The Gaussian process latent variable model (GP-LVM) is a generative approach to non-linear low dimensional embedding, that pro-vides a smooth probabilistic mapping from latent to data space. It is also a non-linear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most ap-proaches to non-linear dimensionality meth-ods focus on preserving local distances in data space, the GP-LVM focusses on exactly the opposite. Being a smooth mapping from latent to data space, it focusses on keep-ing things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduc-tion techniques, placing the emphasis on the kind of distance relation preserved. We then show how the GP-LVM can be generalized, through back constraints, to additionally pre-serve local distances. We give illustrative ex-periments on common data sets.
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