On one model of single-dimensional scaling

An optimizing model is proposed for single-dimensional scaling whereby an image of the initial space of features (general totality of objects) is constructed into a singledimensional space which representee to the fullest possible extent the proximity structure of the initial space. In a general case the existence of such extremal mapping, the saling function, is demonstrated. For a class of singular proximity functions a finiteparametric representation of the scaling function.