Federated domain generalization (FDG) for time-series classification (TSC) poses a critical challenge for modern intelligent web services, which rely on edge-collected time-series signals from diverse mobile applications and web devices (e.g., wearables sensors) to support decision-making. The source heterogeneity and temporal dynamics give rise to out-of-distribution (OOD) patterns, which hinder the model's ability to generalize to previously unseen users and devices. In this work, we propose Federated Generalization via Diversity Generation (FedDiG), a diffusion-based FDG framework that captures intra-client distribution shifts from a frequency-domain perspective and employs cross-frequency sampling to synthesize time-series data with diverse spectral patterns. Specifically, FedDiG first performs frequency-proxy representation learning on clients to serve as diffusion conditions. The server then aggregates client-side frequency proxies to construct a global proxy pool and applies class-wise mixup to create novel frequency features. These features guide a global diffusion model to produce diverse data, enabling the simulation of previously unseen patterns and thereby enhancing model training. Extensive experiments on four cross-domain time-series benchmarks demonstrate that FedDiG significantly outperforms state-of-the-art federated learning and FDG baselines, particularly under small-data regimes and large-scale client scenarios, achieving robust generalization to unseen domains in federated settings. This work bridges distribution-diversity synthesis and FDG for time-series to support robust, scalable web applications fed by edge-collected signals, delivering web-scale generalization across heterogeneous web, mobile, and IoT clients.

In long-term series forecasting (LTSF), it is imperative for models to adeptly discern and distill from historical time series data to forecast future states. Although Transformer-based models excel at capturing long-term dependencies in LTSF, their practical use is limited by issues like computational inefficiency, noise sensitivity, and overfitting on smaller datasets. Therefore, we introduce a novel time series lightweight interactive Mamba with an adaptive Fourier filter model (Affirm). Specifically, (i) we propose an adaptive Fourier filter block. This neural operator employs Fourier analysis to refine feature representation, reduces noise with learnable adaptive thresholds, and captures inter-frequency interactions using global and local semantic adaptive Fourier filters via element-wise multiplication. (ii) A dual interactive Mamba block is introduced to facilitate efficient intra-modal interactions at different granularities, capturing more detailed local features and broad global contextual information, providing a more comprehensive representation for LTSF. Extensive experiments on multiple benchmarks demonstrate that Affirm consistently outperforms existing SOTA methods, offering a superior balance of accuracy and efficiency, making it ideal for various challenging scenarios with noise levels and data sizes.

Single-domain generalization (SDG) in time series classification (TSC) poses significant challenges for current time-series domain generalization methods due to the extremely limited data available from only one source domain. In this study, we propose Segment-dErived Expansion of Domains (SEED), a diffusion-based method that effectively expands domain diversity for SDG. We reveal that individual instances exhibit intrinsic temporal shifts over time, which provides a principled foundation for creating multiple pseudo domains by segmenting each instance into distinct parts. To do so, SEED extracts two complementary representations from each time-series segment: 1) a segment-specific representation that captures diverse distributional variations, and 2) a segment-invariant representation that preserves class semantics. SEED formulates these representations as pseudo-domain prompts to guide a diffusion model in generating diverse yet semantically consistent time-series data. Additionally, SEED introduces a novel prompt-fused sampling for diffusion, enabling flexible recombination of segment-specific features to continuously expand the pseudo-domain space. We provide both theoretical analysis and extensive empirical evaluations on four widely used TSC benchmarks to validate its ability in reducing generalization error and improving model's performances in SDG. In our experiments, SEED significantly improves classification accuracy by 7.68% on average compared to the strong baselines.

