Blog
About

19
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Bayesian Manifold Learning: The Locally Linear Latent Variable Model (LL-LVM)

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold model with additional probabilistic models that capture the structure of coordinates within the manifold.

          Related collections

          Most cited references 3

          • Record: found
          • Abstract: not found
          • Article: not found

          The isomap algorithm and topological stability.

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Learning nonlinear image manifolds by global alignment of local linear models

             J. Verbeek (2006)
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Robust Local Tangent Space Alignment

                Bookmark

                Author and article information

                Journal
                2014-10-24
                2015-12-01
                Article
                1410.6791

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                62F15
                accepted to NIPS 2015
                stat.ML

                Machine learning

                Comments

                Comment on this article