eprintid: 1452736 rev_number: 75 eprint_status: archive userid: 608 dir: disk0/01/45/27/36 datestamp: 2014-10-27 19:38:10 lastmod: 2020-02-20 04:06:51 status_changed: 2016-01-27 13:10:56 type: proceedings_section metadata_visibility: show item_issues_count: 0 creators_name: Park, M creators_name: Jitkrittum, W creators_name: Qamar, A creators_name: Szabo, Z creators_name: Buesing, L creators_name: Sahani, M title: Bayesian Manifold Learning: The Locally Linear Latent Variable Model (LL-LVM) ispublished: pub divisions: UCL divisions: A01 divisions: B02 divisions: C08 divisions: D76 divisions: B04 divisions: C05 divisions: F48 note: Copyright © The Authors 2015. 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. date: 2014-12-12 publisher: Neural Information Processing Systems Foundation official_url: http://papers.nips.cc/paper/5973-bayesian-manifold-learning-the-locally-linear-latent-variable-model-ll-lvm vfaculties: VFLS oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_source: Manually entered elements_id: 989216 lyricists_name: Jitkrittum, Wittawat lyricists_name: Sahani, Maneesh lyricists_name: Szabo, Zoltan lyricists_id: JWITT76 lyricists_id: MSAHA91 lyricists_id: ZSZAB96 full_text_status: public series: Advances in Neural Information Processing System volume: 28 place_of_pub: Montreal, Canada event_title: Neural Information Processing Systems 2015 book_title: Advances in Neural Information Processing Systems 28 (NIPS 2015) citation: Park, M; Jitkrittum, W; Qamar, A; Szabo, Z; Buesing, L; Sahani, M; (2014) Bayesian Manifold Learning: The Locally Linear Latent Variable Model (LL-LVM). In: Advances in Neural Information Processing Systems 28 (NIPS 2015). Neural Information Processing Systems Foundation: Montreal, Canada. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1452736/1/Szabo_5973-bayesian-manifold-learning-the-locally-linear-latent-variable-model-ll-lvm.pdf