Learning time series representations with sparse labels presents notable challenges. The surge in unsupervised contrastive learning has garnered increasing interest due to its immense advancements in deriving meaningful representations in semi-supervised settings, typically involving a two-stage process: pretraining on large unlabeled data followed by fine-tuning with few labeled samples. However, this approach has inherent drawbacks: poor knowledge transfer, reduced generalizability, and failure to directly utilize unsupervised contrastive loss from pretraining and valuable supervised loss guided by ground truth to impact the downstream tasks. In response, we introduce a novel end-to-end semi-supervised framework, Semi4TSF, for time series forecasting (TSF). It optimizes unsupervised loss on massive unlabeled data and integrates supervised contrastive and forecasting losses on limited labeled data, enabling the model to see other unlabeled embeddings meanwhile learning useful labeled embeddings, improving generalization. The three losses are jointly to refine the encoder and forecaster. Specifically, the unsupervised learning module applies two instance-wise augmentation banks over the entire series to capture long-term dependencies, suggests a learnable Fourier layer, and fuses temporal and frequency information to uncover intricate temporal-frequency correlations through cross-domain interactions to capture nuanced representations. Extensive experiments on five benchmarks demonstrate that Semi4TSF is an effective and superior end-to-end framework that fills the gap in semi-supervised TSF.

In traffic flow prediction, the efficacy of deep learning models is largely contingent upon the availability of extensive training datasets, presenting a formidable challenge in data-scarce environments. Transfer learning has emerged as a promising strategy to address this challenge by leveraging abundant data from source cities to enhance predictive accuracy in target cities with limited data. Nonetheless, existing methods frequently neglect the distinct characteristics and interrelationships among various regions within cities, leading to predominantly city-level knowledge transfers that underutilize the potential of transferred information. In this paper, we present SERT, a fine-grained regional knowledge transfer method specifically designed to mitigate data scarcity in traffic flow prediction. SERT initiates the process by establishing relationships between source and target regions through the integration of satellite imagery and Points of Interest (POI) data, effectively capturing region-specific features to create matched region pairs. Subsequently, we propose an innovative contrastive domain adaptation strategy to align the features of these matched regions, thereby facilitating inter-regional knowledge transfer while maximizing the feature distance of unmatched regions to reduce interference from irrelevant data. This approach enables the effective transfer of valuable knowledge from the source cities to its relevant counterparts in the target city. Comprehensive experimental results demonstrate that SERT outperforms existing methods in terms of prediction accuracy while ensuring significant computational efficiency. The code is available at https://github.com/MobiXg/SERT

Existing domain generalization (DG) methods for cross-person sensor-based activity recognition tasks often struggle to capture both intra- and inter-domain style diversity, leading to significant domain gaps with the target domain. In this study, we explore a novel perspective to tackle this problem, a process conceptualized as domain padding. This proposal aims to enrich the domain diversity by synthesizing intra- and inter-domain style data while maintaining robustness to class labels. We instantiate this concept using a conditional diffusion model and introduce a style-fused sampling strategy to enhance data generation diversity, termed Diversified Intra- and Inter-domain distributions via activity Style-fused Diffusion modeling (DI2SDiff). In contrast to traditional condition-guided sampling, our style-fused sampling strategy allows for the flexible use of one or more random style representations from the same class to guide data synthesis. This feature presents a notable advancement: it allows for the maximum utilization of possible combinations among existing styles to generate a broad spectrum of new style instances. We further extend DI2SDiff into DI2SDiff++ by enhancing the diversity of style guidance. Specifically, DI2SDiff++ integrates a multi-head style conditioner to provide multiple distinct, decomposed substyles and introduces a substyle-fused sampling strategy that allows cross-class substyle fusion for broader guidance. Empirical evaluations on a wide range of datasets demonstrate that our generated data achieves remarkable diversity within the domain space. Both intra- and inter-domain generated data have been proven significant and valuable, enabling DI2SDiff and DI2SDiff++ to surpass state-of-the-art DG methods in various cross-person activity recognition tasks.

