## Abstract

The Gaussian Process Latent Variable Model (GPLVM) [1] is an attractive model

for dimensionality reduction, but the optimization of the GPLVM likelihood with

respect to the latent point locations is difficult, and prone to local optima. Here

we start from the insight that in the GPLVM, we should have that *k*(x_{i}; x_{j}) ≅ s*ij* ,

where *k*(x_{i}; x_{j}) is the kernel function evaluated at latent points x_{i} and x_{j} , and s_{ij}

is the corresponding estimate from the data. For an isotropic covariance function this relationship can be inverted to yield an estimate of the interpoint distances {dij} in the latent space, and these can be fed into a multidimensional scaling

(MDS) algorithm. This yields an initial estimate of the latent locations, which can

be subsequently optimized in the usual GPLVMfashion. We compare two variants

of this approach to the standard PCA initialization and to the ISOMAP algorithm

[2], and show that our initialization converges to the best GPLVM likelihoods on

all six tested motion capture data sets.

Original language | English |
---|---|

Title of host publication | Proceedings of the NIPS 2010 workshop on Challenges of Data Visualization |

Number of pages | 6 |

Publication status | Published - 2010 |