Learning algebraic varieties from samples
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing
methods are studied and new methods are developed. Our focus lies on aspects of topology …
methods are studied and new methods are developed. Our focus lies on aspects of topology …
Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds
S Bouzebda, N Taachouche - Mathematical Methods of Statistics, 2023 - Springer
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 …
(including the kernel density estimator) on Riemannian manifolds with Riemann integrable …
Lizard brain: Tackling locally low-dimensional yet globally complex organization of multi-dimensional datasets
J Bac, A Zinovyev - Frontiers in neurorobotics, 2020 - frontiersin.org
Machine learning deals with datasets characterized by high dimensionality. However, in
many cases, the intrinsic dimensionality of the datasets is surprisingly low. For example, the …
many cases, the intrinsic dimensionality of the datasets is surprisingly low. For example, the …
Intrinsic dimension estimation for locally undersampled data
Identifying the minimal number of parameters needed to describe a dataset is a challenging
problem known in the literature as intrinsic dimension estimation. All the existing intrinsic …
problem known in the literature as intrinsic dimension estimation. All the existing intrinsic …
Estimating the effective dimension of large biological datasets using Fisher separability analysis
Modern large-scale datasets are frequently said to be high-dimensional. However, their data
point clouds frequently possess structures, significantly decreasing their intrinsic …
point clouds frequently possess structures, significantly decreasing their intrinsic …
Local intrinsic dimensionality estimators based on concentration of measure
J Bac, A Zinovyev - 2020 International Joint Conference on …, 2020 - ieeexplore.ieee.org
Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-
dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine …
dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine …
Weighted cluster ensemble based on partition relevance analysis with reduction step
N Ilc - IEEE access, 2020 - ieeexplore.ieee.org
Over the last decade, the advent of the cluster ensemble framework has enabled more
accurate and robust data analysis than traditional single clustering algorithms. The improved …
accurate and robust data analysis than traditional single clustering algorithms. The improved …
On subsampling procedures for support vector machines
R Bárcenas, M Gonzalez-Lima, J Ortega, A Quiroz - Mathematics, 2022 - mdpi.com
Herein, theoretical results are presented to provide insights into the effectiveness of
subsampling methods in reducing the amount of instances required in the training stage …
subsampling methods in reducing the amount of instances required in the training stage …
Effective Estimation of the Dimensions of a Manifold from Random Samples
L Grillet, J Souto - arXiv preprint arXiv:2209.01839, 2022 - arxiv.org
arXiv:2209.01839v2 [cs.CG] 7 Sep 2022 Page 1 EFFECTIVE ESTIMATION OF THE
DIMENSION OF A MANIFOLD FROM RANDOM SAMPLES LUCIEN GRILLET AND JUAN …
DIMENSION OF A MANIFOLD FROM RANDOM SAMPLES LUCIEN GRILLET AND JUAN …
[图书][B] Metric Algebraic Geometry
MA Weinstein - 2021 - search.proquest.com
Algebraic geometry is the study of algebraic varieties, zero sets of systems of polynomial
equations. Metric algebraic geometry concerns properties of real algebraic varieties that …
equations. Metric algebraic geometry concerns properties of real algebraic varieties that …