Fig. 1. The short circuit induced by Euclidean distance is shown on the left. In case
the number of neighbors n is set to a relative high value, the two points in gure can
be treated as neighbors, although they are on the opposite parts of the horseshoe. This
may cause LLE to fail to detect the real global structure of the data. On the right
are shown the benets of the geodesic distance. In this case the two points are not
neighbors, as they are faraway according to the geodesic distance.