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Nonlinear barycentric dimensionality reduction
2010 IEEE International Conference on Image Processing, 2010Many high-dimensional datasets can be mapped onto lower-dimensional linear simplexes, parametrized by barycentric coordinates. We present an unsupervised algorithm that is able to find the barycentric coordinates and corresponding vertices of such a high-dimensional dataset, by combining manifold learning with a distance geometry based algorithm for ...
Rob Heylen, Paul Scheunders
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On Nonlinear Dimensionality Reduction for Face Recognition [PDF]
Image and Vision Computing, 2012 The curse of dimensionality has prompted intensive research in effective methods of mapping high dimensional data. Dimensionality reduction and subspace learning have been studied extensively and widely applied to feature extraction and pattern representation in image and vision applications.
Weilin Huang, Hujun Yin
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Nonlinear methods for clustering and reduction of dimensionality
IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), 2003Analysis of data in computational finance and computational neuroscience share a number of common traits: data are typically massive, noisy, very high dimensional, and governed by complete multi-scale time dynamics. The set of known parameters forms a small subset of the true variates that control the dynamics of the systems from which data is ...
Hamid Eghbalnia +2 more
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Nonlinear dimensionality reduction by curvature minimization
2016 23rd International Conference on Pattern Recognition (ICPR), 2016In this paper, we introduce a nonlinear dimensionality reduction (NLDR) technique that can construct a low-dimensional embedding efficiently and accurately with low embedding distortions. The key idea is to divide NLDR into nonlinearity reduction and linear dimensionality reduction, which simplifies the overall NLDR process.
Yusuke Yoshiyasu, Eiichi Yoshida
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Locally Adaptive Nonlinear Dimensionality Reduction
2006Popular nonlinear dimensionality reduction algorithms, e.g., SIE and Isomap suffer a difficulty in common: global neighborhood parameters often fail in tackling data sets with high variation in local manifold. To improve the availability of nonlinear dimensionality reduction algorithms in the field of machine learning, an adaptive neighbors selection ...
Yuexian Hou, Hongmin Yang, Pilian He
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Nonlinear Dimensionality Reduction by Locally Linear Inlaying
IEEE Transactions on Neural Networks, 2009High-dimensional data is involved in many fields of information processing. However, sometimes, the intrinsic structures of these data can be described by a few degrees of freedom. To discover these degrees of freedom or the low-dimensional nonlinear manifold underlying a high-dimensional space, many manifold learning algorithms have been proposed ...
Yuexian Hou +4 more
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Nonlinear Dimensionality Reduction With Relative Distance Comparison
Neurocomputing, 2009This paper proposes a new algorithm for nonlinear dimensionality reduction. Our basic idea is to explore and exploit the local geometry of the manifold with relative distance comparisons. All such comparisons derived from local neighborhoods are enumerated to constrain the manifold to be learned.
Feiping Nie, Shiming Xiang, Yangqiu Song
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Incremental nonlinear dimensionality reduction by manifold learning
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold learning.
Martin H. C. Law, Anil K. Jain 0001
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Some aspects of nonlinear dimensionality reduction
Computational StatisticszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liwen Wang +3 more
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