100 Quantifying and Learning Linear Symmetry-Based Disentanglement (LSBD) Table 4.10: Hyperparameters for the different variants submitted to the SHREC 2021 3D object retrieval challenge. Submission Epochs d λTL λRE λKL λLSBD TL 100 100 1 - - - AE-TL 200 10 1 1 - - VAE-TL 200 100 100 1 1 - ∆VAE-TL 200 100 100 1 1 - LSBD-VAE-TL 100 100 100000 1 1 1 highest ranked retrieved object. • FT: First-Tier. Given a query, FT measures the precision for the Chighestranked retrieved objects, where Cis the number of relevant objects for the query in the training set. • ST: Second-Tier. Given a query, ST measures the precision for the 2 · C highest-ranked retrieved objects, where Cis the number of relevant objects for the query in the training set. • mAP: Mean average precision. Given several queries, the mean average precision is the mean of average precisions of each query, where the average precision of a single query is the average of precision values computed in the ranked list positions where a relevant object appears. • nDCG: Normalised discounted cumulative gain. Given a query, nDCG is a measure that weighs the retrieved objects according to their position in the ranked list. In retrieval applications, it is preferred that relevant objects appear first in the list. The results for the retrieval-by-shape challenge are shown in Table 4.11. For completeness and comparison, we also include the results of other submitted methods. The results show that our ∆VAE-TL method actually scores best for two out of the five metrics, and also scores well on the other three. The LSBD-VAE-TL method doesn’t really score competitively, although it outperforms a fair amount of other submissions. In particular though, it scores worse than our simple TL method without any kind of autoencoding. We believe that our LSBD-VAE-TL method doesn’t score better because it is a rather restricted model, and doesn’t learn to disentangle orientation from shape properties well enough. Moreover, certain objects in the challenge look quite similar under different rotations,
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