Semi-Supervised Learning on Riemannian Manifolds

By Mikhail Belkin, Partha Niyogi. 2004

894 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

Simplifying Graph Convolutional Networks (2019, background): “Graph Laplacian regularization (Zhu et al., 2003; Zhou et al., 2004; Belkin & Niyogi, 2004; Belkin et al., 2006) introduce an additional regularization term based on graph structure which forces nodes to have similar labels to their neighbors and helps the models generalize.”
MS-Celeb-1M: A Dataset and Benchmark for Large-Scale Face Recognition (2016, background): “For example, people could adopt one of the cutting-edge unsupervised/semi-supervised clustering algorithms [21] [22] [23] [24] on our training dataset, and/or develop new algorithms which can accurately locate and remove outliers in a large, real dataset.”
A Survey on Metric Learning for Feature Vectors and Structured Data (2013, background): “(2008, 2010) propose to follow the principles of manifold regularization for semi-supervised learning (Belkin and Niyogi, 2004) by resorting to a weight matrix W that encodes the similarity between pairs of points.”
Machine Learning on Graphs: A Model and Comprehensive Taxonomy (2020, background): “cut information often used for spectral graph clustering) but can also serve as a basis for smooth functions defined on the graph for semi-supervised learning (Belkin and Niyogi, 2004).”
Semi-Supervised Graph-Based Hyperspectral Image Classification (2007, methodology): “is akin to that in [20] and [35]–[38] and is often called the cluster assumption [20], [37].”
Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions (2005, background): “( 6 ) One usually introduces the matrices D and W defined as follows.”
Scalable Semi-Supervised Learning by Efficient Anchor Graph Regularization (2016, background): “[2] proposed a classification function which is defined only on the”
Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian (2007, background): “The first is that graph eigenfunctions are global objects and any 1 Examples of such disparate applications include document analysis [15], face recognition [26], clustering [37, 1], machine learning [4, 38, 52, 34, 33, 53], nonlinear image denoising and segmentation [45, 52], processing of articula”
Discrete Signal Processing on Graphs: Sampling Theory (2015, background): “e assumed to be smooth with respect to underlying graphs, from noisy, missing, or corrupted samples [23]. Previous works studied signal recovery on graphs from different perspectives. For example, in [47], the authors considered that a graph is a discrete representation of a manifold, and aimed at r”
Self-Training: A Survey (2022, neutral): “A third hypothesis, known as the manifold assumption, stipulates that in high-dimensional spaces, instances re-side on low-dimensional topological spaces that are locally Euclidean (Figure 1 (c)), which is supported by a variety of semi-supervised models called graphical approaches [6].”
Covariate Shift Adaptation by Importance Weighted Cross Validation (2007, methodology): “…for any parameter learning method; this means that, e.g., an importance weighted variant of support vector machines (Vapnik, 1998; Schölkopf and Smola, 2002; Huang et al., 2007) or graph regularization techniques (Bousquet et al., 2004; Belkin and Niyogi, 2004; Hein, 2006) can also be employed.”
Statistical topology via Morse theory, persistence and nonparametric estimation (2009, background): “There is also a growing interest in function estimation over manifolds in the learning theory literature [7, 31, 2]; see also the references cited therein.”
Data Classification: Algorithms and Applications (2014, background): “An argument for the effectiveness of semi-supervised learning that uses the spectral clustering structure of the data may be found in [18].”
Advanced Lectures on Machine Learning (2004, background): “Many of the approaches to this problem attempt to infer a manifold, graph structure, or treestructure from the unlabelled data and use spread in this structure to determine how labels will generalise to new unlabelled points [72, 73, 74, 75].”
A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data (2005, background): “Figure 6: Comparison with similar settings in BN04 (Belkin and Niyogi, 2004) on 20 newsgroup.”
Revisiting Graph Neural Networks: All We Have is Low-Pass Filters (2019, methodology): “The graph filter h(λ) = 1− λ can also be derived from a first-order approximation of a Laplacian regularized least squares [3].”