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118
SemiSupervised Learning Literature Survey
, 2006
"... We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter ..."
Abstract

Cited by 475 (8 self)
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We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter excerpt from the author’s
doctoral thesis (Zhu, 2005). However the author plans to update the online version frequently to incorporate the latest development in the field. Please obtain the latest
version at http://www.cs.wisc.edu/~jerryzhu/pub/ssl_survey.pdf
SemiSupervised Classification by Low Density Separation
, 2005
"... We believe that the cluster assumption is key to successful semisupervised learning. Based on this, we propose three semisupervised algorithms: 1. deriving graphbased distances that emphazise low density regions between clusters, followed by training a standard SVM; 2. optimizing the Transd ..."
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Cited by 127 (9 self)
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We believe that the cluster assumption is key to successful semisupervised learning. Based on this, we propose three semisupervised algorithms: 1. deriving graphbased distances that emphazise low density regions between clusters, followed by training a standard SVM; 2. optimizing the Transductive SVM objective function, which places the decision boundary in low density regions, by gradient descent; 3. combining the first two to make maximum use of the cluster assumption. We compare with state of the art algorithms and demonstrate superior accuracy for the latter two methods.
Label propagation through linear neighborhoods
 ICML06, 23rd International Conference on Machine Learning
, 2006
"... A novel semisupervised learning approach is proposed based on a linear neighborhood model, which assumes that each data point can be linearly reconstructed from its neighborhood. Our algorithm, named Linear Neighborhood Propagation (LNP), can propagate the labels from the labeled points to the whol ..."
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Cited by 60 (9 self)
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A novel semisupervised learning approach is proposed based on a linear neighborhood model, which assumes that each data point can be linearly reconstructed from its neighborhood. Our algorithm, named Linear Neighborhood Propagation (LNP), can propagate the labels from the labeled points to the whole dataset using these linear neighborhoods with sufficient smoothness. We also derive an easy way to extend LNP to outofsample data. Promising experimental results are presented for synthetic data, digit and text classification tasks. 1.
Nonlinear dimensionality reduction by semidefinite programming and kernel matrix factorization
 in Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics
, 2005
"... We describe an algorithm for nonlinear dimensionality reduction based on semidefinite programming and kernel matrix factorization. The algorithm learns a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. In earlier work, the kernel matrix was learned by maximiz ..."
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Cited by 50 (5 self)
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We describe an algorithm for nonlinear dimensionality reduction based on semidefinite programming and kernel matrix factorization. The algorithm learns a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. In earlier work, the kernel matrix was learned by maximizing the variance in feature space while preserving the distances and angles between nearest neighbors. In this paper, adapting recent ideas from semisupervised learning on graphs, we show that the full kernel matrix can be very well approximated by a product of smaller matrices. Representing the kernel matrix in this way, we can reformulate the semidefinite program in terms of a much smaller submatrix of inner products between randomly chosen landmarks. The new framework leads to orderofmagnitude reductions in computation time and makes it possible to study much larger problems in manifold learning. 1
Nonparametric function induction in semisupervised learning
 In Proc. Artificial Intelligence and Statistics
, 2005
"... There has been an increase of interest for semisupervised learning recently, because of the many datasets with large amounts of unlabeled examples and only a few labeled ones. This paper follows up on proposed nonparametric algorithms which provide an estimated continuous label for the given unlabe ..."