Existing domain generalization (DG) methods for cross-person generalization tasks often face challenges in capturing intra- and inter-domain style diversity, resulting in domain gaps with the target domain. In this study, we explore a novel perspective to tackle this problem, a process conceptualized as domain padding. This proposal aims to enrich the domain diversity by synthesizing intra- and inter-domain style data while maintaining robustness to class labels. We instantiate this concept using a conditional diffusion model and introduce a style-fused sampling strategy to enhance data generation diversity. In contrast to traditional condition-guided sampling, our style-fused sampling strategy allows for the flexible use of one or more random styles to guide data synthesis. This feature presents a notable advancement: it allows for the maximum utilization of possible permutations and combinations among existing styles to generate a broad spectrum of new style instances. Empirical evaluations on a broad range of datasets demonstrate that our generated data achieves remarkable diversity within the domain space. Both intra- and inter-domain generated data have proven to be significant and valuable, contributing to varying degrees of performance enhancements. Notably, our approach outperforms state-of-the-art DG methods in all human activity recognition tasks.

Learning semantic-rich representations from unlabeled time series data with intricate dynamics is a notable challenge. Traditional contrastive learning techniques predominantly focus on segment-level augmentations through time slicing, a practice that, while valuable, often results in sampling bias and suboptimal performance due to the loss of global context. Furthermore, they typically disregard the vital frequency information to enrich data representations. To this end, we propose a novel self-supervised general-purpose framework called Temporal-Frequency and Contextual Consistency (TFCC). Specifically, this framework first performs two instance-level augmentation families over the entire series to capture nuanced representations alongside critical long-term dependencies. Then, TFCC advances by initiating dual cross-view forecasting tasks between the original series and its augmented counterpart in both time and frequency domains to learn robust representations. Finally, three specially designed consistency modules 'temporal, frequency, and temporal-frequency' aid in further developing discriminative representations on top of the learned robust representations. Extensive experiments on multiple benchmarks demonstrate TFCC's superiority over the state-of-the-art classification and forecasting methods and exhibit exceptional efficiency in semi-supervised and transfer learning scenarios.

Standard k -means clustering necessitates computing pairwise Euclidean distances between each instance x in a data set D and all cluster centers, resulting in inadequate efficiency when dealing with high-dimensional data sets. Given its widespread usage, it is imperative that k -means clustering should be performed quickly to ensure efficient solutions. This paper is dedicated to exploring ways to improve the efficiency of the k -means algorithm in high-dimensional space. Unlike approximated approaches, our proposed method LBKC can achieve acceleration while yielding clustering results that are the same as what standard k -means clustering generates. LBKC utilizes the lower bound of Euclidean distance to safely avoid a large number of unnecessary distance calculations, thus achieving the goal of accelerating k -means process. Three carefully designed lower bounds based on the block vector, segment mean, and nonlinear embedding are presented in this paper, and they are employed in the proposed method. Furthermore, our approach LBKC is orthogonal to state-of-the-art methods, and we show how LBKC can be naturally combined with them to further improve their performance. Comprehensive experiments are conducted on a variety of data sets to evaluate the performance of the proposed approaches and related competitors, and the experimental results verify the effectiveness of our proposals.

While one-dimensional convolutional neural networks (1D-CNNs) have been empirically proven effective in time series classification tasks, we find that there remain undesirable outcomes that could arise in their application, motivating us to further investigate and understand their underlying mechanisms. In this work, we propose a Temporal Convolutional Explorer (TCE) to empirically explore the learning behavior of 1D-CNNs from the perspective of the frequency domain. Our TCE analysis highlights that deeper 1D-CNNs tend to distract the focus from the low-frequency components leading to the accuracy degradation phenomenon, and the disturbing convolution is the driving factor. Then, we leverage our findings to the practical application and propose a regulatory framework, which can easily be integrated into existing 1D-CNNs. It aims to rectify the suboptimal learning behavior by enabling the network to selectively bypass the specified disturbing convolutions. Finally, through comprehensive experiments on widely-used UCR, UEA, and UCI benchmarks, we demonstrate that 1) TCE's insight into 1D-CNN's learning behavior; 2) our regulatory framework enables state-of-the-art 1D-CNNs to get improved performances with less consumption of memory and computational overhead.