Supplementary material:

- rotated7_time_error.gif: GIF animation, for the rotated MNIST-7 digits
  experiment of the paper, of the performance of (1) the nested objective
  function and (2) our auxiliary-coordinates objective function and its
  continuation with the nested objective function. The upper left panel
  shows the regression error and the time spent by the different
  algorithms to achieve the same error (indicated over iterations by the
  moving vertical bar). The upper right plot shows the embedding F(X) of
  the nested approach. The lower panels correspond to our
  auxiliary-coordinates approach: the left panel shows the embedding Z
  (before switching to the nested approach) and the lower right panel
  shows the embedding F(X) and its continuation with the nested approach. 
  Both approaches use an RBF network for F and a linear mapping for g,
  initialized from Isomap. Different markers correspond to different
  original images and its continuously rotated versions. As in the
  comparison with the nested approach in the paper for the serpentine
  robot experiment, our approach achieves a nearly unbiased optimum much
  faster than the nested approach (about two orders of magnitude).

- rotated7_animation.gif: GIF animation, for the rotated MNIST-7 digits
  experiment of the paper. A larger view of the embedding Z of our
  auxiliary-coordinates approach as it evolves during the optimization.

- robot.gif: GIF animation for the serpentine robot forward kinematics
  experiment of the paper. A serpentine 10-joint robot arm (blue) is
  holding a camera (red box) at its end-effector while performing a test
  motion. The plots show the ground truth (left column) and the prediction
  of our algorithm (right column) using both RBF networks for F and g.

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