skip to main content
10.1145/1143844.1143894acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicmlConference Proceedingsconference-collections
Article

An analysis of graph cut size for transductive learning

Published: 25 June 2006 Publication History

Abstract

I consider the setting of transductive learning of vertex labels in graphs, in which a graph with n vertices is sampled according to some unknown distribution; there is a true labeling of the vertices such that each vertex is assigned to exactly one of k classes, but the labels of only some (random) subset of the vertices are revealed to the learner. The task is then to find a labeling of the remaining (unlabeled) vertices that agrees as much as possible with the true labeling. Several existing algorithms are based on the assumption that adjacent vertices are usually labeled the same. In order to better understand algorithms based on this assumption, I derive data-dependent bounds on the fraction of mislabeled vertices, based on the number (or total weight) of edges between vertices differing in predicted label (i.e., the size of the cut).

References

[1]
Benczúr, A., & Karger, D. (1996). Approximating s-t minimum cuts in ÕÕ(n2) time. ACM Symposium on Theory of Computing.
[2]
Blum, A., & Chawla, S. (2001). Learning from labeled and unlabeled data using graph mincuts. Proceedings of the International Conference on Machine Learning.
[3]
Blum, A., Lafferty, J., Rwebangira, M., & Reddy, R. (2004). Semi-supervised learning using randomized mincuts. International Conference on Machine Learning.
[4]
Blum, A., & Langford, J. (2003). PAC-MDL bounds. 16th Annual Conference on Learning Theory.
[5]
Chandran, L. S., & Ram, L. S. (2004). On the number of minimum cuts in a graph. SIAM Journal of Discrete Mathematics, 18, 177--194.
[6]
Cheung, K. K. H., Cunningham, W. H., & Tang, L. (2005). Optimal 3-terminal cuts and linear programming. Mathematical Programming.
[7]
Cormen, T., Leiserson, C., Rivest, R., & Stein, C. (2001). Introduction to algorithms. MIT Press. 2nd edition.
[8]
Călinescu, G., Karloff, H., & Rabani, Y. (2000). An improved approximation algorithm for multiway cut. Journal of Computer and System Sciences, 60, 564--574.
[9]
Dahlhaus, E., Johnson, D., Papadimitriou, C., Seymour, P., & Yannakakis, M. (1994). The complexity of multiterminal cuts. SIAM Journal on Computing, 23.
[10]
Derbeko, P., El-Yaniv, R., & Meir, R. (2004). Explicit learning curves for transduction and application to clustering and compression algorithms. Journal of Artificial Intelligence Research.
[11]
Goldschmidt, O., & Hochbaum, D. S. (1994). A polynomial algorithm for the k-cut problem for fixed k. Mathematics of Operations Research, 19, 24--37.
[12]
Joachims, T. (2003). Transductive learning via spectral graph partitioning. Proceedings of the International Conference on Machine Learning.
[13]
Karger, D. (1996). Minimum cuts in near-linear time. ACM Symposium on the Theory of Computing.
[14]
Karger, D. (1999). Random sampling in cut, flow, and network design problems. Mathematics of Operations Research, 24, 383--413.
[15]
Karger, D. R., Klein, P., Stein, C., Thorup, M., & Young, N. E. (2004). Rounding algorithms for a geometric embedding of minimum multiway cut. Mathematics of Operations Research, 29, 436--461.
[16]
Kleinberg, J., Sandler, M., & Slivkins, A. (2004). Network failure detection and graph connectivity. 15th ACM-SIAM Symposium on Discrete Algorithms.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences
ICML '06: Proceedings of the 23rd international conference on Machine learning
June 2006
1154 pages
ISBN:1595933832
DOI:10.1145/1143844
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 June 2006

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Article

Acceptance Rates

ICML '06 Paper Acceptance Rate 140 of 548 submissions, 26%;
Overall Acceptance Rate 140 of 548 submissions, 26%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)11
  • Downloads (Last 6 weeks)0
Reflects downloads up to 28 Dec 2024

Other Metrics

Citations

Cited By

View all
  • (2009)Learning unknown graphsProceedings of the 20th international conference on Algorithmic learning theory10.5555/1813231.1813247(110-125)Online publication date: 3-Oct-2009
  • (2009)Transductive Rademacher complexity and its applicationsJournal of Artificial Intelligence Research10.5555/1641503.164150835:1(193-234)Online publication date: 1-Jun-2009
  • (2008)Large margin vs. large volume in transductive learningMachine Language10.1007/s10994-008-5071-972:3(173-188)Online publication date: 1-Sep-2008
  • (2007)Transductive Rademacher Complexity and Its ApplicationsLearning Theory10.1007/978-3-540-72927-3_13(157-171)Online publication date: 2007

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media