Related papers: Manifold Learning Using Kernel Density Estimation …

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…

The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…

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…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

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…

Given a random sample from a density function supported on a manifold $M$, a new method for the estimating highest density regions of the underlying population is introduced. The new proposal is based on the empirical version of the opening…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

Let $\mathcal{M}\subset \mathbb{R}^n$ be a compact and sufficiently smooth manifold of dimension $d$. Suppose $\mathcal{M}$ is nowhere completely flat. Let $N_{\mathcal{M}}(\delta,Q)$ denote the number of rational vectors $\mathbf{a}/q$…

We analyze the performance of a class of manifold-learning algorithms that find their output by minimizing a quadratic form under some normalization constraints. This class consists of Locally Linear Embedding (LLE), Laplacian Eigenmap,…

We present Extended Riemannian Stochastic Derivative-Free Optimization (Extended RSDFO), a novel population-based stochastic optimization algorithm on Riemannian manifolds that addresses the locality and implicit assumptions of manifold…

The inapplicability of amino acid covariation methods to small protein families has limited their use for structural annotation of whole genomes. Recently, deep learning has shown promise in allowing accurate residue-residue contact…

Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

In the field of computer vision, the numerical encoding of 3D surfaces is crucial. It is classical to represent surfaces with their Signed Distance Functions (SDFs) or Unsigned Distance Functions (UDFs). For tasks like representation…

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 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.…

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes…

Deep neural networks have proven to be highly effective when large amounts of data with clean labels are available. However, their performance degrades when training data contains noisy labels, leading to poor generalization on the test…

We show that DBSCAN can estimate the connected components of the $\lambda$-density level set $\{ x : f(x) \ge \lambda\}$ given $n$ i.i.d. samples from an unknown density $f$. We characterize the regularity of the level set boundaries using…

Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimizations. While many efficient…