Fig. 3: Visualisation of the data geometric structure in the feature extraction network.

a, b The feature extraction network based on VAE, trained by using geometry images with WIs (a) and without WIs (b), and an example of input and output images. c, d UMAP data points generated in the latent space, trained with the geometry images together with WIs (c), and without WIs (d). \(\left(x,y\right)\) represents the location of the antidot defect. The data structure is mapped onto a three-dimensional space from the seven-dimensional latent space by using UMAP to visualise the data geometry. Each data point corresponds to one WI image and is coloured in blue or yellow depending on the parity of \(x\). e The definition of \(\Delta x\). f, g Images of the absolute difference between \(\left(x,y\right)\) data and \(\left(x+\Delta x,{y}\right)\) data, where \(\left(x,{y}\right)=\left(12,33\right)\), for \(\Delta x=1\) (f) and \(\Delta x=2\) (g), respectively. The RMS difference values are shown below the images. h The RMS differences at \((x,33)\).