xvi LIST OF FIGURES 3.9 ELBO density distributions for normal (blue) and anomalous (red) MNISTdigits.............................. 42 3.10 Originals (left), reconstructions (middle), and difference images (right) for anomalous MNIST digits. . . . . . . . . . . . . . . . . 43 3.11 ELBO density distributions for normal (blue) and anomalous (red) 3D-printed products with a 64-dimensional latent space. . . . . . 45 3.12 Original (left), reconstruction (middle), and difference (right) images for 3D-printed products. . . . . . . . . . . . . . . . . . . . 46 3.13 Four nodules generated by the 3D WGAN-GP. . . . . . . . . . . . 47 3.14 GAN-based anomaly detection results for NLST 3D nodules. . . . 48 3.15 VAE-based anomaly detection results for NLST 3D nodules. . . . . 49 4.1 A dataset of images from a rotating object expressed in terms of the group G=SO(2) acting on a base image x0........... 62 4.2 Intuitive description of the practical computation of DLSBD. . . . 67 4.3 Overview of the supervised part of LSBD-VAE. . . . . . . . . . . . 71 4.4 Example images from each of the datasets used. . . . . . . . . . . 73 4.5 Example paths of consecutive observations. . . . . . . . . . . . . 76 4.6 DLSBD scores for all methods on all datasets. . . . . . . . . . . . 80 4.7 Box plots for DLSBD scores over 10 training repetitions for different numbers of labelled pairs L,foralldatasets. . . . . . . . . . . 82 4.8 Results from Quessard et al. (2020)’s method on the Arrow dataset. 83 4.9 Comparing DLSBD to previous disentanglement metrics. . . . . . 84 4.10 Images obtained by decoding latent variables sampled according to the prior over the latent space for different models trained on COIL-100andModelNet40. ..................... 89 4.11 Image generation by traversing the circular latent variable for a sampledobjectidentity. ....................... 90 4.12 Diagrams illustrating the interpolation between the latent variablesassociatedtotwoobjects. . . . . . . . . . . . . . . . . . . . 91 4.13 Images produced from the decoding of interpolated latent variables using cc-VAE and LSBD-VAE trained with COIL-100. . . . . 92 4.14 Sample objects for every class of the retrieval-by-shape dataset. . 94 4.15 Sample objects for every class of the retrieval-by-culture dataset. 95 4.16 Diagram of the multi-view data generation. . . . . . . . . . . . . 96 4.17 Diagrams with the architectures used in the Triplet Loss (TL), Autoencoder with Triplet Loss (AE-TL) and LSBD-VAE with Triplet Loss (LSBD-VAE-TL) submissions. . . . . . . . . . . . . . . . . . . 99
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