Abstract
In this paper, we propose a geometric framework, called Vector Bundle Learning (VBL) for feature extraction. In our framework, a vector bundle is considered as the intrinsic structure to extract features from high dimensional data. By defining a manifold to model the structure of sample set, features sampled from each fibre of a vector bundle can be obtained by metric learning on the manifold. A number of existing algorithms can be reformulated and explained in this unified framework. Based on the proposed framework, a novel supervised feature extraction algorithm called Vector Bundle Discriminant Analysis (VBDA) is proposed for recognition and classification. Experimental results on face recognition and handwriting digits classification demonstrate the excellent performance of our VBDA algorithm.
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- 1.
It will be discussed in Sect. 8.3.
- 2.
The details are given in the supplementary material due to the page limit.
- 3.
Available at http://www.cs.toronto.edu/~roweis/data.html.
- 4.
For MFA, LDE, ANMM and SRDA, the choice of \(\mathcal{S}_{x_{i}}\) uses the class information as they are supervised dimensionality reduction techniques. See the details that follow.
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Acknowledgements
We thank Prof. Zhouchen Lin for valuable comments and suggestions for improving this work. This work is partly supported by National Natural Science Foundation of China (Nos. 61300086, 61173103, 61432003, 6157209) and Fundamental Research Funds for the Central Universities (No. DUT15QY15).
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Liu, R., Su, Z. (2015). Feature Extraction via Vector Bundle Learning. In: Mathematical Problems in Data Science. Springer, Cham. https://doi.org/10.1007/978-3-319-25127-1_8
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DOI: https://doi.org/10.1007/978-3-319-25127-1_8
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