Related papers: Coarse Graining of Data via Inhomogeneous Diffusio…

Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…

We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating from disparate modalities, or to correct batch effects while preserving intrinsic data…

$\textbf{Graph Coarsening (GC)}$ is a prominent graph reduction technique that compresses large graphs to enable efficient learning and inference. However, existing GC methods generate only one coarsened graph per run and must recompute…

Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still…

Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…

Dataset Distillation aims to distill an entire dataset's knowledge into a few synthetic images. The idea is to synthesize a small number of synthetic data points that, when given to a learning algorithm as training data, result in a model…

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…

In this work, a coarse-graining method previously proposed by the authors in a companion paper based on solving diffusion equations is applied to CFD-DEM simulations, where coarse graining is used to obtain solid volume fraction, particle…

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when one expects regression coefficients…

Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…

Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…

It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most…

Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we…

In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

Feature matters. How to train a deep network to acquire discriminative features across categories and polymerized features within classes has always been at the core of many computer vision tasks, specially for large-scale recognition…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…