Embedding new data points for manifold learning via coordinate propagation

Shiming Xiang; Feiping Nie; Yangqiu Song; Changshui Zhang; Chunxia Zhang

doi:10.1007/978-3-540-71701-0_33

Embedding new data points for manifold learning via coordinate propagation

Shiming Xiang^*, Feiping Nie, Yangqiu Song, 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

3 Citations (Scopus)

Abstract

In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction (NLDR). Most of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we propose an extension approach, i.e., embedding new data points into the previously-learned manifold. The core idea of our approach is to propagate the known coordinates to each of the new data points. We first formulate this task as a quadratic programming, and then develop an iterative algorithm for coordinate propagation. Smoothing splines are used to yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results illustrate the validity of our approach.

Original language	English
Title of host publication	Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings
Publisher	Springer Verlag
Pages	332-343
Number of pages	12
ISBN (Print)	9783540717003
DOIs	https://doi.org/10.1007/978-3-540-71701-0_33
Publication status	Published - 2007
Event	11th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2007 - Nanjing, China Duration: 22 May 2007 → 25 May 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4426 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2007
Country/Territory	China
City	Nanjing
Period	22/05/07 → 25/05/07

Access to Document

10.1007/978-3-540-71701-0_33

Cite this

Xiang, S., Nie, F., Song, Y., Zhang, C., & Zhang, C. (2007). Embedding new data points for manifold learning via coordinate propagation. In Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings (pp. 332-343). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4426 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-540-71701-0_33

Xiang, Shiming ; Nie, Feiping ; Song, Yangqiu et al. / Embedding new data points for manifold learning via coordinate propagation. Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings. Springer Verlag, 2007. pp. 332-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Embedding new data points for manifold learning via coordinate propagation",

abstract = "In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction (NLDR). Most of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we propose an extension approach, i.e., embedding new data points into the previously-learned manifold. The core idea of our approach is to propagate the known coordinates to each of the new data points. We first formulate this task as a quadratic programming, and then develop an iterative algorithm for coordinate propagation. Smoothing splines are used to yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results illustrate the validity of our approach.",

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

year = "2007",

doi = "10.1007/978-3-540-71701-0_33",

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

publisher = "Springer Verlag",

pages = "332--343",

booktitle = "Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings",

address = "Germany",

note = "11th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2007 ; Conference date: 22-05-2007 Through 25-05-2007",

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Xiang, S, Nie, F, Song, Y, Zhang, C & Zhang, C 2007, Embedding new data points for manifold learning via coordinate propagation. in Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4426 LNAI, Springer Verlag, pp. 332-343, 11th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2007, Nanjing, China, 22/05/07. https://doi.org/10.1007/978-3-540-71701-0_33

Embedding new data points for manifold learning via coordinate propagation. / Xiang, Shiming; Nie, Feiping; Song, Yangqiu et al.
Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings. Springer Verlag, 2007. p. 332-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4426 LNAI).

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

TY - GEN

T1 - Embedding new data points for manifold learning via coordinate propagation

AU - Xiang, Shiming

AU - Nie, Feiping

AU - Song, Yangqiu

AU - Zhang, Changshui

AU - Zhang, Chunxia

PY - 2007

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N2 - In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction (NLDR). Most of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we propose an extension approach, i.e., embedding new data points into the previously-learned manifold. The core idea of our approach is to propagate the known coordinates to each of the new data points. We first formulate this task as a quadratic programming, and then develop an iterative algorithm for coordinate propagation. Smoothing splines are used to yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results illustrate the validity of our approach.

AB - In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction (NLDR). Most of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we propose an extension approach, i.e., embedding new data points into the previously-learned manifold. The core idea of our approach is to propagate the known coordinates to each of the new data points. We first formulate this task as a quadratic programming, and then develop an iterative algorithm for coordinate propagation. Smoothing splines are used to yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results illustrate the validity of our approach.

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

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BT - Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings

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Xiang S, Nie F, Song Y, Zhang C, Zhang C. Embedding new data points for manifold learning via coordinate propagation. In Advances in Knowledge Discovery and Data Mining - 11th Pacific-Asia Conference, PAKDD 2007, Proceedings. Springer Verlag. 2007. p. 332-343. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-71701-0_33

Embedding new data points for manifold learning via coordinate propagation

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