Dimensionality Reduction

Rudolf Mathar (), Gholamreza Alirezaei (), Emilio Balda and Arash Behboodi
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Rudolf Mathar: RWTH Aachen University, Institute for Theoretical Information Technology
Gholamreza Alirezaei: RWTH Aachen University, Chair and Institute for Communications Engineering
Emilio Balda: RWTH Aachen University, Institute for Theoretical Information Technology
Arash Behboodi: RWTH Aachen University, Institute for Theoretical Information Technology

Chapter Chapter 4 in Fundamentals of Data Analytics, 2020, pp 45-67 from Springer

Abstract: Abstract In many cases data analytics has to cope with the extremely high dimension of the input. Structures may be well hidden not only by the sheer amount of data but also by very high-dimensional noise added to relatively low-dimensional signals. The aim of this chapter is to introduce methods which represent high-dimensional data in a low-dimensional space in a way that only a minimum of core information is lost. Optimality will mostly refer to projections in Hilbert spaces. If dimension one, two or three is sufficient to represent the raw data, a computer aided graphical visualization may help to identify clusters or outlying objects.

Date: 2020
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DOI: 10.1007/978-3-030-56831-3_4

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