Καμπύλες του Andrews και γενικεύσεις

Καπίδης, Χαράλαμπος

Andrews curves and their generalizations

Master Thesis

Author

Καπίδης, Χαράλαμπος

Date

2021-06

Abstract

The aim of the current thesis is to present a relatively new technique in the representation of multidimensional data, which was first presented by Andrews in 1972. This technique is named Andrews Curves and concerns the representation of each observation of a dataset through a curve. Due to the mathematical nature of the function that is used to draw the curves, this technique presents some good qualities that can be reclaimed in various uses. In the first chapter, a short introduction to the multidimensional data analysis and the visual representation of multidimensional data are presented. Also, there is an introduction to the Andrews Curves technique. In the second chapter, the definition of the function of the Andrews Curves is given, as well as the curves that result from the visualization of this function. Additionally, some of the most important and useful properties of the Andrews Curves are presented. The criticism that this technique has received is also shown in this chapter and solutions to the issues arose are given. In the third chapter, the reader can find multiple variations of the technique, that can be found in related papers. More specifically, four different categories are shown. The first category of variations is related to the usage of Fourier base, exactly like in the Andrews Curves. The second category concerns the variations in which the trigonometric functions are used without using the Fourier base. In the third category, the variations in three dimensions are described and in the fourth category the variations without the usage of trigonometric functions are shown. In the fourth chapter, the most common uses of the method are described. More specifically, the clustering and classification of observations, the determination of outliers, the specification of significant and non-significant variables and the finding of period in time series data. In the fifth chapter, three applications of the Andrews Curves are presented. The application in non-classified data, in classified data and time series data are given. In this chapter, the conclusions of these three applications are drawn.

Postgraduate Studies Programme

Εφαρμοσμένη Στατιστική

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/13495
http://dx.doi.org/10.26267/unipi_dione/918

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Show full item record

Except where otherwise noted, this item's license is described as
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα