Andrews ‘Plots

A graphical display of multivariate data in which an observation, x0 = [x1, x2, . . . , xq] is represented can be represented in the form of function

A set of the multivariate observations is then displayed as the collection of these kind of plots and it can be shown that those functions which remain close together for all values of t correspond to the observations which are close to one another in the terms of their Euclidean distance. This property states that such plots can often be used to detect groups of similar observations and identify outliers in  multivariate data both. The example given in the Fig drawn below consists of plots for the sample of 30 observations each of which having five variable values.

The plot signifies the presence of three groups in the data. These type of plots can cope only with a reasonable number of observations before becoming very complicated to unravel.