Modern Multidimensional Scaling 8. A Majorization Algorithm for Solving MDS

Generalized Cores

Modern Multidimensional Scaling 8. A Majorization Algorithm for Solving MDS2009-02-25 shju@ml.ssu.ac.kr1The Stress Function for MDSSix definitionsn denotes the number of empirical objects.Stimuli, variables, items, questions, and so on, depending on contextIf an observation has been made for a pair of objects i and j, a proximity value pij is given.proximity both similarity and dissimilaritymissing value If pij is undefinedDissimilarity is a proximity that indicates how dissimilar two objects are.X denotes(a) a point configuration (i.e., a set of n points in m-dimensional space)(b) the n*m matrix of the coordinates of the n points relative to m Cartesian coordinate axes.The Euclidean distance between any two points i and j in X is the length of a straight line connection points i and j in X.The term f(pij) denotes a mapping of pij, that is the number assigned to pij according to rule f.

We define an error of representation byeij 2 = (dij - ij) 2

The final version of raw stressr(X) = i