Ghodsi 1 Metric Multidimensional Scaling ( MDS )

An alternative perspective on dimensionality reduction is offered by Multidimensional scaling (MDS). MDS is another classical approach that maps the original high dimensional space to a lower dimensional space, but does so in an attempt to preserve pairwise distances. That is MDS addresses the problem of constructing a configuration of t points in Euclidean space by using information about the distances between the t patterns. A t × t matrix D is called a distance or affinity matrix if it is symmetric, dii = 0, and dij > 0, i 6= j. Given a distance matrix D, MDS attempts to find t data points y1, ..., yt in d dimensions, such that if d (Y ) ij denotes the Euclidean distance between yi and yj, then D Y is similar to D. In particular, we consider metric MDS [1], which minimizes