Accurate and Efficient Multivariate Time Series Forecasting via Offline Clustering

Accurate and efficient multivariate time series (MTS) forecasting is essential for applications such as traffic management and weather prediction, which depend on capturing long-range temporal dependencies and interactions between entities. Existing methods, particularly those based on Transformer architectures, compute pairwise dependencies across all time steps, leading to a computational complexity that scales quadratically with the length of the input. To overcome these challenges, we introduce the Forecaster with Offline Clustering Using Segments (FOCUS), a novel approach to MTS forecasting that simplifies long-range dependency modeling through the use of prototypes extracted via offline clustering. These prototypes encapsulate high-level events in the real-world system underlying the data, summarizing the key characteristics of similar time segments. In the online phase, FOCUS dynamically adapts these patterns to the current input and captures dependencies between the input segment and high-level events, enabling both accurate and efficient forecasting. By identifying prototypes during the offline clustering phase, FOCUS reduces the computational complexity of modeling long-range dependencies in the online phase to linear scaling. Extensive experiments across diverse benchmarks demonstrate that FOCUS achieves state-of-the-art accuracy while significantly reducing computational costs.

Ranked differences Pearson correlation dissimilarity with an application to electricity users time series clustering

Time series clustering is an unsupervised learning method for classifying time series data into groups with similar behavior. It is used in applications such as healthcare, finance, economics, energy, and climate science. Several time series clustering methods have been introduced and used for over four decades. Most of them focus on measuring either Euclidean distances or association dissimilarities between time series. In this work, we propose a new dissimilarity measure called ranked Pearson correlation dissimilarity (RDPC), which combines a weighted average of a specified fraction of the largest element-wise differences with the well-known Pearson correlation dissimilarity. It is incorporated into hierarchical clustering. The performance is evaluated and compared with existing clustering algorithms. The results show that the RDPC algorithm outperforms others in complicated cases involving different seasonal patterns, trends, and peaks. Finally, we demonstrate our method by clustering a random sample of customers from a Thai electricity consumption time series dataset into seven groups with unique characteristics.

LLM4FTS: Enhancing Large Language Models for Financial Time Series Prediction

Predicting financial time series presents significant challenges due to inherent low signal-to-noise ratios and intricate temporal patterns. Traditional machine learning models exhibit limitations in this forecasting task constrained by their restricted model capacity. Recent advances in large language models (LLMs), with their greatly expanded parameter spaces, demonstrate promising potential for modeling complex dependencies in temporal sequences. However, existing LLM-based approaches typically focus on fixed-length patch analysis due to the Transformer architecture, ignoring market data's multi-scale pattern characteristics. In this study, we propose $LLM4FTS$, a novel framework that enhances LLM capabilities for temporal sequence modeling through learnable patch segmentation and dynamic wavelet convolution modules. Specifically,we first employ K-means++ clustering based on DTW distance to identify scale-invariant patterns in market data. Building upon pattern recognition results, we introduce adaptive patch segmentation that partitions temporal sequences while preserving maximal pattern integrity. To accommodate time-varying frequency characteristics, we devise a dynamic wavelet convolution module that emulates discrete wavelet transformation with enhanced flexibility in capturing time-frequency features. These three modules work together to improve large language model's ability to handle scale-invariant patterns in financial time series. Extensive experiments on real-world financial datasets substantiate the framework's efficacy, demonstrating superior performance in capturing complex market patterns and achieving state-of-the-art results in stock return prediction. The successful deployment in practical trading systems confirms its real-world applicability, representing a significant advancement in LLM applications for financial forecasting.

