Data Models and Structures of Kernels of DR

  • Jianzhong Wang


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.


Dimensionality Reduction Local Linear Embedding Euclidean Distance Matrix Semisupervised Learning Principal Component Analysis Project 
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© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jianzhong Wang
    • 1
  1. 1.Department of Mathematics and StatisticsSam Houston State UniversityHuntsvilleUSA

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