Related papers: Nonlinear Dimensionality Reduction via Path-Based …
The purpose of this paper is to explore a new way of autonomous mapping. Current systems using perception techniques like LAZER or SONAR use probabilistic methods and have a drawback of allowing considerable uncertainty in the mapping…
Accurate mapping of large-scale environments is an essential building block of most outdoor autonomous systems. Challenges of traditional mapping methods include the balance between memory consumption and mapping accuracy. This paper…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix…
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low-dimensional coordinates which represent the intrinsic…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:\mathbb{R}^d\rightarrow\mathbb{R}$, $d\gg1$. Our objective is to identify a nonlinear feature map $g:\mathbb{R}^d\rightarrow\mathbb{R}^m$, with a…
In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be…
Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Three-dimensional (3D) reconstruction from two-dimensional images is an active research field in computer vision, with applications ranging from navigation and object tracking to segmentation and three-dimensional modeling. Traditionally,…
In this paper, we present a new approach for improving 3D point and line mapping regression for camera re-localization. Previous methods typically rely on feature matching (FM) with stored descriptors or use a single network to encode both…
We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…
We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear…
Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather…
Channel charting is an unsupervised learning task whose objective is to encode channels so that the obtained representation reflects the relative spatial locations of the corresponding users. It has many potential applications, ranging from…