相关论文: Optimized Kernel-based Projection Space of Riemann…

This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…

Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the…

Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, $V_k(\mathbb{R}^N)$ and $Gr(k, \mathbb{R}^N)$ respectively, and benefit from projection onto lower-dimensional Stiefel and Grassmannian manifolds. In this…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…

Recent advances in {matrix-mimetic} tensor frameworks have made it possible to preserve linear algebraic properties for multilinear data analysis and, as a result, to obtain optimal representations of multiway data. Matrix mimeticity arises…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…

We propose a novel evolutionary algorithm for optimizing real-valued objective functions defined on the Grassmann manifold Gr}(k,n), the space of all k-dimensional linear subspaces of R^n. While existing optimization techniques on Gr}(k,n)…

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…

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…

We present Neural Kernel Fields: a novel method for reconstructing implicit 3D shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art results when reconstructing 3D objects and large scenes from sparse…

The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when…

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…

We consider the theory of regression on a manifold using reproducing kernel Hilbert space methods. Manifold models arise in a wide variety of modern machine learning problems, and our goal is to help understand the effectiveness of various…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…