arXiv subjects

Guancen Lin

Publications and source records attributed to Guancen Lin.

2 recordsLinked to original sources

arXiv2026

SheafIQ: Sheaf-Theoretic Information Quantification of Vector Fields on Geometric Graphs

Vector fields on graph structures naturally arise in diverse biological and engineered systems, where vector-valued states are defined on the nodes and evolve through the network interactions. Existing methods primarily characterize either the graph topology or individual signals, but generally do not quantify how local interactions among node-associated vectors are organized across the graph. To address this limitation, a sheaf-theoretic framework, termed SheafIQ, is proposed to represent neighboring vectors in a common edge-associated coordinate system, map local incompatibilities to a residual energy distribution, and quantify its global organization through entropy. Across proteins, functional brain networks, urban traffic systems, and power grids, SheafIQ consistently reveals complementary organizational information beyond conventional graph- and signal-based descriptors. More broadly, it establishes a unified information-theoretic framework for quantifying the organization of vector-valued states on geometric graphs, extending network analysis beyond graph topology alone.

cs.IT↗

arXiv2024

Higher-order Cross-structural Embedding Model for Time Series Analysis

Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the interaction patterns across different timestamps. Current approaches struggle to model higher-order interactions within time series, and focus on learning temporal or spatial dependencies separately, which limits performance in downstream tasks. To address these gaps, we propose Higher-order Cross-structural Embedding Model for Time Series (High-TS), a novel framework that jointly models both temporal and spatial perspectives by combining multiscale Transformer with Topological Deep Learning (TDL). Meanwhile, High-TS utilizes contrastive learning to integrate these two structures for generating robust and discriminative representations. Extensive experiments show that High-TS outperforms state-of-the-art methods in various time series tasks and demonstrate the importance of higher-order cross-structural information in improving model performance.

cs.LG↗