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Statistics, Data Mining, and Machine Learning in AstronomyA Practical Python Guide for the Analysis of Survey Data$
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Željko Ivezic, Andrew J. Connolly, Jacob T VanderPlas, and Alexander Gray

Print publication date: 2014

Print ISBN-13: 9780691151687

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691151687.001.0001

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Dimensionality and Its Reduction

Dimensionality and Its Reduction

Chapter:
(p.289) 7 Dimensionality and Its Reduction
Source:
Statistics, Data Mining, and Machine Learning in Astronomy
Author(s):

Andrew J. Connolly

Jacob T. VanderPlas

Alexander Gray

Andrew J. Connolly

Jacob T. VanderPlas

Alexander Gray

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691151687.003.0007

With the dramatic increase in data available from a new generation of astronomical telescopes and instruments, many analyses must address the question of the complexity as well as size of the data set. This chapter deals with how we can learn which measurements, properties, or combinations thereof carry the most information within a data set. It describes techniques that are related to concepts discussed when describing Gaussian distributions, density estimation, and the concepts of information content. The chapter begins with an exploration of the problems posed by high-dimensional data. It then describes the data sets used in this chapter, and introduces perhaps the most important and widely used dimensionality reduction technique, principal component analysis (PCA). The remainder of the chapter discusses several alternative techniques which address some of the weaknesses of PCA.

Keywords:   data analysis, Gaussian distributions, density estimation, high-dimensional data, dimensionality reduction, principal component analysis

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