Constrained unidimensional scaling with application to genomics

A constrained unidimensional scaling model where the objects are required to be placed in a given order on the real line, is studied. A procedure formulated as a least squares problem with nonnegativity is considered to solve this problem. An application to linkage disequilibrium (LD) maps for human genome is presented to demonstrate the proposed model. The LD maps are also constructed for four populations from Hapmap data sets, and analyze some of their similarities.