To address the above outlined problems occurring to LLE when employed
with a high number of neighbors, we propose the usage of LLE with geodesic
distance (ISOLLE). More specically, the n nearest neighbors are searched with
respect to the geodesic distance. This metric has already been employed in other
methods for nonlinear dimensional data reduction such as Isomap [8], Curvi-
linear Distance Analysis [9] and Self-organizing Maps [10]. The geodesic distance
between two data points can be intuitively thought as their distance along the
contour of an object (see Fig. 1 right). For example let us consider the distance
between Paris and New York. Their geodesic distance is the distance along the
curvature of the Earth. Their Euclidean distance instead is the length of the
straight line connecting the two cities which is below the level of the ground.
Points faraway from each other, as measured by the geodesic distance, may
appear deceptively close in the high-dimensional input space as measured by the
Euclidean distance.