## Speaker:

## Institution:

## Time:

## Location:

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 proximities. I'll discuss MDS applied to a specific dataset: the 2005 United States House of Representatives roll call votes. In this case, MDS outputs 'horseshoes' that are characteristic of dimensionality reduction techniques. I'll 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 insight into manifold learning in the special case where the manifold is a curve. This work is joint with Persi Diaconis and Susan Holmes.