2014/10/24 by Mijung Park, Wittawat Jitkrittum, Park, Mijung +9
Computer Science · #62F15 #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #G.3 #Gaussian Processes and Bayesian Inference #I.2.6 #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.1410.6791
openalex publication_date 2014/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the Locally Linear Latent Variable Model (LL-LVM), a\nprobabilistic model for non-linear manifold discovery that describes a joint\ndistribution over observations, their manifold coordinates and locally linear\nmaps conditioned on a set of neighbourhood relationships. The model allows\nstraightforward variational optimisation of the posterior distribution on\ncoordinates and locally linear maps from the latent space to the observation\nspace given the data. Thus, the LL-LVM encapsulates the local-geometry\npreserving intuitions that underlie non-probabilistic methods such as locally\nlinear embedding (LLE). Its probabilistic semantics make it easy to evaluate\nthe quality of hypothesised neighbourhood relationships, select the intrinsic\ndimensionality of the manifold, construct out-of-sample extensions and to\ncombine the manifold model with additional probabilistic models that capture\nthe structure of coordinates within the manifold.\n