Unified Taxonomy for Multivariate Time Series Anomaly Detection using Deep Learning

The topic of Multivariate Time Series Anomaly Detection (MTSAD) has grown rapidly over the past years, with a steady rise in publications and Deep Learning (DL) models becoming the dominant paradigm. To address the lack of systematization in the field, this study introduces a novel and unified taxonomy with eleven dimensions over three parts (Input, Output and Model) for the categorization of DL-based MTSAD methods. The dimensions were established in a two-fold approach. First, they derived from a comprehensive analysis of methodological studies. Second, insights from review papers were incorporated. Furthermore, the proposed taxonomy was validated using an additional set of recent publications, providing a clear overview of methodological trends in MTSAD. Results reveal a convergence toward Transformer-based and reconstruction and prediction models, setting the foundation for emerging adaptive and generative trends. Building on and complementing existing surveys, this unified taxonomy is designed to accommodate future developments, allowing for new categories or dimensions to be added as the field progresses. This work thus consolidates fragmented knowledge in the field and provides a reference point for future research in MTSAD.

MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting

Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to address the frequency (spectral) leakage restricting high-quality low-rank decomposition, MLOW enables a flexible selection of input horizons and frequency levels via a mathematical mechanism. Visual analysis demonstrates that MLOW enables interpretable and hierarchical multiple-effect decomposition, robust to noises. It can also enable plug-and-play in existing TSF backbones with remarkable performance improvement but minimal architectural modifications.

Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing

Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical thresholds, known as tipping points, pose a prediction problem of both theoretical and practical significance, yet remain largely unresolved. To address this, we articulate a model-free framework that integrates the measures characterizing the stability and sensitivity of dynamical systems with the reservoir computing (RC), a lightweight machine learning technique, using only observational time series data. The framework consists of two stages. The first stage involves using RC to robustly learn local complex dynamics from observational data segmented into windows. The second stage focuses on accurately detecting early warning signals of tipping points by analyzing the learned autonomous RC dynamics through dynamical measures, including the dominant eigenvalue of the Jacobian matrix, the maximum Floquet multiplier, and the maximum Lyapunov exponent. Furthermore, when these dynamical measures exhibit trend-like patterns, their extrapolation enables ultra-early prediction of tipping points significantly prior to the occurrence of critical transitions. We conduct a rigorous theoretical analysis of the proposed method and perform extensive numerical evaluations on a series of representative synthetic systems and eight real-world datasets, as well as quantitatively predict the tipping time of the Atlantic Meridional Overturning Circulation system. Experimental results demonstrate that our framework exhibits advantages over the baselines in comprehensive evaluations, particularly in terms of dynamical interpretability, prediction stability and robustness, and ultra-early prediction capability.

Unpaired Cross-Domain Calibration of DMSP to VIIRS Nighttime Light Data Based on CUT Network

Defense Meteorological Satellite Program (DMSP-OLS) and Suomi National Polar-orbiting Partnership (SNPP-VIIRS) nighttime light (NTL) data are vital for monitoring urbanization, yet sensor incompatibilities hinder long-term analysis. This study proposes a cross-sensor calibration method using Contrastive Unpaired Translation (CUT) network to transform DMSP data into VIIRS-like format, correcting DMSP defects. The method employs multilayer patch-wise contrastive learning to maximize mutual information between corresponding patches, preserving content consistency while learning cross-domain similarity. Utilizing 2012-2013 overlapping data for training, the network processes 1992-2013 DMSP imagery to generate enhanced VIIRS-style raster data. Validation results demonstrate that generated VIIRS-like data exhibits high consistency with actual VIIRS observations (R-squared greater than 0.87) and socioeconomic indicators. This approach effectively resolves cross-sensor data fusion issues and calibrates DMSP defects, providing reliable attempt for extended NTL time-series.

Deep Learning Network-Temporal Models For Traffic Prediction

Time series analysis is critical for emerging net- work intelligent control and management functions. However, existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time series. The intricate topological interdependency and complex temporal patterns in network data demand new model approaches. In this paper, based on a systematic multivariate time series model study, we present two deep learning models aiming for learning both temporal patterns and network topological correlations at the same time: a customized network-temporal graph attention network (GAT) model and a fine-tuned multi-modal large language model (LLM) with a clustering overture. Both models are studied against an LSTM model that already outperforms the statistical methods. Through extensive training and performance studies on a real-world network dataset, the LLM-based model demonstrates superior overall prediction and generalization performance, while the GAT model shows its strength in reducing prediction variance across the time series and horizons. More detailed analysis also reveals important insights into correlation variability and prediction distribution discrepancies over time series and different prediction horizons.

Multimodal Deep Learning for Early Prediction of Patient Deterioration in the ICU: Integrating Time-Series EHR Data with Clinical Notes

Early identification of patients at risk for clinical deterioration in the intensive care unit (ICU) remains a critical challenge. Delayed recognition of impending adverse events, including mortality, vasopressor initiation, and mechanical ventilation, contributes to preventable morbidity and mortality. We present a multimodal deep learning approach that combines structured time-series data (vital signs and laboratory values) with unstructured clinical notes to predict patient deterioration within 24 hours. Using the MIMIC-IV database, we constructed a cohort of 74,822 ICU stays and generated 5.7 million hourly prediction samples. Our architecture employs a bidirectional LSTM encoder for temporal patterns in physiologic data and ClinicalBERT embeddings for clinical notes, fused through a cross-modal attention mechanism. We also present a systematic review of existing approaches to ICU deterioration prediction, identifying 31 studies published between 2015 and 2024. Most existing models rely solely on structured data and achieve area under the curve (AUC) values between 0.70 and 0.85. Studies incorporating clinical notes remain rare but show promise for capturing information not present in structured fields. Our multimodal model achieves a test AUROC of 0.7857 and AUPRC of 0.1908 on 823,641 held-out samples, with a validation-to-test gap of only 0.6 percentage points. Ablation analysis validates the multimodal approach: clinical notes improve AUROC by 2.5 percentage points and AUPRC by 39.2% relative to a structured-only baseline, while deep learning models consistently outperform classical baselines (XGBoost AUROC: 0.7486, logistic regression: 0.7171). This work contributes both a thorough review of the field and a reproducible multimodal framework for clinical deterioration prediction.

