RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs

Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning stands out as its theoretical underpinnings on symmetric positive definite (SPD) allows revealing structural connectivity analysis in a physics-grounded manner. However, current SPD-based methods focus predominantly on statistical aggregation of EEGs, with frequency-specific synchronization and local topological structures of brain regions neglected. Given this, we propose RepSPD, a novel geometric deep learning (GDL)-based model. RepSPD implements a cross-attention mechanism on the Riemannian manifold to modulate the geometric attributes of SPD with graph-derived functional connectivity features. On top of this, we introduce a global bidirectional alignment strategy to reshape tangent-space embeddings, mitigating geometric distortions caused by curvature and thereby enhancing geometric consistency. Extensive experiments demonstrate that our proposed framework significantly outperforms existing EEG representation methods, exhibiting superior robustness and generalization capabilities.

ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks

Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model continuous brain dynamics through discretizing time with recurrent architecture, which necessarily results in compounded cumulative prediction errors and failure of capturing instantaneous, nonlinear characteristics of EEGs. We propose ODEBRAIN, a Neural ODE latent dynamic forecasting framework to overcome these challenges by integrating spatio-temporal-frequency features into spectral graph nodes, followed by a Neural ODE modeling the continuous latent dynamics. Our design ensures that latent representations can capture stochastic variations of complex brain states at any given time point. Extensive experiments verify that ODEBRAIN can improve significantly over existing methods in forecasting EEG dynamics with enhanced robustness and generalization capabilities.

TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series

Nonstationary time series forecasting suffers from the distribution shift issue due to the different distributions that produce the training and test data. Existing methods attempt to alleviate the dependence by, e.g., removing low-order moments from each individual sample. These solutions fail to capture the underlying time-evolving structure across samples and do not model the complex time structure. In this paper, we aim to address the distribution shift in the frequency space by considering all possible time structures. To this end, we propose a Time-Invariant Frequency Operator (TIFO), which learns stationarity-aware weights over the frequency spectrum across the entire dataset. The weight representation highlights stationary frequency components while suppressing non-stationary ones, thereby mitigating the distribution shift issue in time series. To justify our method, we show that the Fourier transform of time series data implicitly induces eigen-decomposition in the frequency space. TIFO is a plug-and-play approach that can be seamlessly integrated into various forecasting models. Experiments demonstrate our method achieves 18 top-1 and 6 top-2 results out of 28 forecasting settings. Notably, it yields 33.3% and 55.3% improvements in average MSE on the ETTm2 dataset. In addition, TIFO reduces computational costs by 60% -70% compared to baseline methods, demonstrating strong scalability across diverse forecasting models.

Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.

Multi-Aspect Mining and Anomaly Detection for Heterogeneous Tensor Streams

Analysis and anomaly detection in event tensor streams consisting of timestamps and multiple attributes - such as communication logs(time, IP address, packet length)- are essential tasks in data mining. While existing tensor decomposition and anomaly detection methods provide useful insights, they face the following two limitations. (i) They cannot handle heterogeneous tensor streams, which comprises both categorical attributes(e.g., IP address) and continuous attributes(e.g., packet length). They typically require either discretizing continuous attributes or treating categorical attributes as continuous, both of which distort the underlying statistical properties of the data.Furthermore, incorrect assumptions about the distribution family of continuous attributes often degrade the model's performance. (ii) They discretize timestamps, failing to track the temporal dynamics of streams(e.g., trends, abnormal events), which makes them ineffective for detecting anomalies at the group level, referred to as 'group anomalies' (e.g, DoS attacks). To address these challenges, we propose HeteroComp, a method for continuously summarizing heterogeneous tensor streams into 'components' representing latent groups in each attribute and their temporal dynamics, and detecting group anomalies. Our method employs Gaussian process priors to model unknown distributions of continuous attributes, and temporal dynamics, which directly estimate probability densities from data. Extracted components give concise but effective summarization, enabling accurate group anomaly detection. Extensive experiments on real datasets demonstrate that HeteroComp outperforms the state-of-the-art algorithms for group anomaly detection accuracy, and its computational time does not depend on the data stream length.

Fast Mining and Dynamic Time-to-Event Prediction over Multi-sensor Data Streams

Given real-time sensor data streams obtained from machines, how can we continuously predict when a machine failure will occur? This work aims to continuously forecast the timing of future events by analyzing multi-sensor data streams. A key characteristic of real-world data streams is their dynamic nature, where the underlying patterns evolve over time. To address this, we present TimeCast, a dynamic prediction framework designed to adapt to these changes and provide accurate, real-time predictions of future event time. Our proposed method has the following properties: (a) Dynamic: it identifies the distinct time-evolving patterns (i.e., stages) and learns individual models for each, enabling us to make adaptive predictions based on pattern shifts. (b) Practical: it finds meaningful stages that capture time-varying interdependencies between multiple sensors and improve prediction performance; (c) Scalable: our algorithm scales linearly with the input size and enables online model updates on data streams. Extensive experiments on real datasets demonstrate that TimeCast provides higher prediction accuracy than state-of-the-art methods while finding dynamic changes in data streams with a great reduction in computational time.

