Editing Nonlinear dimensionality reduction (section)

=== Gaussian process latent variable models ===

[[Gaussian process latent variable model]]s (GPLVM)<ref>{{cite journal |first=N. |last=Lawrence |url=http://jmlr.csail.mit.edu/papers/v6/lawrence05a.html |title=Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models |journal=Journal of Machine Learning Research |volume=6 |pages=1783–1816 |date=2005}}</ref> are probabilistic dimensionality reduction methods that use Gaussian Processes (GPs) to find a lower dimensional non-linear embedding of high dimensional data. They are an extension of the Probabilistic formulation of PCA. The model is defined probabilistically and the latent variables are then marginalized and parameters are obtained by maximizing the likelihood. Like kernel PCA they use a kernel function to form a non linear mapping (in the form of a [[Gaussian process]]). However, in the GPLVM the mapping is from the embedded(latent) space to the data space (like density networks and GTM) whereas in kernel PCA it is in the opposite direction. It was originally proposed for visualization of high dimensional data but has been extended to construct a shared manifold model between two observation spaces.
GPLVM and its many variants have been proposed specially for human motion modeling, e.g., back constrained GPLVM, GP dynamic model (GPDM), balanced GPDM (B-GPDM) and topologically constrained GPDM. To capture the coupling effect of the pose and gait manifolds in the gait analysis, a multi-layer joint gait-pose manifolds was proposed.<ref>{{cite journal |first1=M. |last1=Ding |first2=G. |last2=Fan |url=https://ieeexplore.ieee.org/document/6985586 |title=Multilayer Joint Gait-Pose Manifolds for Human Gait Motion Modeling |journal=IEEE Transactions on Cybernetics |volume=45 |issue=11 |date=2015|pages=2413–24 |doi=10.1109/TCYB.2014.2373393 |pmid=25532201 |s2cid=15591304 |url-access=subscription }}</ref>