The concise review systematically summarises the state-of-the-art variants of Moving Least
Squares (MLS) method. MLS method is a mathematical tool which could render cogent …

In recent years, identification of nonlinear dynamical systems from data has become
increasingly popular. Sparse regression approaches, such as sparse identification of …

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and
other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of …

A common observation in data-driven applications is that high dimensional data has a low
intrinsic dimension, at least locally. In this work, we consider the problem of estimating a $ d …

In order to avoid the curse of dimensionality, frequently encountered in big data analysis,
there has been vast development in the field of linear and nonlinear dimension reduction …

Manifold learning, which has emerged in recent years, plays an increasingly important role
in machine learning. However, because inevitable noises and outliers destroy the manifold …

Detecting out-of-distribution (OOD) samples poses a significant safety challenge when
deploying models in open-world scenarios. Advanced works assume that OOD and in …

Riemannian optimization is a principled framework for solving optimization problems where
the desired optimum is constrained to a smooth manifold $\mathcal {M} $. Algorithms …

In this article, we consider the manifold learning problem when the data set is invariant
under the action of a compact Lie group $ K $. Our approach consists in augmenting the …

We propose a new method for functional nonparametric regression with a predictor that
resides on a finite-dimensional manifold, but is observable only in an infinite-dimensional …