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On Manifold Regularization

by Mikhail Belkin, Partha Niyogi, Vikas Sindhwani , 2005
"... We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose learner. Some transductive graph learni ..."
Abstract - Cited by 98 (0 self) - Add to MetaCart
We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose learner. Some transductive graph

Manifold regularization: A geometric framework for learning from labeled and unlabeled examples

by Mikhail Belkin, Partha Niyogi, Vikas Sindhwani - JOURNAL OF MACHINE LEARNING RESEARCH , 2006
"... We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning al ..."
Abstract - Cited by 578 (16 self) - Add to MetaCart
We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning

Vector-valued Manifold Regularization

by Hà Quang Minh, Vikas Sindhwani
"... We consider the general problem of learning an unknown functional dependency, f: X ↦ → Y, between a structured input space X and a structured output space Y, fromlabeled and unlabeled examples. We formulate this problem in terms of data-dependent regularization in Vector-valued Reproducing Kernel Hi ..."
Abstract - Cited by 9 (4 self) - Add to MetaCart
Hilbert Spaces (Micchelli & Pontil, 2005) whichelegantlyextendfamiliarscalarvalued kernel methods to the general setting where Y has a Hilbert space structure. Our methods provide a natural extension of Manifold Regularization (Belkin et al., 2006) algorithms to also exploit output inter

Large-scale sparsified manifold regularization

by Ivor W. Tsang, James T. Kwok - Advances in Neural Information Processing Systems (NIPS) 19 , 2006
"... Semi-supervised learning is more powerful than supervised learning by using both labeled and unlabeled data. In particular, the manifold regularization framework, together with kernel methods, leads to the Laplacian SVM (LapSVM) that has demonstrated state-of-the-art performance. However, the LapSVM ..."
Abstract - Cited by 24 (3 self) - Add to MetaCart
Semi-supervised learning is more powerful than supervised learning by using both labeled and unlabeled data. In particular, the manifold regularization framework, together with kernel methods, leads to the Laplacian SVM (LapSVM) that has demonstrated state-of-the-art performance. However, the Lap

Manifold Regularization for SIR with Rate Root-n Convergence

by Wei Bian, Dacheng Tao
"... In this paper, we study the manifold regularization for the Sliced Inverse Regression (SIR). The manifold regularization improves the standard SIR in two aspects: 1) it encodes the local geometry for SIR and 2) it enables SIR to deal with transductive and semi-supervised learning problems. We prove ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
In this paper, we study the manifold regularization for the Sliced Inverse Regression (SIR). The manifold regularization improves the standard SIR in two aspects: 1) it encodes the local geometry for SIR and 2) it enables SIR to deal with transductive and semi-supervised learning problems. We prove

Manifold Regularization for Structured Outputs via the Joint Kernel

by Chonghai Hu, James T. Kwok
"... Abstract — By utilizing the label dependencies among both the labeled and unlabeled data, semi-supervised learning often has better generalization performance than supervised learning. In this paper, we extend a popular graph-based semi-supervised learning method, namely, manifold regularization, to ..."
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Abstract — By utilizing the label dependencies among both the labeled and unlabeled data, semi-supervised learning often has better generalization performance than supervised learning. In this paper, we extend a popular graph-based semi-supervised learning method, namely, manifold regularization

Solution Path for Manifold Regularized Semisupervised Classification

by Gang Wang, Fei Wang, Tao Chen, Dit-yan Yeung, Frederick H. Lochovsky
"... Abstract—Traditional learning algorithms use only labeled data for training. However, labeled examples are often difficult or time consuming to obtain since they require substantial human labeling efforts. On the other hand, unlabeled data are often relatively easy to collect. Semisupervised learnin ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
learning addresses this problem by using large quantities of unlabeled data with labeled data to build better learning algorithms. In this paper, we use the manifold regularization approach to formulate the semisupervised learning problem where a regularization framework which balances a tradeoff between

Laplacian Embedded Regression for Scalable Manifold Regularization

by Lin Chen, Ivor W. Tsang, Dong Xu
"... Semi-supervised Learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundat ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
Semi-supervised Learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical

Manifold regularization and semi-supervised learning: some theoretical analysis

by Partha Niyogi, Zoubin Ghahramani , 2008
"... Manifold regularization (Belkin et al., 2006) is a geometrically motivated framework for machine learning within which several semi-supervised algorithms have been constructed. Here we try to provide some theoretical understanding of this approach. Our main result is to expose the natural structure ..."
Abstract - Cited by 19 (0 self) - Add to MetaCart
Manifold regularization (Belkin et al., 2006) is a geometrically motivated framework for machine learning within which several semi-supervised algorithms have been constructed. Here we try to provide some theoretical understanding of this approach. Our main result is to expose the natural structure

Unsupervised Maximum Margin Feature Selection with Manifold Regularization

by Bin Zhao, James Kwok, Fei Wang, Changshui Zhang
"... Feature selection plays a fundamental role in many pattern recognition problems. However, most efforts have been focused on the supervised scenario, while unsupervised feature selection remains as a rarely touched research topic. In this paper, we propose Manifold-Based Maximum Margin Feature Select ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
Feature selection plays a fundamental role in many pattern recognition problems. However, most efforts have been focused on the supervised scenario, while unsupervised feature selection remains as a rarely touched research topic. In this paper, we propose Manifold-Based Maximum Margin Feature
Results 1 - 10 of 1,843