Metric unfolding: Data requirement for unique solution & clarification of Schönemann's algorithm

摘要: The object of this paper is to clarify Schonemann's unfolding algorithm and, in particular, make it clear that the equations numbered (3.2) [1970] article, which define solutions, are not a complete set restraints for purpose defining metric unfoldings. Namely, Schonemann has transformed original an linear and non-linear he uses only his solutions. Given infallible data (solution(s) exist) solutions will include correct If enough available so there uniquely determine single solution, then solution coincide with solution. LetP andQ denote number elements two sets points, interset distances specified by problem. Letm dimensionality Euclidean space into these points be imbedded. equations, (18) herein, used, gives following requirement determined: Max {P − 1,Q 1} ≥m(m + 3)/2. full nonlinear (18–20) amount required locally unique relaxed toP +Q 1 Both results assume independent, been proved.