Isometric Gaussian Process Latent Variable Model for Dissimilarity Data
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We propose a fully generative model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined stochastic distance measure, which is modeled as Nakagami distributions. These stochastic distances are sought to be as similar as possible to observed distances along a neighborhood graph through a censoring process. The model is inferred by variational inference and is therefore fully generative. We demonstrate how the new model can encode invariances in the learned manifolds.
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