Related papers: Nonlinear Dimensionality Reduction on Graphs

Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…

Graph representation learning has many real-world applications, from super-resolution imaging, 3D computer vision to drug repurposing, protein classification, social networks analysis. An adequate representation of graph data is vital to…

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…

In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…

While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data…

Understanding the training dynamics of deep neural networks (DNNs) is important as it can lead to improved training efficiency and task performance. Recent works have demonstrated that representing the wirings of static graph cannot capture…

Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…

Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…

Graph learning aims to infer a network structure directly from observed data, enabling the analysis of complex dependencies in irregular domains. Traditional methods focus on scalar signals at each node, ignoring dependencies along…

Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based…

Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To…

Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…

Recently emerged Topological Deep Learning (TDL) methods aim to extend current Graph Neural Networks (GNN) by naturally processing higher-order interactions, going beyond the pairwise relations and local neighborhoods defined by graph…

We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…