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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  4:15 p.m., Tuesday, September 25, 2007\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Susan Holmes} \\
  Statistics Department\\
  Stanford
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  \subsection*{  Finding Time:\\
A la recherche du temps perdu.
  }
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\noindent


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.

We show examples of finding hidden gradients in high dimensional data, in
particular we analyze in detail multidimensional scaling applied to the
2005 United States House of Representatives roll call votes.


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.
This method is also applied to biological data where synchronization
issues are difficult and retrieving the time gradient essential.

The talk is joint work with Persi Diaconis and Sharad Goel.




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