SSA Models, Measures of Fit, and Their Optimization

Abstract

Some SSA models are defined by specifying their representation functions, i.e., how data are to be mapped into distances. For practical applications, these representation functions are too strict. They are modified into loss functions which define data-distance correspondences that have to be optimized rather than satisfied. Loss functions lead to general badness-of-fit measures such as stress and alienation, and to procedures for iteratively constructing SSA representations by computation. A 2-phase algorithm for that purpose is described. In one phase, target distances for a given SSA configuration are computed. In the second phase, the points are moved such that the resulting distances approximate the given target distances as closely as possible. The latter problem is solved here by the gradient method. Some problems arising from this method are discussed.