Methods of dimensionality reduction provide a way to understand and
visualize the structure of complex data sets. Traditional methods
like principal component analysis and classical metric
multidimensional scaling suffer from being based on linear models.
Until recently, very few methods were able to reduce the data
dimensionality in a nonlinear way. However, since the late
nineties, many new methods have been developed and nonlinear
dimensionality reduction, also called manifold learning, has become
a hot topic. New advances that account for this rapid growth are,
e.g. the use of graphs to represent the manifold topology, and the
use of new metrics like the geodesic distance. In addition, new
optimization schemes, based on kernel techniques and spectral
decomposition, have lead to spectral embedding, which encompasses
many of the
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