Related papers: Tangent-based manifold approximation with locally …

Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Estimates of image gradients play a ubiquitous role in image segmentation and classification problems since gradients directly relate to the boundaries or the edges of a scene. This paper proposes an unified approach to gradient estimation…

In this paper, we present a new method for few-sample supervised feature selection (FS). Our method first learns the manifold of the feature space of each class using kernels capturing multi-feature associations. Then, based on Riemannian…

We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…

Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based…

We solve the convergence case of the generalized Baker-Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our theorems, we do not require monotonicity on the…

The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…

We focus on the problem of finding a good representative of a sample of random curves warped from a common pattern f. We first prove that such a problem can be moved onto a manifold framework. Then, we propose an estimation of the common…

We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress…

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of…

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 present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any…

When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

We consider the problem of domain approximation in finite element methods for Maxwell equations on curved domains, i.e., when affine or polynomial meshes fail to exactly cover the domain of interest. In such cases, one is forced to…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…