A kernel view of the dimensionality reduction of manifolds

Ham, Jihun; Lee, Daniel D.; Mika, Sebastian; Schölkopf, Bernhard

doi:10.1145/1015330.1015417

Cited by 404 publications

(270 citation statements)

References 7 publications

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“…In this section we interpret the algorithm in terms of random walks inspired by (Ham et al, 2003). We will see that this method simply classifies the points by comparing a specific distance measure between them and the labeled points of different classes.…”

Section: Lazy Random Walksmentioning

confidence: 99%

Learning from Labeled and Unlabeled Data Using Random Walks

Zhou

Schölkopf

2004

Lecture Notes in Computer Science

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We consider the general problem of learning from labeled and unlabeled data. Given a set of points, some of them are labeled, and the remaining points are unlabeled. The goal is to predict the labels of the unlabeled points. Any supervised learning algorithm can be applied to this problem, for instance, Support Vector Machines (SVMs). The problem of our interest is if we can implement a classifier which uses the unlabeled data information in some way and has higher accuracy than the classifiers which use the labeled data only. Recently we proposed a simple algorithm, which can substantially benefit from large amounts of unlabeled data and demonstrates clear superiority to supervised learning methods. In this paper we further investigate the algorithm using random walks and spectral graph theory, which shed light on the key steps in this algorithm.

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Section: Lazy Random Walksmentioning

confidence: 99%

Learning from Labeled and Unlabeled Data Using Random Walks

Zhou

Schölkopf

2004

Lecture Notes in Computer Science

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“…Embedding is then obtained through solving an eigenvalue problem on such matrix. It was shown in [25,26] that these approaches are all instances of kernel-based learning, in particular kernel principle component analysis KPCA [27]. Several approaches have been proposed to embed new data points, denoted be out of sample embedding, e.g.…”

Section: Manifold Representationsmentioning

confidence: 99%

Homeomorphic Manifold Analysis (HMA): Generalized separation of style and content on manifolds

Elgammal

Lee

2013

Image and Vision Computing

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The problem of separation of style and content is an essential element of visual perception, and is a fundamental mystery of perception. This problem appears extensively in different computer vision applications. The problem we address in this paper is the separation of style and content when the content lies on a low dimensional nonlinear manifold representing a dynamic object. We show that such a setting appears in many human motion analysis problems. We introduce a framework for learning parameterization of style and content in such settings. Given a set of topologically equivalent manifolds, the Homeomorphic Manifold Analysis (HMA) framework models the variation in their geometries in the space of functions that maps between a topologically-equivalent common representation and each of them. The framework is based on decomposing the style parameters in the space of nonlinear functions that map between a unified embedded representation of the content manifold and style-dependent visual observations. We show the application of the framework in synthesis, recognition, and tracking of certain human motions that follow this setting, such as gait and facial expressions.

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“…This inspires the use of kernel machine, which explores the non-linearity of the data space. The extended nonlinear alternative, KPCA [19,23] and KDA [20], are used.…”

Section: Subspace Projectionmentioning

confidence: 99%

An Integrated Two-Stage Framework for Robust Head Pose Estimation

Trivedi

2005

Lecture Notes in Computer Science

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Abstract. Subspace analysis has been widely used for head pose estimation. However, such techniques are usually sensitive to data alignment and background noise. In this paper a two-stage approach is proposed to address this issue by combining the subspace analysis together with the topography method. The first stage is based on the subspace analysis of Gabor wavelets responses. Different subspace techniques were compared for better exploring the underlying data structure. Nearest prototype matching using Euclidean distance was used to get the pose estimate. The single pose estimated was relaxed to a subset of poses around it to incorporate certain tolerance to data alignment and background noise. In the second stage, the uncertainty is eliminated by analyzing finer geometrical structure details captured by bunch graphs. This coarse-tofine framework was evaluated with a large data set. We examined 86 poses, with the pan angle spanning from −90 o to 90 o and the tilt angle spanning from −60 o to 45 o . The experimental results indicate that the integrated approach has a remarkably better performance than using subspace analysis alone.

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A kernel view of the dimensionality reduction of manifolds

Abstract: kernel view of the dimensionality reduction of manifolds", . July 2004.

Cited by 404 publications

References 7 publications

Learning from Labeled and Unlabeled Data Using Random Walks

Learning from Labeled and Unlabeled Data Using Random Walks

Homeomorphic Manifold Analysis (HMA): Generalized separation of style and content on manifolds

An Integrated Two-Stage Framework for Robust Head Pose Estimation

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