An analysis of classical multidimensional scaling with applications to clustering
Classical multidimensional scaling is a widely used dimension reduction technique. Yet few
theoretical results characterizing its statistical performance exist. This paper provides a …
theoretical results characterizing its statistical performance exist. This paper provides a …
Non-asymptotic analysis of tangent space perturbation
DN Kaslovsky, FG Meyer - … and Inference: a Journal of the IMA, 2014 - ieeexplore.ieee.org
Constructing an efficient parameterization of a large, noisy data set of points lying close to
asmooth manifold in high dimension remains a fundamental problem. One approach …
asmooth manifold in high dimension remains a fundamental problem. One approach …
High-dimensional data modeling techniques for detection of chemical plumes and anomalies in hyperspectral images and movies
We briefly review recent progress in techniques for modeling and analyzing hyperspectral
images and movies, in particular for detecting plumes of both known and unknown …
images and movies, in particular for detecting plumes of both known and unknown …
Statistical exploration of the Manifold Hypothesis
Abstract The Manifold Hypothesis is a widely accepted tenet of Machine Learning which
asserts that nominally high-dimensional data are in fact concentrated near a low …
asserts that nominally high-dimensional data are in fact concentrated near a low …
Manifold curvature learning from hypersurface integral invariants
Integral invariants obtained from Principal Component Analysis on a small kernel domain of
a submanifold encode important geometric information classically defined in differential …
a submanifold encode important geometric information classically defined in differential …
Heuristic framework for multiscale testing of the multi-manifold hypothesis
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 …
number of parameters required. In such cases, we may ask whether the data lies on or near …
Ricci curvature and the manifold learning problem
AG Ache, MW Warren - Advances in Mathematics, 2019 - Elsevier
Consider a sample of n points taken iid from a submanifold Σ of Euclidean space. We show
that there is a way to estimate the Ricci curvature of Σ with respect to the induced metric from …
that there is a way to estimate the Ricci curvature of Σ with respect to the induced metric from …
Local eigenvalue decomposition for embedded Riemannian manifolds
Abstract Local Principal Component Analysis can be performed over small domains of an
embedded Riemannian manifold in order to relate the covariance analysis of the underlying …
embedded Riemannian manifold in order to relate the covariance analysis of the underlying …
Performance Degradation Prediction and Assessment Based on Geometric Space Transformation and Morphology Recognition
C Lu, L Tao, J Ma, Y Cheng, Y Ding - Fault Diagnosis and Prognostics …, 2025 - Springer
Based on the geometric description and conceptual system of performance degradation, this
chapter investigates the generalized process and method of performance degradation …
chapter investigates the generalized process and method of performance degradation …
Covariance integral invariants of embedded Riemannian manifolds for manifold learning
This thesis develops an effective theoretical foundation for the integral invariant approach to
study submanifold geometry via the statistics of the underlying point-set, ie, Manifold …
study submanifold geometry via the statistics of the underlying point-set, ie, Manifold …