Effective Dataset Distillation for Spatio-Temporal Forecasting with Bi-dimensional Compression

Spatio-temporal time series are widely used in real-world applications, including traffic prediction and weather forecasting. They are sequences of observations over extensive periods and multiple locations, naturally represented as multidimensional data. Forecasting is a central task in spatio-temporal analysis, and numerous deep learning methods have been developed to address it. However, as dataset sizes and model complexities continue to grow in practice, training deep learning models has become increasingly time- and resource-intensive. A promising solution to this challenge is dataset distillation, which synthesizes compact datasets that can effectively replace the original data for model training. Although successful in various domains, including time series analysis, existing dataset distillation methods compress only one dimension, making them less suitable for spatio-temporal datasets, where both spatial and temporal dimensions jointly contribute to the large data volume. To address this limitation, we propose STemDist, the first dataset distillation method specialized for spatio-temporal time series forecasting. A key idea of our solution is to compress both temporal and spatial dimensions in a balanced manner, reducing training time and memory. We further reduce the distillation cost by performing distillation at the cluster level rather than the individual location level, and we complement this coarse-grained approach with a subset-based granular distillation technique that enhances forecasting performance. On five real-world datasets, we show empirically that, compared to both general and time-series dataset distillation methods, datasets distilled by our STemDist method enable model training (1) faster (up to 6X) (2) more memory-efficient (up to 8X), and (3) more effective (with up to 12% lower prediction error).

FreqCycle: A Multi-Scale Time-Frequency Analysis Method for Time Series Forecasting

Mining time-frequency features is critical for time series forecasting. Existing research has predominantly focused on modeling low-frequency patterns, where most time series energy is concentrated. The overlooking of mid to high frequency continues to limit further performance gains in deep learning models. We propose FreqCycle, a novel framework integrating: (i) a Filter-Enhanced Cycle Forecasting (FECF) module to extract low-frequency features by explicitly learning shared periodic patterns in the time domain, and (ii) a Segmented Frequency-domain Pattern Learning (SFPL) module to enhance mid to high frequency energy proportion via learnable filters and adaptive weighting. Furthermore, time series data often exhibit coupled multi-periodicity, such as intertwined weekly and daily cycles. To address coupled multi-periodicity as well as long lookback window challenges, we extend FreqCycle hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions. Extensive experiments on seven diverse domain benchmarks demonstrate that FreqCycle achieves state-of-the-art accuracy while maintaining faster inference speeds, striking an optimal balance between performance and efficiency.

The Density of Cross-Persistence Diagrams and Its Applications

Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of these features across scales. While effective for analyzing individual manifolds, persistence diagrams do not account for interactions between pairs of them. Cross-persistence diagrams (cross-barcodes), introduced recently, address this limitation by characterizing relationships between topological features of two point clouds. In this work, we present the first systematic study of the density of cross-persistence diagrams. We prove its existence, establish theoretical foundations for its statistical use, and design the first machine learning framework for predicting cross-persistence density directly from point cloud coordinates and distance matrices. Our statistical approach enables the distinction of point clouds sampled from different manifolds by leveraging the linear characteristics of cross-persistence diagrams. Interestingly, we find that introducing noise can enhance our ability to distinguish point clouds, uncovering its novel utility in TDA applications. We demonstrate the effectiveness of our methods through experiments on diverse datasets, where our approach consistently outperforms existing techniques in density prediction and achieves superior results in point cloud distinction tasks. Our findings contribute to a broader understanding of cross-persistence diagrams and open new avenues for their application in data analysis, including potential insights into time-series domain tasks and the geometry of AI-generated texts. Our code is publicly available at https://github.com/Verdangeta/TDA_experiments

Geometric Framework for Robust Order Detection in Delay-Coordinates Dynamic Mode Decomposition

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced by noise and order overestimation. We show that model order detection and mode selection in DC-DMD are fundamentally problems of subspace geometry. Specifically, true modes are characterized by concentration within a low-dimensional signal subspace, whereas spurious modes necessarily retain non-negligible components outside any moderate overestimate of that subspace. This geometric distinction yields a perturbation-robust definition of true and spurious modes and yields fully data-driven selection criteria. This geometric framework leads to two complementary data-driven selection criteria. The first is derived directly from the geometric distinction and uses a data-driven proxy of the signal-subspace to compute a residual score. The second arises from a new operator-theoretic analysis of delay embedding. Using a block-companion formulation, we show that all modes exhibit a Kronecker-Vandermonde (KV) structure induced by the delay-coordinates, and true modes are distinguished by the degree to which they conform to it. Importantly, we also show that this deviation is governed precisely by the geometric residual. In addition, our analysis provides a principled explanation for the empirical behavior of magnitude- and norm-based heuristics, clarifying when and why they fail under delay-coordinates. Extensive numerical experiments confirm the theoretical predictions and demonstrate that the proposed geometric and structure-based methods achieve robust and accurate order detection and mode selection, consistently better than existing baselines across noise levels, spectral separations, damping regimes, and embedding lengths.