Related papers: Manifold Fitting under Unbounded Noise

Consider a target moving with a constant velocity on a unit-circumference circle, starting from an arbitrary location. To acquire the target, any region of the circle can be probed for its presence, but the associated measurement noise…

Consider an unknown smooth function $f: [0,1]^d \rightarrow \mathbb{R}$, and say we are given $n$ noisy mod 1 samples of $f$, i.e., $y_i = (f(x_i) + \eta_i)\mod 1$, for $x_i \in [0,1]^d$, where $\eta_i$ denotes the noise. Given the samples…

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…

We consider reconstruction of a manifold, or, invariant manifold learning, where a smooth Riemannian manifold $M$ is determined from intrinsic distances (that is, geodesic distances) of points in a discrete subset of $M$. In the studied…

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…

In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…

We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence…

Determining the optimal model for a given task often requires training multiple models from scratch, which becomes impractical as dataset and model sizes grow. A more efficient alternative is to expand smaller pre-trained models, but this…

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

Data augmentation is an area of research which has seen active development in many machine learning fields, such as in image-based learning models, reinforcement learning for self driving vehicles, and general noise injection for point…

Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Fusion and inference from multiple and massive disparate data sources - the requirement for our most challenging data analysis problems and the goal of our most ambitious statistical pattern recognition methodologies - -has many and varied…

Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. The state-of-art tensor regression techniques have effectively been used for analysis of structured point cloud…

Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases…

In this paper we introduce a new sampling and reconstruction approach for multi-dimensional analog signals. Building on top of the Unlimited Sensing Framework (USF), we present a new folded sampling operator called the multi-dimensional…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution…