Abstract
In the dimensionality reduction processing, observed data have two different types. In the first type, the data set consists of high-dimensional vectors, which represent the objects of interest. In the second type, the data describe the similarities (or dissimilarities) of objects that cannot be digitized or hidden. The output of a DR processing with an input of the first type is a low-dimensional data set, having the same cardinality as the input and preserving the similarities of the input. When the input is of the second type, the output is a configuration of the input similarities. In Section 1 of this chapter, we discuss the models of input data and the constraints on output data. In Sections 2, we discuss the construction of the kernels in DR methods.
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© 2012 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
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Wang, J. (2012). Data Models and Structures of Kernels of DR. In: Geometric Structure of High-Dimensional Data and Dimensionality Reduction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27497-8_4
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DOI: https://doi.org/10.1007/978-3-642-27497-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27496-1
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