Isometric Gaussian Process Latent Variable Model for Dissimilarity Data
This work addresses the challenge of accurately representing complex data structures for applications in machine learning and data analysis, though it appears incremental as it builds on existing latent variable models.
The paper tackles the problem of modeling dissimilarity data by developing a probabilistic model that respects both distances and topology in the latent space, using Nakagami distributions and variational inference, and demonstrates its ability to encode invariances in learned manifolds.
We present a probabilistic 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 locally 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 based on observations of pairwise distances. We demonstrate how the new model can encode invariances in the learned manifolds.