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594
Distance Metric Learning, With Application To Clustering With SideInformation
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 15
, 2003
"... Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as Kmeans initially fails to find one that is meaningful to a user, the only recourse may be for the us ..."
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Cited by 799 (14 self)
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Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as Kmeans initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar." For instance, we may ask them to provide examples. In this paper, we present an algorithm that, given examples of similar (and, if desired, dissimilar) pairs of points in R , learns a distance metric over R that respects these relationships. Our method is based on posing metric learning as a convex optimization problem, which allows us to give efficient, localoptimafree algorithms. We also demonstrate empirically that the learned metrics can be used to significantly improve clustering performance.
Searching in metric spaces
, 2001
"... The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather gen ..."
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Cited by 432 (38 self)
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The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather general case where the similarity criterion defines a metric space, instead of the more restricted case of a vector space. Many solutions have been proposed in different areas, in many cases without crossknowledge. Because of this, the same ideas have been reconceived several times, and very different presentations have been given for the same approaches. We present some basic results that explain the intrinsic difficulty of the search problem. This includes a quantitative definition of the elusive concept of “intrinsic dimensionality. ” We also present a unified
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. ..."
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Cited by 383 (11 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.
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 268 (10 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.
Global Versus Local Methods in Nonlinear Dimensionality Reduction
, 2003
"... Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the adva ..."
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Cited by 208 (6 self)
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Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the advantages of the global approach with what have previously been exclusive advantages of local methods: computational sparsity and the ability to invert conformal maps.
Learning a distance metric from relative comparisons
 In Proc. Advances in Neural Information Processing Systems
, 2003
"... This paper presents a method for learning a distance metric from relative comparison such as “A is closer to B than A is to C”. Taking a Support Vector Machine (SVM) approach, we develop an algorithm that provides a flexible way of describing qualitative training data as a set of constraints. We sh ..."
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Cited by 191 (0 self)
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This paper presents a method for learning a distance metric from relative comparison such as “A is closer to B than A is to C”. Taking a Support Vector Machine (SVM) approach, we develop an algorithm that provides a flexible way of describing qualitative training data as a set of constraints. We show that such constraints lead to a convex quadratic programming problem that can be solved by adapting standard methods for SVM training. We empirically evaluate the performance and the modelling flexibility of the algorithm on a collection of text documents. 1
Partial and approximate symmetry detection for 3D geometry
 ACM TRANSACTIONS ON GRAPHICS
, 2006
"... “Symmetry is a complexityreducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and manmade objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a com ..."
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Cited by 180 (28 self)
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“Symmetry is a complexityreducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and manmade objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important highlevel information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc.
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 175 (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.
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 175 (11 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.
A Kernel View Of The Dimensionality Reduction Of Manifolds
, 2003
"... We interpret several wellknown algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithm ..."
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Cited by 155 (7 self)
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We interpret several wellknown algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.