Curvature analysis of frequency modulated manifolds in dimensionality reduction

Guillemard, Mijail; Iske, Armin

doi:10.1007/s10092-010-0031-8

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…Shanghai, China 1 The authors would like to thank anonymous reviewers to improve the quality of this paper, and the researcher of the Research scientist in machine learning and computer vision Laurens van der Maaten for the programming framework support, the anonymous reviewers who provide the valuable comments to improve quality of this paper greatly. 2 Speaker…”

Section: -23 July 2017mentioning

confidence: 99%

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Improved Locally Linear Embedding by Using Adaptive Neighborhood Selection Techniques

Zhang¹,

Zhou²,

Shao³

et al. 2017

Proceedings of the 7th International Conference on Computer Engineering and Networks — PoS(CENet2017)

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Unsupervised learning algorithm locally linear embedding (LLE) is a typical technique which applies the preserving embedding method of high dimensional data to low dimension. The number of neighborhood nodes of LLE is a decisive parameter because the improper value will affect the manifold structure in the local neighborhood and lead to the lower computational efficiency. Based on the fact that the shortest path in low-density can be established easily, this paper proposes an improved LLE method by using the sparse matrix in combination with the weights related to each point used for the linear combination in local neighborhood. The correlation dimension between high and low dimension is used to estimate the proper number of the reduced dimension, thereby selecting the best upper bound for the non-uniform manifold. Finally, we provide the experimental evaluation to verify the effectiveness of the proposed algorithm.

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Section: -23 July 2017mentioning

confidence: 99%

“…The number of available data used for observation or measurement about the engineering, economics and population is on the rise. This increases the difficultly of the theoretical analysis related to the multi-dimensional data such as signals, two-dimensional or three-dimensional images and stereo space etc in the statistical pattern [1].…”

Section: Introductionmentioning

confidence: 99%

Improved Locally Linear Embedding by Using Adaptive Neighborhood Selection Techniques

Zhang¹,

Zhou²,

Shao³

et al. 2017

Proceedings of the 7th International Conference on Computer Engineering and Networks — PoS(CENet2017)

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Adaptive Approximation Algorithms for Sparse Data Representation

Guillemard

Heinen

Iske

et al. 2014

Extraction of Quantifiable Information From Complex Systems

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On the Complexity of Computing Quadrature Formulas for SDEs

Dereich¹,

Müller-Gronbach²,

Ritter³

2012

Foundations of Computational Mathematics, Budapest 2011

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We survey recent results on the constructive approximation of the distribution of the solution of an SDE by probability measures with finite support, i.e., by quadrature formulas with positive weights summing up to one. Here we either consider the distribution on the path space or a marginal distribution on the state space. We provide asymptotic results on the N -th minimal error of deterministic and randomized algorithms, which is the smallest error that can be achieved by any such algorithm not exceeding the cost bound N .

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Curvature analysis of frequency modulated manifolds in dimensionality reduction

Cited by 5 publications

References 20 publications

Improved Locally Linear Embedding by Using Adaptive Neighborhood Selection Techniques

Improved Locally Linear Embedding by Using Adaptive Neighborhood Selection Techniques

Adaptive Approximation Algorithms for Sparse Data Representation

On the Complexity of Computing Quadrature Formulas for SDEs

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