Related papers: Manifold Fitting

Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character…

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean data. Circular data is a classic example, but so is data in…

Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the…

When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…

This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it…

Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold $\mathcal{M}$. Algorithms designed in this framework usually require some geometrical…

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…

Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a…

Many techniques in machine learning attempt explicitly or implicitly to infer a low-dimensional manifold structure of an underlying physical phenomenon from measurements without an explicit model of the phenomenon or the measurement…

The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…