Locality Preserving Projections Thesis Statement

MDPI and ACS Style

Jia, P.; Huang, T.; Wang, L.; Duan, S.; Yan, J.; Wang, L. A Novel Pre-Processing Technique for Original Feature Matrix of Electronic Nose Based on Supervised Locality Preserving Projections. Sensors2016, 16, 1019.

AMA Style

Jia P, Huang T, Wang L, Duan S, Yan J, Wang L. A Novel Pre-Processing Technique for Original Feature Matrix of Electronic Nose Based on Supervised Locality Preserving Projections. Sensors. 2016; 16(7):1019.

Chicago/Turabian Style

Jia, Pengfei; Huang, Tailai; Wang, Li; Duan, Shukai; Yan, Jia; Wang, Lidan. 2016. "A Novel Pre-Processing Technique for Original Feature Matrix of Electronic Nose Based on Supervised Locality Preserving Projections." Sensors 16, no. 7: 1019.

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Locality Preserving Projections (LPP) are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) -- a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. LPP may be conducted in the original space or in the reproducing kernel Hilbert space into which data points are mapped. This gives rise to kernel LPP.

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