The dynamic processes of AggMap restructuring of the randomized MNIST. Each frame is one epoch of the low-dimensional graph layout optimization. There is a total of 500 frames(epochs). The learning rate (lr) is set to 0.5, the cross-entropy loss (CE_loss) and the Pearson correlation coefficient (PCC) of the two weighted graphs (Eqn. 9 and 10) are calculated in each epoch. The five handwritten numbers 1,3,5,7, and 9 are used as trackers to illustrate how they are restructured. The Ground Truth images are the original images, the Randomized images are the pixel randomly permutated images, the Embedded images are the 2D-embedding scatter plots of the feature points (pixels). The Restructured images are the 2D regular grid plots of the feature points. The black dots in the Embedded and Restructured images are the pixels value of the corresponding Ground Truth images.
Flowchart the of self-supervised AggMap fitting process, the dynamic process of MNIST restructuring from randomly permuted images with 500 epochs is available in Video above. The Input is the M× N matrix, where M is number of the samples, and N is number of the FPs with arbitrary order, i.e. the randomly permuted MNIST pixels across all training set of MNIST data (M = 60 000, N = 784). Step 1 to Step 9 are the steps in the fitting stages and Step 10 is the transform stage. The Step 3 to Step 7 are the basic ideas of UMAP 2D embedding. One sample, the handwritten number “9”, is used as a tracker to illustrate how it will be restructured. The blank dots in the object E, D, F, F’, G, H and Iare the pixels value of the number “9”. The colors in the object G’, H’ and I’are the same five colors (clusters) as shown in object C, and the five colors stand for five clusters in hierarchical clustering C. The outputs are the single-channel or multi-channel Fmaps.