Supplementary material:

- icml10-proofs: supplemental proofs (bounds for eigenvalues and homotopy
  parameter, design of search directions and proof of convergence).

- spiral_mexhat.gif: GIF animation of the homotopy EE result with a 200-point
  2D spiral projected to 1D (Wp are Gaussian affinities with sigma=0.05). 
  Note how, for large enough lambda, EE manages to get out of a bad local
  optimum (that folds the spiral) and to space uniformly the points
  without boundary effects (as they are in the 2D spiral). The
  colour-coded affinity matrix and the affinities for 4 selected points
  evolve from purely Gaussian to develop negative lobes and, when a good
  solution is achieved, look like Mexican-hat functions.

- swissroll.gif: GIF animation of the homotopy EE result with a 2000-point
  3D Swissroll projected to 2D as in fig. 3. The lower contour plot shows
  the affinities for a point near the centre of the map.
  The X produced by EE arise diagonally oriented, since both dimensions
  expand along the same, minor eigenvector of the learned Laplacian at the
  critical lambda. X has been rotated by 45 degrees for visualisation
  purposes.

- COIL-20.gif: GIF animation of the out-of-sample projections in latent
  space and reconstructions in image space of 3 image sequences for the EE
  result of fig. 5.

- oos_sine.gif: GIF animation of the out-of-sample mapping for a 2D dataset
  (sine curve).

All these animations may be seen with a web browser or with specialized
GIF image viewers.