Related papers: Bigeometric Organization of Deep Nets

We propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs.The method is based on a class of analytically solvable generative models, where vertices…

Deep graph embedding is an important approach for community discovery. Deep graph neural network with self-supervised mechanism can obtain the low-dimensional embedding vectors of nodes from unlabeled and unstructured graph data. The…

Objective: The paper focuses on development of robust and accurate processing solutions for continuous and cuff-less blood pressure (BP) monitoring. In this regard, a robust deep learning-based framework is proposed for computation of low…

We present and discuss a new method to extract parton distribution functions from hard scattering processes based on an alternative type of neural network, the Self-Organizing Map. Quantitative results including a detailed treatment of…

Dense indoor scene modeling from 2D images has been bottlenecked due to the absence of depth information and cluttered occlusions. We present an automatic indoor scene modeling approach using deep features from neural networks. Given a…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…

Tomographic synthetic aperture radar (TomoSAR) imaging algorithms based on deep learning can effectively reduce computational costs. The idea of existing researches is to reconstruct the elevation for each range-azimuth cell in…

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate…

Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features.…

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…

Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…

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…

Machine Learning (ML) is increasingly being used for computer aided diagnosis of brain related disorders based on structural magnetic resonance imaging (MRI) data. Most of such work employs biologically and medically meaningful hand-crafted…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

Human brain atlases provide spatial reference systems for data characterizing brain organization at different levels, coming from different brains. Cytoarchitecture is a basic principle of the microstructural organization of the brain, as…

Large amount of data is often required to train and deploy useful machine learning models in industry. Smaller enterprises do not have the luxury of accessing enough data for machine learning, For privacy sensitive fields such as banking,…