Results 1  10
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143
SemiSupervised Learning Using Gaussian Fields and Harmonic Functions
 IN ICML
, 2003
"... An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning ..."
Abstract

Cited by 490 (14 self)
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An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds
 Journal of Machine Learning Research
, 2003
"... The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. ..."
Abstract

Cited by 252 (8 self)
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The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation.
Probability Estimates for Multiclass Classification by Pairwise Coupling
 Journal of Machine Learning Research
, 2003
"... Pairwise coupling is a popular multiclass classification method that combines together all pairwise comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement. ..."
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Cited by 187 (1 self)
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Pairwise coupling is a popular multiclass classification method that combines together all pairwise comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement.
Unsupervised Learning of Image Manifolds by Semidefinite Programming
, 2004
"... Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be ..."
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Cited by 162 (9 self)
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Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be used to analyze high dimensional data that lies on or near a low dimensional manifold. It overcomes certain limitations of previous work in manifold learning, such as Isomap and locally linear embedding. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and solid objects.
Modeling the manifolds of images of handwritten digits
 IEEE Transactions on Neural Networks
, 1997
"... description length, density estimation. ..."
Stochastic Neighbor Embedding
 Advances in Neural Information Processing Systems 15
"... We describe a probabilistic approach to the task of placing objects, described by highdimensional vectors or by pairwise dissimilarities, in a lowdimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the highdimensional space and the densities ..."
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Cited by 118 (9 self)
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We describe a probabilistic approach to the task of placing objects, described by highdimensional vectors or by pairwise dissimilarities, in a lowdimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the highdimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the lowdimensional "images" of the objects. A natural cost function is a sum of KullbackLeibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the lowdimensional images.
Learning from Labeled and Unlabeled Data with Label Propagation
, 2002
"... We investigate the use of unlabeled data to help labeled data in classification. We propose a simple iterative algorithm, label propagation, to propagate labels through the dataset along high density areas defined by unlabeled data. We give the analysis of the algorithm, show its solution, and its c ..."
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Cited by 113 (0 self)
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We investigate the use of unlabeled data to help labeled data in classification. We propose a simple iterative algorithm, label propagation, to propagate labels through the dataset along high density areas defined by unlabeled data. We give the analysis of the algorithm, show its solution, and its connection to several other algorithms. We also show how to learn parameters by minimum spanning tree heuristic and entropy minimization, and the algorithm's ability to do feature selection. Experiment results are promising.
Learning a kernel matrix for nonlinear dimensionality reduction
 In Proceedings of the Twenty First International Conference on Machine Learning (ICML04
, 2004
"... We investigate how to learn a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. Noting that the kernel matrix implicitly maps the data into a nonlinear feature space, we show how to discover a mapping that “unfolds ” the underlying manifold from which the data ..."
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Cited by 112 (7 self)
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We investigate how to learn a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. Noting that the kernel matrix implicitly maps the data into a nonlinear feature space, we show how to discover a mapping that “unfolds ” the underlying manifold from which the data was sampled. The kernel matrix is constructed by maximizing the variance in feature space subject to local constraints that preserve the angles and distances between nearest neighbors. The main optimization involves an instance of semidefinite programming—a fundamentally different computation than previous algorithms for manifold learning, such as Isomap and locally linear embedding. The optimized kernels perform better than polynomial and Gaussian kernels for problems in manifold learning, but worse for problems in large margin classification. We explain these results in terms of the geometric properties of different kernels and comment on various interpretations of other manifold learning algorithms as kernel methods.
Joint Induction of Shape Features and Tree Classifiers
 IEEE Trans. PAMI
, 1997
"... We introduce a very large family of binary features for twodimensional shapes. The salient ones for separating particular shapes are determined by inductive learning during the construction of classi cation trees. There is a feature for every possible geometric arrangement of local topographic code ..."
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Cited by 76 (6 self)
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We introduce a very large family of binary features for twodimensional shapes. The salient ones for separating particular shapes are determined by inductive learning during the construction of classi cation trees. There is a feature for every possible geometric arrangement of local topographic codes. The arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial a ne and nonlinear deformations. They are also partially ordered, which makes it possible to narrow the search for informative ones at each node of the tree. Di erent trees correspond to di erent aspects of shape. They are statistically weakly dependent due to randomization and are aggregated in a simple way. Adapting the algorithm to a shape family is then fully automatic once training samples are provided. As an illustration, we classify handwritten digits from the NIST database � the error rate is:7%.
Combining Active Learning and SemiSupervised Learning Using Gaussian Fields and Harmonic Functions
 ICML 2003 workshop on The Continuum from Labeled to Unlabeled Data in Machine Learning and Data Mining
, 2003
"... Active and semisupervised learning are important techniques when labeled data are scarce. We combine the two under a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The semisupervi ..."
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Cited by 76 (5 self)
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Active and semisupervised learning are important techniques when labeled data are scarce. We combine the two under a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The semisupervised learning problem is then formulated in terms of a Gaussian random field on this graph, the mean of which is characterized in terms of harmonic functions. Active learning is performed on top of the semisupervised learning scheme by greedily selecting queries from the unlabeled data to minimize the estimated expected classification error (risk); in the case of Gaussian fields the risk is efficiently computed using matrix methods. We present experimental results on synthetic data, handwritten digit recognition, and text classification tasks. The active learning scheme requires a much smaller number of queries to achieve high accuracy compared with random query selection. 1.