arXiv:2511.18197v1 Announce Type: cross 
Abstract: This paper evaluates Tucker decomposition and Singular Value Decomposition (SVD) for compressing neuroimaging data. Tucker decomposition preserves multi-dimensional relationships, achieving superior reconstruction fidelity and perceptual similarity. SVD excels in extreme compression but sacrifices fidelity. The results highlight Tucker decomposition's suitability for applications requiring the preservation of structural and temporal relationships.

دراسة حديثة تقيم فعالية تحليل تاكر وتحليل القيم الفردية (SVD) في ضغط بيانات التصوير العصبي، مشيرة إلى قدرة تحليل تاكر على الحفاظ على العلاقات متعددة الأبعاد وتحقيق دقة إعادة بناء متفوقة مقارنة بـ SVD، الذي يقدم ضغطًا شديدًا على حساب الدقة.

Un estudio reciente evalúa la efectividad de la descomposición de Tucker y la descomposición en valores singulares (SVD) en la compresión de datos de neuroimagen, destacando la capacidad de la descomposición de Tucker para mantener relaciones multidimensionales y lograr una fidelidad de reconstrucción superior en comparación con la SVD, que ofrece compresión extrema a costa de la fidelidad.

Une étude récente évalue l'efficacité de la décomposition de Tucker et de la décomposition en valeurs singulières (SVD) pour la compression des données de neuroimagerie, soulignant la capacité de la décomposition de Tucker à maintenir les relations multidimensionnelles et à atteindre une fidélité de reconstruction supérieure par rapport à la SVD, qui offre une compression extrême au prix de la fidélité.

A recent study evaluates the effectiveness of Tucker decomposition and Singular Value Decomposition (SVD) in compressing neuroimaging data, highlighting Tucker decomposition's ability to maintain multi-dimensional relationships and achieve superior reconstruction fidelity compared to SVD, which offers extreme compression at the cost of fidelity.

Linear Algebraic Approaches to Neuroimaging Data Compression: A Comparative Analysis of Matrix and Tensor Decomposition Methods for High-Dimensional Medical Images

arXiv:2601.08230v1 Announce Type: new 
Abstract: While Graph Neural Networks (GNNs) excel on graph-structured data, their performance is fundamentally limited by the quality of the observed graph, which often contains noise, missing links, or structural properties misaligned with GNNs' underlying assumptions. To address this, graph structure learning aims to infer a more optimal topology. Existing methods, however, often incur high computational costs due to complex generative models and iterative joint optimization, limiting their practical utility. In this paper, we propose GADPN, a simple yet effective graph structure learning framework that adaptively refines graph topology via low-rank denoising and generalized structural perturbation. Our approach makes two key contributions: (1) we introduce Bayesian optimization to adaptively determine the optimal denoising strength, tailoring the process to each graph's homophily level; and (2) we extend the structural perturbation method to arbitrary graphs via Singular Value Decomposition (SVD), overcoming its original limitation to symmetric structures. Extensive experiments on benchmark datasets demonstrate that GADPN achieves state-of-the-art performance while significantly improving efficiency. It shows particularly strong gains on challenging disassortative graphs, validating its ability to robustly learn enhanced graph structures across diverse network types.

تم اقتراح إطار عمل جديد يسمى GADPN لتحسين الشبكات العصبية الرسومية (GNN) من خلال تحسين بنية الرسم البياني عبر إزالة الضوضاء ذات الرتبة المنخفضة والاضطراب الهيكلي العام، مما يعالج مشكلات الضوضاء والروابط المفقودة في البيانات الهيكلية.

Se ha propuesto un nuevo marco llamado GADPN para mejorar las Redes Neuronales de Grafos (GNN) refinando la topología del grafo a través de un desruido de rango bajo y una perturbación estructural generalizada, abordando problemas de ruido y enlaces faltantes en datos estructurados en grafos.

Un nouveau cadre nommé GADPN a été proposé pour améliorer les réseaux de neurones graphiques (GNN) en affinant la topologie des graphes grâce à un débruitage de rang faible et à une perturbation structurelle généralisée, abordant les problèmes de bruit et de liens manquants dans les données structurées en graphes.

A new framework named GADPN has been proposed to enhance Graph Neural Networks (GNNs) by refining graph topology through low-rank denoising and generalized structural perturbation, addressing issues of noise and missing links in graph-structured data.

Linear Algebraic Approaches to Neuroimaging Data Compression: A Comparative Analysis of Matrix and Tensor Decomposition Methods for High-Dimensional Medical Images

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