id: 06015096
dt: b
an: 06015096
au: Wang, Jianzhong
ti: Geometric structure of high-dimensional data and dimensionality reduction.
so: Berlin: Springer; Beijing: Higher Education Press (ISBN 978-3-642-27496-1;
    978-7-04-031704-6/hbk). xix, 356~p. EUR~79.95/net; SFR~106.50;
    \sterling~72.00; \$~109.00 (2012).
py: 2012
pu: Berlin: Springer; Beijing: Higher Education Press
la: EN
cc: 
ut: high dimensional data; nonlinear dimensionality reduction; manifold
    embedding technique; geometry of data; isomaps; maximum variance
    unfolding; locally linear embedding; local tangent space alignment;
    Laplacian eigenmaps; Hessian locally linear embedding; diffusion maps
ci: 
li: 
ab: The book treats the subject of dimensionality reduction in a nonlinear
    fashion. It specifically addresses the manifold learning area which
    presumes that every high dimensional data resides on a low dimensional
    manifold. It more explicitly focuses on the geometric approach to
    nonlinear dimensionality reduction which learns the geometry of the
    manifold from the neighborhood structure of the data, creates a kernel
    to represent the learned geometry and uses its spectral decomposition
    to reach the manifold embedding. Making reference also to the classical
    linear techniques for dimensionality reduction, different nonlinear
    models are then presented in detail. This includes intuitive
    descriptions, theoretical demonstrations, underlying algorithms
    implemented in MATLAB and explicative tables and figures. The
    applicative side of the methods is shown on real-world examples, such
    as face recognition, image segmentation, data classification, data
    visualization and hyperspectral imagery data analysis. The book
    addresses a wide variety of readers, from computer scientists,
    mathematicians, statisticians and data analysts to even scientists
    working in economy or geophysics.
rv: Catalin Stoean (Craiova)