A theorem on the generalized canonical projective vectors

doi:10.1016/j.patcog.2004.08.009

Pattern Recognition

Volume 38, Issue 3, March 2005, Pages 449-452

https://doi.org/10.1016/j.patcog.2004.08.009 Get rights and content

Abstract

This paper proposes a kind of generalized canonical projective vectors (GCPV), based on the framework of canonical correlation analysis (CCA) applying image recognition. Apart from canonical projective vectors (CPV), the process of obtaining GCPV contains the class information of samples, such that the combined features extracted according to the basis of GCPV can give a better classification performance. The experimental result based on the Concordia University CENPARMI handwritten Arabian numeral database has proved that our method is superior to the method based on CPV.

Introduction

Canonical correlation analysis (CCA) is an important multiple data processing technique [1], [2], [3], [4]. In Ref. [4], we have proposed the canonical projective vectors (CPV), based on the idea of feature fusion, and established a framework of (CCA) for the use of image recognition, and then applied the CPV to fields like face automatic recognition and handwritten characters recognition. Although canonical discriminant features extracted based on CCA perform better, the process of obtaining CPV contain no class information of the samples. In case of pattern classification the extracted features may not be optimum.

In the light of this, we propose a kind of generalized canonical projective vectors (GCPV) to increase the class information of the training samples by improving the canonical correlation criterion function; the discriminant feature extracted on the basis of improved criterion function has shown its physical significance, and excellent classification performance. The experimental result based on the Concordia University CENPARMI handwritten numeral database has proved that GCPV proposed in this paper is superior to CPV.

Section snippets

Theory of GCPV

Suppose A and B are two feature sets defined on pattern sample space $Ω$ . For any pattern sample $ξ \in Ω$ , the corresponding two feature vectors are $x \in A \subset Ω$ and $y \in B \subset Ω$ .

Experiments and analysis

We have tested our method on the well-known Concordia University CENPARMI handwritten numeral database. In this database, there are 10 classes, i.e. 10 digits (from 0 to 9), and 600 samples for each. The training samples and testing samples are 4000 and 2000, respectively. In Ref. [5], Hu et al. had performed some preprocessing work and extracted four kinds of features as follows:

$X^{G}$ : 256-dimensional Gabor transformation feature;

$X^{L}$ : 121-dimensional Legendre moment feature;

$X^{P}$ : 36-dimensional

Conclusion

In this paper, we have generalized the theory of CCA in consideration of pattern classification. The GCPV set forth in this paper can make the extracted canonical feature more advantageous to the classification due to increased class information of samples. That is the main cause for the adoption of GCPV superior to that of CPV, while this has been shown by the experimental results. Our future research direction is to investigate its application to the other fields of image recognition.

Acknowledgements

This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region under Earmarked Research Grant (project no. CUHK4185/00E.

About the Author—QUAN-SEN SUN is an associate professor in the Department of Mathematics at Jinan University. At the same time, he is working for his Ph.D. degree in pattern recognition and intelligence system from Nanjing University of Science and Technology (NUST). His current interests include pattern recognition, image processing, computer vision and data fusion.

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