Geospatial and Temporal Trends in Urban Transportation: A Study of NYC Taxis and Pathao Food Deliveries

Urban transportation plays a vital role in modern city life, affecting how efficiently people and goods move around. This study analyzes transportation patterns using two datasets: the NYC Taxi Trip dataset from New York City and the Pathao Food Trip dataset from Dhaka, Bangladesh. Our goal is to identify key trends in demand, peak times, and important geographical hotspots. We start with Exploratory Data Analysis (EDA) to understand the basic characteristics of the datasets. Next, we perform geospatial analysis to map out high-demand and low-demand regions. We use the SARIMAX model for time series analysis to forecast demand patterns, capturing seasonal and weekly variations. Lastly, we apply clustering techniques to identify significant areas of high and low demand. Our findings provide valuable insights for optimizing fleet management and resource allocation in both passenger transport and food delivery services. These insights can help improve service efficiency, better meet customer needs, and enhance urban transportation systems in diverse urban environments.

Early Detection of Multidrug Resistance Using Multivariate Time Series Analysis and Interpretable Patient-Similarity Representations

Background and Objectives: Multidrug Resistance (MDR) is a critical global health issue, causing increased hospital stays, healthcare costs, and mortality. This study proposes an interpretable Machine Learning (ML) framework for MDR prediction, aiming for both accurate inference and enhanced explainability. Methods: Patients are modeled as Multivariate Time Series (MTS), capturing clinical progression and patient-to-patient interactions. Similarity among patients is quantified using MTS-based methods: descriptive statistics, Dynamic Time Warping, and Time Cluster Kernel. These similarity measures serve as inputs for MDR classification via Logistic Regression, Random Forest, and Support Vector Machines, with dimensionality reduction and kernel transformations improving model performance. For explainability, patient similarity networks are constructed from these metrics. Spectral clustering and t-SNE are applied to identify MDR-related subgroups and visualize high-risk clusters, enabling insight into clinically relevant patterns. Results: The framework was validated on ICU Electronic Health Records from the University Hospital of Fuenlabrada, achieving an AUC of 81%. It outperforms baseline ML and deep learning models by leveraging graph-based patient similarity. The approach identifies key risk factors -- prolonged antibiotic use, invasive procedures, co-infections, and extended ICU stays -- and reveals clinically meaningful clusters. Code and results are available at \https://github.com/oscarescuderoarnanz/DM4MTS. Conclusions: Patient similarity representations combined with graph-based analysis provide accurate MDR prediction and interpretable insights. This method supports early detection, risk factor identification, and patient stratification, highlighting the potential of explainable ML in critical care.

Flexibility of German gas-fired generation: evidence from clustering empirical operation

A key input to energy models are assumptions about the flexibility of power generation units, i.e., how quickly and often they can start up. These assumptions are usually calibrated on the technical characteristics of the units, such as installed capacity or technology type. However, even if power generation units technically can dispatch flexibly, service obligations and market incentives may constrain their operation. Here, we cluster over 60% of German national gas generation (generation units of 100 MWp or above) based on their empirical flexibility. We process the hourly dispatch of sample units between 2019 and 2023 using a novel deep learning approach, that transforms time series into easy-to-cluster representations. We identify two clusters of peaker units and two clusters of non-peaker units, whose different empirical flexibility is quantified by cluster-level ramp rates. Non-peaker units, around half of the sample, are empirically less flexible than peakers, and make up for more than 83% of sample must-run generation. Regulatory changes addressing the low market responsiveness of non-peakers are needed to unlock their flexibility.

Adapting to the Unknown: Robust Meta-Learning for Zero-Shot Financial Time Series Forecasting

Financial time series forecasting in the zero-shot setting is essential for risk management and investment decision-making, particularly during abrupt market regime shifts or in emerging markets with limited historical data. While Model-Agnostic Meta-Learning (MAML)-based approaches have shown promise in this domain, existing meta task construction strategies often lead to suboptimal performance, especially when dealing with highly turbulent financial time series. To address this challenge, we propose a novel task construction method that leverages learned embeddings for more effective meta-learning in the zero-shot setting. Specifically, we construct two complementary types of meta-tasks based on the learned embeddings: intra-cluster tasks and inter-cluster tasks. To capture diverse fine-grained patterns, we apply stochastic projection matrices to the learned embeddings and use clustering algorithm to form the tasks. Additionally, to improve generalization capabilities, we employ hard task mining strategies and leverage inter-cluster tasks to identify invariant patterns across different time series. Extensive experiments on the real world financial dataset demonstrate that our method significantly outperforms existing approaches, showing better generalization ability in the zero-shot scenario.

