engleski

On directional bias of the L_p-norm

We look at the so-called directional bias of the L_p-norm (1<= p<=infty) (see Brimberg-Love-1995). The L_p-norm is a popular distance measure in the problems of estimating the distances among objects. Distance | x-y|_p between any two points x and y depends on a particular set of orthogonal reference axes, except for the L_2-norm (i.e. euclidean norm). The axes and the distance function should be chosen in accordance with the directional bias. Particularly, we consider the directional bias of norms in 3 dimensional space R^3 and in n dimensional space R^n. (In Brimberg-Love-1995 the concept of the directional bias function of the norm in 2-dimensional space R^2 is analysed.)

directional bias; L_p-norm

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