Spline embedding for nonlinear dimensionality reduction

Shiming Xiang; Feiping Nie; Changshui Zhang; Chunxia Zhang

doi:10.1007/11871842_85

Spline embedding for nonlinear dimensionality reduction

Shiming Xiang^*, Feiping Nie, Changshui Zhang, Chunxia Zhang

^*Corresponding author for this work

School of Computer Science and Technology

Tsinghua University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Citations (Scopus)

Abstract

This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.

Original language	English
Title of host publication	Machine Learning
Subtitle of host publication	ECML 2006 - 17th European Conference on Machine Learning, Proceedings
Publisher	Springer Verlag
Pages	825-832
Number of pages	8
ISBN (Print)	354045375X, 9783540453758
DOIs	https://doi.org/10.1007/11871842_85
Publication status	Published - 2006
Event	17th European Conference on Machine Learning, ECML 2006 - Berlin, Germany Duration: 18 Sept 2006 → 22 Sept 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4212 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th European Conference on Machine Learning, ECML 2006
Country/Territory	Germany
City	Berlin
Period	18/09/06 → 22/09/06

Access to Document

10.1007/11871842_85

Cite this

Xiang, S., Nie, F., Zhang, C., & Zhang, C. (2006). Spline embedding for nonlinear dimensionality reduction. In Machine Learning: ECML 2006 - 17th European Conference on Machine Learning, Proceedings (pp. 825-832). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4212 LNAI). Springer Verlag. https://doi.org/10.1007/11871842_85

Xiang, Shiming ; Nie, Feiping ; Zhang, Changshui et al. / Spline embedding for nonlinear dimensionality reduction. Machine Learning: ECML 2006 - 17th European Conference on Machine Learning, Proceedings. Springer Verlag, 2006. pp. 825-832 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{8e6f1a7098da489a9ceeb9d8ba1f8331,

title = "Spline embedding for nonlinear dimensionality reduction",

abstract = "This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.",

author = "Shiming Xiang and Feiping Nie and Changshui Zhang and Chunxia Zhang",

year = "2006",

doi = "10.1007/11871842_85",

language = "English",

isbn = "354045375X",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "825--832",

booktitle = "Machine Learning",

address = "Germany",

note = "17th European Conference on Machine Learning, ECML 2006 ; Conference date: 18-09-2006 Through 22-09-2006",

}

Xiang, S, Nie, F, Zhang, C & Zhang, C 2006, Spline embedding for nonlinear dimensionality reduction. in Machine Learning: ECML 2006 - 17th European Conference on Machine Learning, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4212 LNAI, Springer Verlag, pp. 825-832, 17th European Conference on Machine Learning, ECML 2006, Berlin, Germany, 18/09/06. https://doi.org/10.1007/11871842_85

Spline embedding for nonlinear dimensionality reduction. / Xiang, Shiming; Nie, Feiping; Zhang, Changshui et al.
Machine Learning: ECML 2006 - 17th European Conference on Machine Learning, Proceedings. Springer Verlag, 2006. p. 825-832 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4212 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Nie, Feiping

AU - Zhang, Changshui

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N2 - This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.

AB - This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.

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SN - 9783540453758

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Xiang S, Nie F, Zhang C, Zhang C. Spline embedding for nonlinear dimensionality reduction. In Machine Learning: ECML 2006 - 17th European Conference on Machine Learning, Proceedings. Springer Verlag. 2006. p. 825-832. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11871842_85

Spline embedding for nonlinear dimensionality reduction

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