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APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE by Dayanand N. Naik, Ravindra Khattree

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2.4. Andrews Function Plots

Andrews (1972) suggests an innovative method to pictorially display the multivariate data points as curves. This pictorial representation can sometimes be very helpful in visually grouping similar objects together and in searching for any striking dissimilarities between the objects or the groups of the objects on which the multivariate data are collected.

Andrews' approach consists of representing a p-dimensional vector y = (y1,...,yp)′ by a function fy(t) of a single variable t. This function when plotted on a two-dimensional space over t leads to a periodic curve. Andrews suggested the function fy(t) to be the finite Fourier series

By storing the coefficients of y1, y2,... in a column vector

we can write

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