Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples

By Mikhail Belkin, Partha Niyogi, Vikas Sindhwani. 2006

4,291 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Semi-Supervised Classification with Graph Convolutional Networks (2016, background): “…where label information is smoothed over the graph via some form of explicit graph-based regularization (Zhu et al., 2003; Zhou et al., 2004; Belkin et al., 2006; Weston et al., 2012), e.g. by using a graph Laplacian regularization term in the loss function: (1) Here, L 0 denotes the…”
Graph Attention Networks (2017, methodology): “…assess the beneﬁts of the attention mechanism, we further evaluate a GCN model that computes 64 hidden features, attempting both the ReLU and (Belkin et al., 2006) 59.5% 60.1% 70.7% SemiEmb (Weston et al., 2012) 59.0% 59.6% 71.7% LP (Zhu et al., 2003) 68.0% 45.3% 63.0% DeepWalk (Perozzi et…”
Adversarial Training Methods for Semi-Supervised Text Classification (2016, background): “…adversarial training resemble some semi-supervised or transductive SVM approaches (Joachims, 1999; Chapelle & Zien, 2005; Collobert et al., 2006; Belkin et al., 2006) in that both families of methods push the decision boundary far from training examples (or in the case of transductive SVMs,…”
Revisiting Semi-Supervised Learning with Graph Embeddings (2016, methodology): “Graph-based semi-supervised learning deﬁnes the loss function as a weighted sum of the supervised loss over labeled instances and a graph Laplacian regularization term (Zhu et al., 2003; Zhou et al., 2004; Belkin et al., 2006; Weston et al., 2012).”
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs (2016, neutral): “ManiReg [4] 59.5% 70.7% SemiEmb [58] 59.0% 71.1% LP [63] 68.0% 63.0% DeepWalk [36] 67.2% 65.3% Planetoid [60] 75.7% 77.2% DCNN [2] 76.80 ± 0.60% 73.00 ± 0.52% GCN [26] 81.59 ± 0.42% 78.72 ± 0.25% MoNet 81.69 ± 0.48% 78.81 ± 0.44% in all the poses were used for training (800 shapes in total); the…”
Deep learning via semi-supervised embedding (2008, methodology): “LapSVM (Belkin et al., 2006) uses the Laplacian Eigenmaps type regularizer with an SVM: minimize LL+U uu ||w||2 + .”
Incentivizing Exploration In Reinforcement Learning With Deep Predictive Models (2015, methodology): “We found that the reconstructed input achieves a small but non-trivial residual on the test set regardless of which auto encoder training technique is utilized, suggesting that in both cases it learns underlying features of the state space while avoiding overﬁtting.”
Conditional variance penalties and domain shift robustness (2017, background): “The right hand side can also be interpreted as the graph Laplacian (Belkin et al., 2006) of an appropriately weighted graph that fully connects all observations i ∈ Sj for each j ∈ {1, .”
Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels (2014, background): “thematically well-founded non-parametricmodeling techniques for a wide range of problems in machine learning. These include nonlinear classiﬁcatio n, regression, clustering, semi-supervised learning [Belkin et al., 2006], time-series analysis [Parzen, 1970], sequence modeling [Song et al., 2013], dy”
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.”
Attention-based Graph Neural Network for Semi-supervised Learning (2018, methodology): “ManiReg [5] replaces supervised loss with that of a support vector machine.”
Good Semi-supervised Learning That Requires a Bad GAN (2017, methodology): “Traditional graph-based methods [2, 26] were extended to deep neural networks [22, 23, 8], which involves applying convolutional neural networks [10] and feature learning techniques to graphs so that the underlying manifold structure can be exploited.”
A Convex Formulation for Learning Task Relationships in Multi-Task Learning (2010, methodology): “In our future research, we will consider incorporating additional data sources into our regularization formulation in a way similar to manifold regularization [5] to further boost the learning performance under the multi-task learning setting.”
A Comprehensive Survey on Transfer Learning (2019, background): “In light of the manifold assumption [30] and the graph-based regularizer [117], [118], fast-DAM designs a domain-dependent regularizer.”
Smooth Neighbors on Teacher Graphs for Semi-Supervised Learning (2017, methodology): “Previous work usually constructs the graph in advance using prior knowledge or manual labeling and the graph remains fixed in the following training process [4, 50].”
A Survey on Deep Semi-Supervised Learning (2021, neutral): “ods, including generative models [9], [10], semi-supervised support vector machines [11], [12], [13], [14], graph-based methods [15], [16], [17], [18], and co-training [19].”
Multi-View Clustering and Feature Learning via Structured Sparsity (2013, background): “However, in most real-world applications, the independence assumption of the feature sets is not well satisfied, such that these methods may not effectively work (Belkin et al., 2006).”