Related papers: Inductive Global and Local Manifold Approximation …

Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these…

Deep learning has become the state-of-the-art approach to medical tomographic imaging. A common approach is to feed the result of a simple inversion, for example the backprojection, to a multiscale convolutional neural network (CNN) which…

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional…

The Uniform Manifold Approximation and Projection (UMAP) algorithm has become widely popular for its ease of use, quality of results, and support for exploratory, unsupervised, supervised, and semi-supervised learning. While many algorithms…

Though manifold-based clustering has become a popular research topic, we observe that one important factor has been omitted by these works, namely that the defined clustering loss may corrupt the local and global structure of the latent…

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…

Visual odometry (VO) and SLAM have been using multi-view geometry via local structure from motion for decades. These methods have a slight disadvantage in challenging scenarios such as low-texture images, dynamic scenarios, etc. Meanwhile,…

Visualization methods based on the nearest neighbor graph, such as t-SNE or UMAP, are widely used for visualizing high-dimensional data. Yet, these approaches only produce meaningful results if the nearest neighbors themselves are…

Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…

Recent research on Simultaneous Localization and Mapping (SLAM) based on implicit representation has shown promising results in indoor environments. However, there are still some challenges: the limited scene representation capability of…

Learning efficient representations of local features is a key challenge in feature volume-based 3D neural mapping, especially in large-scale environments. In this paper, we introduce Decomposition-based Neural Mapping (DNMap), a…

TSNE and UMAP are two of the most popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. However, while attempts have been made to improve on TSNE's computational complexity, no existing…

Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

Neighbor embedding methods $t$-SNE and UMAP are the de facto standard for visualizing high-dimensional datasets. Motivated from entirely different viewpoints, their loss functions appear to be unrelated. In practice, they yield strongly…

Global localization is an important and widely studied problem for many robotic applications. Place recognition approaches can be exploited to solve this task, e.g., in the autonomous driving field. While most vision-based approaches match…

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…

Guided image super-resolution (GISR) aims to obtain a high-resolution (HR) target image by enhancing the spatial resolution of a low-resolution (LR) target image under the guidance of a HR image. However, previous model-based methods mainly…