EvoBrain: Dynamic Multi-channel EEG Graph Modeling for Time-evolving Brain Network

Dynamic GNNs, which integrate temporal and spatial features in Electroencephalography (EEG) data, have shown great potential in automating seizure detection. However, fully capturing the underlying dynamics necessary to represent brain states, such as seizure and non-seizure, remains a non-trivial task and presents two fundamental challenges. First, most existing dynamic GNN methods are built on temporally fixed static graphs, which fail to reflect the evolving nature of brain connectivity during seizure progression. Second, current efforts to jointly model temporal signals and graph structures and, more importantly, their interactions remain nascent, often resulting in inconsistent performance. To address these challenges, we present the first theoretical analysis of these two problems, demonstrating the effectiveness and necessity of explicit dynamic modeling and time-then-graph dynamic GNN method. Building on these insights, we propose EvoBrain, a novel seizure detection model that integrates a two-stream Mamba architecture with a GCN enhanced by Laplacian Positional Encoding, following neurological insights. Moreover, EvoBrain incorporates explicitly dynamic graph structures, allowing both nodes and edges to evolve over time. Our contributions include (a) a theoretical analysis proving the expressivity advantage of explicit dynamic modeling and time-then-graph over other approaches, (b) a novel and efficient model that significantly improves AUROC by 23% and F1 score by 30%, compared with the dynamic GNN baseline, and (c) broad evaluations of our method on the challenging early seizure prediction tasks.

Robust and Explainable Detector of Time Series Anomaly via Augmenting Multiclass Pseudo-Anomalies

Unsupervised anomaly detection in time series has been a pivotal research area for decades. Current mainstream approaches focus on learning normality, on the assumption that all or most of the samples in the training set are normal. However, anomalies in the training set (i.e., anomaly contamination) can be misleading. Recent studies employ data augmentation to generate pseudo-anomalies and learn the boundary separating the training samples from the augmented samples. Although this approach mitigates anomaly contamination if augmented samples mimic unseen real anomalies, it suffers from several limitations. (1) Covering a wide range of time series anomalies is challenging. (2) It disregards augmented samples that resemble normal samples (i.e., false anomalies). (3) It places too much trust in the labels of training and augmented samples. In response, we propose RedLamp, which employs diverse data augmentations to generate multiclass pseudo-anomalies and learns the multiclass boundary. Such multiclass pseudo-anomalies cover a wide variety of time series anomalies. We conduct multiclass classification using soft labels, which prevents the model from being overconfident and ensures its robustness against contaminated/false anomalies. The learned latent space is inherently explainable as it is trained to separate pseudo-anomalies into multiclasses. Extensive experiments demonstrate the effectiveness of RedLamp in anomaly detection and its robustness against anomaly contamination.

D-Tracker: Modeling Interest Diffusion in Social Activity Tensor Data Streams

Large quantities of social activity data, such as weekly web search volumes and the number of new infections with infectious diseases, reflect peoples' interests and activities. It is important to discover temporal patterns from such data and to forecast future activities accurately. However, modeling and forecasting social activity data streams is difficult because they are high-dimensional and composed of multiple time-varying dynamics such as trends, seasonality, and interest diffusion. In this paper, we propose D-Tracker, a method for continuously capturing time-varying temporal patterns within social activity tensor data streams and forecasting future activities. Our proposed method has the following properties: (a) Interpretable: it incorporates the partial differential equation into a tensor decomposition framework and captures time-varying temporal patterns such as trends, seasonality, and interest diffusion between locations in an interpretable manner; (b) Automatic: it has no hyperparameters and continuously models tensor data streams fully automatically; (c) Scalable: the computation time of D-Tracker is independent of the time series length. Experiments using web search volume data obtained from GoogleTrends, and COVID-19 infection data obtained from COVID-19 Open Data Repository show that our method can achieve higher forecasting accuracy in less computation time than existing methods while extracting the interest diffusion between locations. Our source code and datasets are available at {https://github.com/Higashiguchi-Shingo/D-Tracker.

ExPath: Towards Explaining Targeted Pathways for Biological Knowledge Bases

Biological knowledge bases provide systemically functional pathways of cells or organisms in terms of molecular interaction. However, recognizing more targeted pathways, particularly when incorporating wet-lab experimental data, remains challenging and typically requires downstream biological analyses and expertise. In this paper, we frame this challenge as a solvable graph learning and explaining task and propose a novel pathway inference framework, ExPath, that explicitly integrates experimental data, specifically amino acid sequences (AA-seqs), to classify various graphs (bio-networks) in biological databases. The links (representing pathways) that contribute more to classification can be considered as targeted pathways. Technically, ExPath comprises three components: (1) a large protein language model (pLM) that encodes and embeds AA-seqs into graph, overcoming traditional obstacles in processing AA-seq data, such as BLAST; (2) PathMamba, a hybrid architecture combining graph neural networks (GNNs) with state-space sequence modeling (Mamba) to capture both local interactions and global pathway-level dependencies; and (3) PathExplainer, a subgraph learning module that identifies functionally critical nodes and edges through trainable pathway masks. We also propose ML-oriented biological evaluations and a new metric. The experiments involving 301 bio-networks evaluations demonstrate that pathways inferred by ExPath maintain biological meaningfulness. We will publicly release curated 301 bio-network data soon.