Local Coordinates Alignment and Its Linearization

Authors:
Tianhao Zhang;Xuelong Li;Dacheng Tao;Jie Yang
Affiliations:
Institute of IP & PR, Shanghai Jiao Tong Univ., P.R. China and Dept. of Computing, Hong Kong Polytechnic Univ., Hong Kong,;Sch. of Comp. Sci. and Info. Sys., Birkbeck, Univ. of London, U.K.;Dept. of Computing, Hong Kong Polytechnic Univ., Hong Kong,;Institute of IP & PR, Shanghai Jiao Tong Univ., P.R. China
Venue:
Neural Information Processing
Year:
2007

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Abstract

Manifold learning has been demonstrated to be an effective way to discover the intrinsic geometrical structure of a number of samples. In this paper, a new manifold learning algorithm, Local Coordinates Alignment (LCA), is developed based on the alignment technique. LCA first obtains the local coordinates as representations of a local neighborhood by preserving the proximity relations on the patch which is Euclidean; and then the extracted local coordinates are aligned to yield the global embeddings. To solve the out of sample problem, the linearization of LCA (LLCA) is also proposed. Empirical studies on both synthetic data and face images show the effectiveness of LCA and LLCA in comparing with existing manifold learning algorithms and linear subspace methods.