Abstract
We present a novel method for dimensionality reduction and recognition based on Linear Discriminant Analysis (LDA), which specifically deals with the Small Sample Size (SSS) problem in Computer Vision applications. Unlike the traditional methods, which impose specific assumptions to address the SSS problem, our approach introduces a variant of bootstrap bumping technique, which is a general framework in statistics for model search and inference. An intermediate linear representation is first hypothesized from each bootstrap sample. Then LDA is performed in the reduced subspace. Lastly, the final model is selected among all hypotheses for the best classification. Experiments on synthetic and real datasets demonstrate the advantages of our Bootstrap Bumping LDA (BB-LDA) approach over the traditional LDA based methods.
Chapter PDF
Similar content being viewed by others
Keywords
- Bootstrap Sample
- Sampling Ratio
- Quadratic Discriminant Analysis
- Gait Recognition
- Computer Vision Application
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Jain, A., Duin, R., Mao, J.: Statistical pattern recognition: a review. IEEE Trans. Patt. Analy. and Mach. Intell. 22(1), 4–37 (2000)
Belhumeur, P., Hespanha, J., Kriegman, D.: Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection. IEEE Trans. Patt. Analy. and Mach. Intell. 19(7), 711–720 (1997)
Liu, C., Wechsler, H.: Enhanced Fisher linear discriminant models for face recognition. In: Proc. Int. Conf. Pat. Rec., pp. 1368–1372. IEEE, Los Alamitos (1998)
Cui, Y., Swets, D., Weng, J.: Learning-based hand sign recognition using SHOSLIF-M. In: Proc. Int. Conf. Comp. Vis., pp. 631–636. IEEE, Los Alamitos (1995)
Huang, P., Harris, C., Nixon, M.: Human gait recognition in canonical space using temporal templates. In: Proc. Vision Image Signal Process, vol. 146, pp. 93–100. IEE (1999)
Krzanowski, W., Jonathan, P., McCarthy, W., Thomas, M.: Discriminant analysis with singular covariance matrices: methods and applications to spectroscopic data. Applied Statistics 44, 101–115 (1995)
Yu, H., Yang, J.: A direct LDA algorithm for high-dimensional data - with application to face recognition. Pattern Recognition 34, 2067–2070 (2001)
Friedman, J.: Regularized discriminant analysis. J. Am. Statistical Assoc. 84(405), 165–175 (1989)
Tibshirani, R., Knight, K.: Model search by bootstrap “bumping”. J. of Computational and Graphical Statistics 8(4), 671–686 (1999)
Fisher, R.: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7(Part II), 179–188 (1936)
Rao, C.: The utilization of multiple measurements in problems of biological classification. J. Royal Statistical Soc., B 10, 159–203 (1948)
Campbell, N.: Canonical variate analysis - a general model formulation. Australian J. Statistics 26, 86–96 (1984)
Duda, R., Hart, P., Stork, D.: Pattern Classification. John Wiley & Sons, New York (2001)
Gao, H., Davis, J.: Why Direct LDA is not equivalent to LDA. In Pattern Recognition (2006) (to appear)
Baudat, G., Anouar, F.: Generalized discriminant analysis using a kernel approach. Neural Computation 12(10), 2385–2404 (2000)
Kim, T., Kittler, J.: Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image. IEEE Trans. Patt. Analy. and Mach. Intell. 27(3), 318–327 (2005)
Torre, F., Kanade, T.: Oriented discriminant analysis (ODA). In: Brit. Mach. Vis. Conf., pp. 132–141 (2004)
Liu, X., Srivastava, A., Gallivan, K.: Optimal linear representations of images for object recognition. IEEE Trans. Patt. Analy. and Mach. Intell. 26(5), 662–666 (2004)
Efron, B.: Bootstrap methods: another look at the jackknife. Annals of Statistics 7, 1–26 (1979)
Breiman, L.: Bagging predictors. Machine Learning Journal 24(2), 123–140 (1996)
Schapire, R.: The strength of weak learnability. Machine Learning 5(2), 197–227 (1990)
Freund, Y.: Boosting a weak learning algorithm by majority. Information and Computation 121(2), 256–285 (1995)
Freund, Y., Schapire, R.: Experiments with a new boosting algorithm. In: Machine Learning: Proc. of the 13th Int. Conf., pp. 148–156 (1996)
Viola, P., Jones, M., Snow, D.: Detecting pedestrians using patterns of motion and appearance. In: Proc. Int. Conf. Comp. Vis., pp. 734–741 (2003)
Skurichina, M., Duin, R.: Bagging, boosting and the random subspace method for linear classifiers. Pattern Analysis & Applications 5, 121–135 (2002)
Lu, X., Jain, A.K.: Resampling for face recognition. In: Int. Conf. on Audio and Video Based Biometric Person Auth., pp. 869–877 (2003)
Efron, B., Tibshirani, R.: An Introduction to the Bootstrap. Chapman and Hall, New York (1993)
Samaria, F., Harter, A.: Parameterisation of a stochastic model for human face identification. In: 2nd IEEE Workshop on Applications of Computer Vision (1994)
Gross, R., Shi, J.: The CMU motion of body (MoBo) database. Technical Report CMU-RITR-01-18, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA (2001)
Davis, J., Bobick, A.: The representation and recognition of action using temporal templates. In: Comp. Vis. and Pattern Rec., pp. 928–93421. IEEE, Los Alamitos (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gao, H., Davis, J.W. (2006). Sampling Representative Examples for Dimensionality Reduction and Recognition – Bootstrap Bumping LDA. In: Leonardis, A., Bischof, H., Pinz, A. (eds) Computer Vision – ECCV 2006. ECCV 2006. Lecture Notes in Computer Science, vol 3953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11744078_22
Download citation
DOI: https://doi.org/10.1007/11744078_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33836-9
Online ISBN: 978-3-540-33837-6
eBook Packages: Computer ScienceComputer Science (R0)