skip to main content
10.1145/1101149.1101239acmconferencesArticle/Chapter ViewAbstractPublication PagesmmConference Proceedingsconference-collections
Article

Learning with non-metric proximity matrices

Published: 06 November 2005 Publication History

Abstract

Many emerging applications formulate non-metric proximity matrices (non-positive semidefinite), and hence cannot fit into the framework of kernel machines. A popular approach to this problem is to transform the spectrum of the similarity matrix so as to generate a positive semidefinite kernel matrix. In this paper, we explore four representative transformation methods: denoise, flip, diffusion, and shift. Theoretically, we discuss a generalization problem where the test data are not available during transformation, and thus propose an efficient algorithm to address the problem of updating the cross-similarity matrix between test and training data. Extensive experiments have been conducted to evaluate the performance of these methods on several real-world (dis)similarity matrices with semantic meanings.

References

[1]
ALTSCHUL, S. F., GISH, W., MILLER, W., MYERS, E. W., AND LIPMAN, D. J. A basic local alignment search tool. Journal of Molecular Biology 215 (1990), 403--410.
[2]
CARRIER, J., GREENGARD, L., AND ROKHLIN, V. A fast adaptive multipole algorithm for particle simulations. 669--686.
[3]
COX, T. F., AND COX, M. A. A. Multidimensional Scaling. Chapman & Hall/CRC, 2001.
[4]
GRAEPEL, T., HERBRICH, R., BOLLMANN-SDORRA, P., AND OBERMAYER, K. Classification on pairwise proximity data. In In NIPS 11 (1999).
[5]
GU, M., AND EISENSTAT, S. C. A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. SIAM J. Matrix Anal. Appl. 16, 1 (1995), 172--191.
[6]
HAASDONK, B. Feature space interpretation of svms with indefinite kernels. To appear in IEEE Trans. on PAMI (2004).
[7]
HASSDONK, B., AND KEYSERS, D. Tangent distance kernels for support vector machines. In In ICPR'02 (2002).
[8]
KIMELDORF, G. S., AND WAHBA, G. A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. The Annals of Mathematical Statistics 41 (1970), 495--502.
[9]
KONDOR, R. I., AND LAFFERTY, J. Diffusion kernels on graphs and other discrete input spaces. In In ICML'02 (2002).
[10]
LIN, H.-T., AND LIN, C.-J. A study on sigmoid kernels for svm and the training of non-psd kernels by smo-type methods. Tech. rep., National Taiwan Univ., 2003.
[11]
PEKALSKA, E., PACLIK, P., AND DUIN, R. P. W. A generalized kernel approach to dissimilarity-based classification. Journal of Machine Learning Research 2 (2002), 175--211.
[12]
QAMRA, A., MENG, Y., AND CHANG, E. Y. Enhanced perceptual distance functions and indexing for image replica recognition. IEEE Trans. on PAMI 27, 3 (March 2005), 379--391.
[13]
ROTH, V., LAUB, J., KAWANABE, M., AND BUHMANN, J. M. Optimal cluster preserving embedding of non-metric proximity data. IEEE Trans. on PAMI 25, 12 (December 2003).
[14]
RUBNER, Y., TOMASI, C., AND GUIBAS, L. J. The earth mover's distance as a metric for image retrieval. International Journal of Computer Vision 40, 2 (2000), 99--121.
[15]
SHIMODAIRA, H., ICHI NOMA, K., NAKAI, M., AND SAGAYAMA, S. Dynamic time-alignment kernel in support vector machine. In In NIPS 14 (2001).
[16]
SIMARD, P., CUN, Y. L., AND DENKER, J. Efficient pattern recognition using a new transformation distance. In In NIPS 5 (1993).
[17]
VAPNIK, V. The Nature of Statistical Learning Theory. Springer, New York, 1995.
[18]
WILKINSON, J. H. The Algebraic Eigenvalue Problem. Oxford University Press, 1988.
[19]
WU, G., CHANG, E. Y., AND ZHANG, Z. An analysis of transformation on non-positive semidefinite similarity matrix for kernel machines. In UCSB Technical Report (2005).

Cited By

View all
  • (2019)A review on distance based time series classificationData Mining and Knowledge Discovery10.1007/s10618-018-0596-433:2(378-412)Online publication date: 1-Mar-2019
  • (2015)Pairwised Specific Distance Learning from Physical LinkagesACM Transactions on Knowledge Discovery from Data10.1145/27004059:3(1-27)Online publication date: 1-Apr-2015
  • (2015)On Recursive Edit Distance Kernels With Application to Time Series ClassificationIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2014.233387626:6(1121-1133)Online publication date: Jun-2015
  • Show More Cited By

Index Terms

  1. Learning with non-metric proximity matrices
    Index terms have been assigned to the content through auto-classification.

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    MULTIMEDIA '05: Proceedings of the 13th annual ACM international conference on Multimedia
    November 2005
    1110 pages
    ISBN:1595930442
    DOI:10.1145/1101149
    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]

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 06 November 2005

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. kernel machines
    2. non-metric learning

    Qualifiers

    • Article

    Conference

    MM05

    Acceptance Rates

    Overall Acceptance Rate 1,190 of 4,527 submissions, 26%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)1
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 30 Jan 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2019)A review on distance based time series classificationData Mining and Knowledge Discovery10.1007/s10618-018-0596-433:2(378-412)Online publication date: 1-Mar-2019
    • (2015)Pairwised Specific Distance Learning from Physical LinkagesACM Transactions on Knowledge Discovery from Data10.1145/27004059:3(1-27)Online publication date: 1-Apr-2015
    • (2015)On Recursive Edit Distance Kernels With Application to Time Series ClassificationIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2014.233387626:6(1121-1133)Online publication date: Jun-2015
    • (2014)On general purpose time series similarity measures and their use as kernel functions in support vector machinesInformation Sciences: an International Journal10.1016/j.ins.2014.05.025281(478-495)Online publication date: 1-Oct-2014
    • (2009)Non-metric label propagationProceedings of the 21st International Joint Conference on Artificial Intelligence10.5555/1661445.1661663(1357-1362)Online publication date: 11-Jul-2009

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media