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.
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Mathar, R., Alirezaei, G., Balda, E., Behboodi, A. (2020). Dimensionality Reduction. In: Fundamentals of Data Analytics . Springer, Cham. https://doi.org/10.1007/978-3-030-56831-3_4
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DOI: https://doi.org/10.1007/978-3-030-56831-3_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-56830-6
Online ISBN: 978-3-030-56831-3
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