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Article citations


M. Belkin and P. Niyogi, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation,” Technical Report, University of Chicago, Chicago, 2001.

has been cited by the following article:

  • TITLE: Inner Product Laplacian Embedding Based on Semidefinite Programming

    AUTHORS: Xianhua Zeng

    KEYWORDS: Inner Product, Semi-Definite Programming, Geodesic Distance, Laplacian Matrix

    JOURNAL NAME: Journal of Signal and Information Processing, Vol.2 No.3, August 12, 2011

    ABSTRACT: This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.