This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The
idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we …

In the manifold setting, we provide a series of spectral convergence results quantifying how
the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions …

Big data is transforming our world, revolutionizing operations and analytics everywhere,
from financial engineering to biomedical sciences. The complexity of big data often makes …

The temperature field prediction of lithium-ion batteries (LIBs) plays a crucial role in the
safety of electric vehicles and their lifetime. However, it is essentially a nonlinear distributed …

In the present paper, we develop strong uniform consistency results for the generic kernel
(including the kernel density estimator) on Riemannian manifolds with Riemann integrable …

We address a three-tier numerical framework based on nonlinear manifold learning for the
forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to …

statistics represent a fundamental class of statistics from modeling quantities of interest
defined by multi-subject responses.-statistics generalize the empirical mean of a random …

In nonparametric regression, it is common for the inputs to fall in a restricted subset of
Euclidean space. Typical kernel-based methods that do not take into account the intrinsic …

Manifold learning is a central task in modern statistics and data science. Many datasets
(cells, documents, images, molecules) can be represented as point clouds embedded in a …

We study the spectral convergence of graph Laplacians to the Laplace-Beltrami operator
when the kernelized graph affinity matrix is constructed from N random samples on a d …