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Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
This work proposes a geometrically motivated algorithm for representing the high-dimensional data that provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering.
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
A semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner is proposed and properties of reproducing kernel Hilbert spaces are used to prove new Representer theorems that provide theoretical basis for the algorithms.
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering.
Reconciling modern machine-learning practice and the classical bias–variance trade-off
- Mikhail Belkin, Daniel J. Hsu, Siyuan Ma, Soumik Mandal
- Computer ScienceProceedings of the National Academy of Sciences
- 28 December 2018
This work shows how classical theory and modern practice can be reconciled within a single unified performance curve and proposes a mechanism underlying its emergence, and provides evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets.
Beyond the point cloud: from transductive to semi-supervised learning
This paper constructs a family of data-dependent norms on Reproducing Kernel Hilbert Spaces (RKHS) that allow the structure of the RKHS to reflect the underlying geometry of the data.
Semi-Supervised Learning on Riemannian Manifolds
An algorithmic framework to classify a partially labeled data set in a principled manner and models the manifold using the adjacency graph for the data and approximates the Laplace-Beltrami operator by the graph Laplacian.
Regularization and Semi-supervised Learning on Large Graphs
We consider the problem of labeling a partially labeled graph. This setting may arise in a number of situations from survey sampling to information retrieval to pattern recognition in manifold…
Manifold Regularization : A Geometric Framework for Learning from Examples
A semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner is focused on and properties of Reproducing Kernel Hilbert spaces are utilized to prove new Representer theorems that provide theoretical basis for the algorithms.
Laplacian Support Vector Machines Trained in the Primal
This paper presents two strategies to solve the primal LapSVM problem, in order to overcome some issues of the original dual formulation, and presents an extensive experimental evaluation on real world data showing the benefits of the proposed approach.
Two models of double descent for weak features
The "double descent" risk curve was recently proposed to qualitatively describe the out-of-sample prediction accuracy of variably-parameterized machine learning models and it is shown that the risk peaks when the number of features is close to the sample size, but also that therisk decreases towards its minimum as $p$ increases beyond $n$.