Geodesic
A Supervised Manifold Learning Method
Computer Science and Information Systems, Tome 6 (2009) no. 2.

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The Locally Linear Embedding (LLE) algorithm is an unsupervised nonlinear dimensionality-reduction method, which reports a low recognition rate in classification because it gives no consideration to the label information of sample distribution. In this paper, a classification method of supervised LLE (SLLE) based on Linear Discriminant Analysis (LDA) is proposed. First, samples are classified according to their label values, and low dimensional features of intra-class data are expressed through LLE manifold learning. Then, the base vectors in Fisher subspace of the low dimensional features are generated through LDA learning. This method increases inter-class variation, and decreases the intra-class variation when samples are projected to the Fisher subspace. Hence, the samples of different labels can be recognized, and the recognition rate and robustness of the LLE learning are improved. Experiments on handwritten digit recognition show that the proposed method is featuring high recognition rate.
Keywords: Manifold learning, Locally Linear Embedding, fisher subspace, manifold perception 
@article{CSIS_2009_6_2_a10,
     author = {Zuojin Li and Weiren Shi and Xin Shi and Zhi Zhong},
     title = {A {Supervised} {Manifold} {Learning} {Method}},
     journal = {Computer Science and Information Systems},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/CSIS_2009_6_2_a10/}
}
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Zuojin Li; Weiren Shi; Xin Shi; Zhi Zhong. A Supervised Manifold Learning Method. Computer Science and Information Systems, Tome 6 (2009) no. 2. http://geodesic.mathdoc.fr/item/CSIS_2009_6_2_a10/