Related papers: Manifold embedding data-driven mechanics
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
In recent times, an increasing number of researchers have been devoted to utilizing deep neural networks for end-to-end flight navigation. This approach has gained traction due to its ability to bridge the gap between perception and…
Neural networks used for image classification tasks in critical applications must be tested with sufficient realistic data to assure their correctness. To effectively test an image classification neural network, one must obtain realistic…
Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…
Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…
Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases…
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…
In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…
Heterogeneous, interconnected, systems-level, molecular data have become increasingly available and key in precision medicine. We need to utilize them to better stratify patients into risk groups, discover new biomarkers and targets,…
Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex…
Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a…
Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In…
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space.…