showing that it is capable of state-of-the-art prediction accuracy. We also find that MetaGP can capture long-term dependencies and can model meta-knowledge, thereby providing valuable insights into complex time series patterns.

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