  Classical multidimensional scaling (MDS) is a method for visualizing
high-dimensional point clouds by mapping to low-dimensional Euclidean space.
This mapping is defined in terms of eigenfunctions of a matrix of interpoint
dissimilarities. In this paper we analyze in detail multidimensional scaling
applied to a specific dataset: the 2005 United States House of Representatives
roll call votes. Certain MDS and kernel projections output ``horseshoes'' that
are characteristic of dimensionality reduction techniques. We show that, in
general, a latent ordering of the data gives rise to these patterns when one
only has local information. That is, when only the interpoint distances for
nearby points are known accurately. Our results provide a rigorous set of
results and insight into manifold learning in the special case where the
manifold is a curve.
