Geometrically local embedding in manifolds for dimension reduction

Authors:
Shuzhi Sam Ge;Hongsheng He;Chengyao Shen
Affiliations:
Social Robotics Lab, Interactive Digital Media Institute, and Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore and Institute of Inte ...;Social Robotics Lab, Interactive Digital Media Institute, and Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore;Social Robotics Lab, Interactive Digital Media Institute, and Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore and NGS Graduate Scho ...
Venue:
Pattern Recognition
Year:
2012

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Abstract

In this paper, geometrically local embedding (GLE) is presented to discover the intrinsic structure of manifolds as a method in nonlinear dimension reduction. GLE is able to reveal the inner features of the input data in the lower dimension space while suppressing the influence of outliers in the local linear manifold. In addition to feature extraction and representation, GLE behaves as a clustering and classification method by projecting the feature data into low-dimensional separable regions. Through empirical evaluation, the performance of GLE is demonstrated by the visualization of synthetic data in lower dimension, and the comparison with other dimension reduction algorithms with the same data and configuration. Experiments on both pure and noisy data prove the effectiveness of GLE in dimension reduction, feature extraction, data visualization as well as clustering and classification.