ProtoECGNet: Case-Based Interpretable Deep Learning for Multi-Label ECG Classification with Contrastive Learning

Deep learning-based electrocardiogram (ECG) classification has shown impressive performance but clinical adoption has been slowed by the lack of transparent and faithful explanations. Post hoc methods such as saliency maps may fail to reflect a model's true decision process. Prototype-based reasoning offers a more transparent alternative by grounding decisions in similarity to learned representations of real ECG segments, enabling faithful, case-based explanations. We introduce ProtoECGNet, a prototype-based deep learning model for interpretable, multi-label ECG classification. ProtoECGNet employs a structured, multi-branch architecture that reflects clinical interpretation workflows: it integrates a 1D CNN with global prototypes for rhythm classification, a 2D CNN with time-localized prototypes for morphology-based reasoning, and a 2D CNN with global prototypes for diffuse abnormalities. Each branch is trained with a prototype loss designed for multi-label learning, combining clustering, separation, diversity, and a novel contrastive loss that encourages appropriate separation between prototypes of unrelated classes while allowing clustering for frequently co-occurring diagnoses. We evaluate ProtoECGNet on all 71 diagnostic labels from the PTB-XL dataset, demonstrating competitive performance relative to state-of-the-art black-box models while providing structured, case-based explanations. To assess prototype quality, we conduct a structured clinician review of the final model's projected prototypes, finding that they are rated as representative and clear. ProtoECGNet shows that prototype learning can be effectively scaled to complex, multi-label time-series classification, offering a practical path toward transparent and trustworthy deep learning models for clinical decision support.

Virtual Target Trajectory Prediction for Stochastic Targets

Trajectory prediction of other vehicles is crucial for autonomous vehicles, with applications from missile guidance to UAV collision avoidance. Typically, target trajectories are assumed deterministic, but real-world aerial vehicles exhibit stochastic behavior, such as evasive maneuvers or gliders circling in thermals. This paper uses Conditional Normalizing Flows, an unsupervised Machine Learning technique, to learn and predict the stochastic behavior of targets of guided missiles using trajectory data. The trained model predicts the distribution of future target positions based on initial conditions and parameters of the dynamics. Samples from this distribution are clustered using a time series k-means algorithm to generate representative trajectories, termed virtual targets. The method is fast and target-agnostic, requiring only training data in the form of target trajectories. Thus, it serves as a drop-in replacement for deterministic trajectory predictions in guidance laws and path planning. Simulated scenarios demonstrate the approach's effectiveness for aerial vehicles with random maneuvers, bridging the gap between deterministic predictions and stochastic reality, advancing guidance and control algorithms for autonomous vehicles.

Fuzzy Cluster-Aware Contrastive Clustering for Time Series

The rapid growth of unlabeled time series data, driven by the Internet of Things (IoT), poses significant challenges in uncovering underlying patterns. Traditional unsupervised clustering methods often fail to capture the complex nature of time series data. Recent deep learning-based clustering approaches, while effective, struggle with insufficient representation learning and the integration of clustering objectives. To address these issues, we propose a fuzzy cluster-aware contrastive clustering framework (FCACC) that jointly optimizes representation learning and clustering. Our approach introduces a novel three-view data augmentation strategy to enhance feature extraction by leveraging various characteristics of time series data. Additionally, we propose a cluster-aware hard negative sample generation mechanism that dynamically constructs high-quality negative samples using clustering structure information, thereby improving the model's discriminative ability. By leveraging fuzzy clustering, FCACC dynamically generates cluster structures to guide the contrastive learning process, resulting in more accurate clustering. Extensive experiments on 40 benchmark datasets show that FCACC outperforms the selected baseline methods (eight in total), providing an effective solution for unsupervised time series learning.