Some new types of biplot

Gower, J. C. and Ngouenet, R. F (1998). Some new types of biplot. In: Proceeding of the Fourth Sensometrics (Brockhoff, P.B ed.), pp. 60–63.



We give examples of novel biplots based on the ideas developed by Gower and Hand (1996). The basic concept that underpins all these biplots is that of the reference system which acts like sets of high dimensional coordinate axes. We use the term reference system because, although its generality includes the familiar rectangular Cartesian coordinate axes, it also include non-linear axes, termed trajectories, and sets of points termed category level points, which are applicable to categorical, rather than continuous, variables. Like ordinary coordinate axes, the trajectories are equipped with scales by providing markers labelled by numerical values, usually chosen at conveniently equal intervals of the measure associated with the variables. Category level points are labelled by the names of the category levels. A reference system may include both trajectories and sets of category level points. Reference systems act like coordinate axes because they can be constructed so that (i) the coordinates associated with any point in the multidimensional space are given by finding the nearest marker for each variable and (ii) a point may be added to the reference system by taking the vector-sum of the markers associated with its numerical and/or categorical values. For numerical variables, nearest amounts to orthogonal projection onto the trajectories; for categorical variables, nearest merely means determining the nearest category level point for each variable.

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