  Manifold learning methods are useful for high dimensional data analysis. Many
of the existing methods produce a low dimensional representation that attempts
to describe the intrinsic geometric structure of the original data. Typically,
this process is computationally expensive and the produced embedding is limited
to the training data. In many real life scenarios, the ability to produce
embedding of unseen samples is essential. In this paper we propose a Bayesian
non-parametric approach for out-of-sample extension. The method is based on
Gaussian Process Regression and independent of the manifold learning algorithm.
Additionally, the method naturally provides a measure for the degree of
abnormality for a newly arrived data point that did not participate in the
training process. We derive the mathematical connection between the proposed
method and the Nystrom extension and show that the latter is a special case of
the former. We present extensive experimental results that demonstrate the
performance of the proposed method and compare it to other existing
out-of-sample extension methods.
