Related papers: Manifold Repairing, Reconstruction and Denoising f…
In this paper, we consider the fundamental problem of approximation of functions on a low-dimensional manifold embedded in a high-dimensional space, with noise affecting both in the data and values of the functions. Due to the curse of…
In this paper, we present a method for denoising and reconstruction of low-dimensional manifold in high-dimensional space. We suggest a multidimensional extension of the Locally Optimal Projection algorithm which was introduced by Lipman et…
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…
We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…
Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorithms are inefficient. The typical solution is to reduce the…
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-dose CT. We propose a new iterative CT reconstruction algorithm,…
Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…
We consider the problem of reconstructing the intrinsic geometry of a manifold from noisy pairwise distance observations. Specifically, let $M$ denote a diameter 1 d-dimensional manifold and $\mu$ a probability measure on $M$ that is…
This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image…
Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
Mixed-based point cloud augmentation is a popular solution to the problem of limited availability of large-scale public datasets. But the mismatch between mixed points and corresponding semantic labels hinders the further application in…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
We introduce a differentially private manifold denoising framework that allows users to exploit sensitive reference datasets to correct noisy, non-private query points without compromising privacy. The method follows an iterative procedure…