Supplementary material for "Linear-Time Training of Nonlinear Low-Dimensional Embeddings", AISTATS'14

• aistats14b-supp.pdf: formulae and error bounds for the Fast Gauss Transform (FGT) approximation; an extended discussion of the noise model, including a proof of theorem 3.1 from the paper; and additional experiments' figures.

• The following are GIF animations of the elastic embedding algorithm (EE) ran on the infiniteMNIST dataset with N=1020000 images of handwritten digits, using as optimization one of GD (gradient descent), FP (fixed-point iteration) and L-BFGS, where the objective function gradient is approximated using the Fast Gauss Transform (FGT) or the Barnes-Hut (BH) method.

• MNIST.gif: all methods shown at once. For each plot, the runtime grows from 0 to 660 minutes with a step of 10 min.

• GD_FGT.gif, FP_FGT.gif, LBFGS_FGT.gif, GD_BH.gif, FP_BH.gif, LBFGS_BH.gif: each method separately. The runtime is limited to 11 hours for all the methods.

• infiniteMNIST_digits.mov, infiniteMNIST_markers.mov: FGT run with L-BFGS optimization for 13 hours. The first animation shows a subset of 2000 digits shown as actual digits and the second shows all 102000 digits as color markers