Locality preserving embedding for face and handwriting digital recognition |
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Authors: | Zhihui Lai MingHua Wan Zhong Jin |
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Affiliation: | (1) School of Computer Science, Nanjing University of Science and Technology, 210094 Nanjing, Jiangsu, People’s Republic of China |
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Abstract: | Most supervised manifold learning-based methods preserve the original neighbor relationships to pursue the discriminating
power. Thus, structure information of the data distributions might be neglected and destroyed in low-dimensional space in
a certain sense. In this paper, a novel supervised method, called locality preserving embedding (LPE), is proposed to feature
extraction and dimensionality reduction. LPE can give a low-dimensional embedding for discriminative multi-class sub-manifolds
and preserves principal structure information of the local sub-manifolds. In LPE framework, supervised and unsupervised ideas
are combined together to learn the optimal discriminant projections. On the one hand, the class information is taken into
account to characterize the compactness of local sub-manifolds and the separability of different sub-manifolds. On the other
hand, at the same time, all the samples in the local neighborhood are used to characterize the original data distributions
and preserve the structure in low-dimensional subspace. The most significant difference from existing methods is that LPE
takes the distribution directions of local neighbor data into account and preserves them in low-dimensional subspace instead
of only preserving the each local sub-manifold’s original neighbor relationships. Therefore, LPE optimally preserves both
the local sub-manifold’s original neighborhood relationships and the distribution direction of local neighbor data to separate
different sub-manifolds as far as possible. The criterion, similar to the classical Fisher criterion, is a Rayleigh quotient
in form, and the optimal linear projections are obtained by solving a generalized Eigen equation. Furthermore, the framework
can be directly used in semi-supervised learning, and the semi-supervised LPE and semi-supervised kernel LPE are given. The
proposed LPE is applied to face recognition (on the ORL and Yale face databases) and handwriting digital recognition (on the
USPS database). The experimental results show that LPE consistently outperforms classical linear methods, e.g., principal
component analysis and linear discriminant analysis, and the recent manifold learning-based methods, e.g., marginal Fisher
analysis and constrained maximum variance mapping. |
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