An Improved Locally Linear Embedding Method for Feature Extraction

Abstract:

In this work, a feature extraction approach based on improved Locally Linear Embedding(LLE) is proposed. In the algorithm, tangent space distance is introduced to LLE, which overcomes the shortcoming of original LLE method based on Euclidean distance. It can satisfy the requirement of locally linear much better and so can express the I/O mapping quality better than classical method. Simulation results are given to demonstrate the effectiveness of the improved LLE method.

• Periodical: Key Engineering Materials (Volumes 467-469)
• Pages: 487-492
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.467-469.487
• Online since: February 2011
• Authors: Wei Zhang, Wei Jia Zhou
• Keywords: Feature Extraction, Locally Linear Embedding (LLE), Tangent Space Distance

References

[1] PEARSON K. On lines and planes of closest fit to systems of points in space[J]. Philos Mag, 1901, 6(2): 559 - 572.

[2] SAMUEL A L. Some studies in machine learning using the game of checkers[J]. IBM Journal Research and Development, 1967, 11(4 ): 601-617.

DOI: 10.1147/rd.116.0601

[3] DUNIA R, QIN S Joe, EDGAR T F, MCAVOY T J. Use of principal component analysis for sensor fault identification[J]. Computers chem. Eng, 1996, 20(7): 13-718.

DOI: 10.1016/0098-1354(96)00128-7

[4] CHIANG L H, RUSSELL E L, BRAATZ R D. Fault detection and diagnosis in industrial systems [M]. London: Springer-Verlag London Limited, (2001).

[5] PÖLLÄNEN K, HÄKKINEN A, REINIKAINEN S P, RANTANENJ, MINKKINEN P. Dynamic PCA-based MSPC charts for nucleation prediction in batch cooling crystallization processes [J]. Chemometrics and Intelligent Laboratory Systems, 2006, 84(1/2): 126−133.

DOI: 10.1016/j.chemolab.2006.04.016

[6] HE Qing-hua, HE Xiang-yu, ZHU Jian-xin. Fault detection of excavator's hydraulic system based on dynamic principal component analysis[J]. Journal of Central South University of Technology, 2008, 15: 700-705.

DOI: 10.1007/s11771-008-0130-8

[7] SCHOLKOPF B, SMOLA A, Muller K R. Nonlinear component analysis as a kernel eigenvalue[ J ]. Neural Computation, 1998, 10 (5): 1299-1319.

DOI: 10.1162/089976698300017467

[8] XU Y, ZHANG D, SONG F X, YANG J Y, JING Z, LI M. A method for speeding up feature extraction based on KPCA[J]. Neurocomputing, 2007, 70: 1056-1061.

DOI: 10.1016/j.neucom.2006.09.005

[9] ROWEIS S T, SAUL L K. Nonlinear dimensionality reduction by locally linear embedding[J]. Science, 2000, 290(22): 2323-2326.

DOI: 10.1126/science.290.5500.2323

[10] L'HEUREUXA P J, CARREAUA J, BENGIOA Y, DELALLEAUA O, YUEB S Y. Locally Linear Embedding for dimensionality reduction in QSAR[J]. Journal of Computer-Aided Molecular Design, 2004, 18: 475-482.

DOI: 10.1007/s10822-004-5319-9

[11] ROWEIS S T, SAUL L K. Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds[J]. Journal of Machine Learning Research, 2003, 4: 119-155.

[12] MIN Wan-lin, LU Ke, He Xiao-fei. Locality pursuit embedding[J]. Pattern Recognition, 2004, 37(4): 781–788.

DOI: 10.1016/j.patcog.2003.09.005