Local distance preservation in the GP-LVM through back constraints

Abstract

The Gaussian process latent variable model (GP-LVM) is a generative approach to nonlinear low dimensional embedding, that provides 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 approaches to non-linear dimensionality methods 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 keeping things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduction 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 preserve local distances. We give illustrative experiments on common data sets.

Articulated tracking with manifold regularized particle filter

“…This model is called bidirectional silhouette likelihood [20] and can be defined as follows: where S I denotes binary silhouette obtained by subtracting background from the input image I, and S I (x) denotes binary silhouette obtained by projecting a body model generated from a given pose x onto the image I. Additional constant value in (12) corresponds to the normalizing coefficient in the probability distribution that is independent of the image. We use a simple body model composed of articulately connected cylindrical elements.…”

“…This issue is undesirable in the proposed filtering procedure (2) since the distribution p(z t |x t−1 ) is multi-modal and thus hard to determine. However, this effect can be reduced by introducing back constraints that leads to back-constrained GPLVM (BC-GPLVM) [12].…”

Latent spaces for dynamic movement primitives

“…Unfortunately our experiments show that this kind of model is still not sufficient for generalisation of DMPs in latent space. Similarly, Lawrence and QuinoneroCandela [16] try to strengthen neighbourhood relations between points by constraining the mapping from data to latent space to be smooth as well. Consequently, the modification we present below is aimed at further constraining the latent positions in a useful way and thereby, regularising the GPLVM problem.…”

Combining spatial and temporal priors for articulated human tracking with online learning

“…For examples, Gaussian Processing Dynamic Models (GPDM) [19] were specifically designed for human motion tracking by introducing a dynamic model on the latent variable that can be used to produce tracking hypothesis in a latent space [18]. Back Constrained-GPLVM (BC-GPLVM) [11] improves the continuity in the latent space by enforcing the local proximities in both the LD and HD spaces. Consequentially, BC-GPLVM produces a smooth motion trajectory in the latent space that can be used as a non-parametric dynamic model for human tracking [8].…”

“…To ensure a smooth trajectory in the latent state space for temporal series data, BC-GPLVM was proposed in [11] that enforces local proximities in both the LD and HD spaces. In our work, BC-GPLVM is used to learn a compact LD representation of human motion in the latent space and a probabilistic reverse mapping from the LD latent space to the HD observation space.…”