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Cited by 41 (5 self)
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There has been an increase of interest for semisupervised learning recently, because of the many datasets with large amounts of unlabeled examples and only a few labeled ones. This paper follows up on proposed nonparametric algorithms which provide an estimated continuous label for the given unlabeled examples. First, it extends them to function induction algorithms that minimize a regularization criterion applied to an outofsample example, and happen to have the form of Parzen windows regressors. This allows to predict test labels without solving again a linear system of dimension n (the number of unlabeled and labeled training examples), which can cost O(n 3). Second, this function induction procedure gives rise to an efficient approximation of the training process, reducing the linear system to be solved to m ≪ n unknowns, using only a subset of m examples. An improvement of O(n 2 /m 2) in time can thus be obtained. Comparative experiments are presented, showing the good performance of the induction formula and approximation algorithm. 1
Harmonic mixtures: combining mixture models and graphbased methods for inductive and scalable semisupervised learning
 In Proc. Int. Conf. Machine Learning
, 2005
"... Graphbased methods for semisupervised learning have recently been shown to be promising for combining labeled and unlabeled data in classification problems. However, inference for graphbased methods often does not scale well to very large data sets, since it requires inversion of a large matrix or ..."
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Cited by 38 (2 self)
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Graphbased methods for semisupervised learning have recently been shown to be promising for combining labeled and unlabeled data in classification problems. However, inference for graphbased methods often does not scale well to very large data sets, since it requires inversion of a large matrix or solution of a large linear program. Moreover, such approaches are inherently transductive, giving predictions for only those points in the unlabeled set, and not for an arbitrary test point. In this paper a new approach is presented that preserves the strengths of graphbased semisupervised learning while overcoming the limitations of scalability and noninductive inference, through a combination of generative mixture models and discriminative regularization using the graph Laplacian. Experimental results show that this approach preserves the accuracy of purely graphbased transductive methods when the data has “manifold structure, ” and at the same time achieves inductive learning with significantly reduced computational cost. 1.
Combining graph Laplacians for semisupervised learning
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 18
, 2005
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Ranking on graph data
 In ICML
, 2006
"... In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a realvalued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function when the data is represented as a ..."
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Cited by 34 (1 self)
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In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a realvalued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function when the data is represented as a graph, in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in regularization theory for graphs and corresponding Laplacianbased methods for classification, we develop an algorithmic framework for learning ranking functions on graph data. We provide generalization guarantees for our algorithms via recent results based on the notion of algorithmic stability, and give experimental evidence of the potential benefits of our framework. 1.
Online learning over graphs
 Proc. 22nd Int. Conf. Machine Learning
, 2005
"... We apply classic online learning techniques similar to the perceptron algorithm to the problem of learning a function defined on a graph. The benefit of our approach includes simple algorithms and performance guarantees that we naturally interpret in terms of structural properties of the graph, such ..."
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Cited by 32 (9 self)
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We apply classic online learning techniques similar to the perceptron algorithm to the problem of learning a function defined on a graph. The benefit of our approach includes simple algorithms and performance guarantees that we naturally interpret in terms of structural properties of the graph, such as the algebraic connectivity or the diameter of the graph. We also discuss how these methods can be modified to allow active learning on a graph. We present preliminary experiments with encouraging results. 1.
The curse of highly variable functions for local kernel machines
 In Advances in Neural Information Processing Systems 18
, 2006
"... We present a series of theoretical arguments supporting the claim that a large class of modern learning algorithms that rely solely on the smoothness prior – with similarity between examples expressed with a local kernel – are sensitive to the curse of dimensionality, or more precisely to the variab ..."
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Cited by 29 (14 self)
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We present a series of theoretical arguments supporting the claim that a large class of modern learning algorithms that rely solely on the smoothness prior – with similarity between examples expressed with a local kernel – are sensitive to the curse of dimensionality, or more precisely to the variability of the target. Our discussion covers supervised, semisupervised and unsupervised learning algorithms. These algorithms are found to be local in the sense that crucial properties of the learned function at x depend mostly on the neighbors of x in the training set. This makes them sensitive to the curse of dimensionality, well studied for classical nonparametric statistical learning. We show in the case of the Gaussian kernel that when the function to be learned has many variations, these algorithms require a number of training examples proportional to the number of variations, which could be large even though there may exist short descriptions of the target function, i.e. their Kolmogorov complexity may be low. This suggests that there exist nonlocal learning algorithms that at least have the potential to learn about such structured but apparently complex functions (because locally they have many variations), while not using very specific prior domain knowledge. 1