We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model (GPLVM), but optimized with a hidden Markov model dynamical prior. The GPDMM combines multiple GPDMs in a probabilistic mixture-of-experts framework, utilizing embedded geometric features to allow for diverse sequences to be encoded in a single latent space, enabling the categorization and generation of each sequence class. GPDMs and our mixture model are particularly advantageous in addressing the challenges of modeling human movement in scenarios where data is limited and model interpretability is vital, such as in patient-specific medical applications like prosthesis control. We score the GPDMM on classification accuracy and generative ability in single-example learning, showcase model variations, and benchmark it against LSTMs, VAEs, and transformers.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space. We demonstrate the approach on human motion capture data in which each pose is 62-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces.

The recently proposed Gaussian process dynamical models (GPDMs) have been successfully applied to time series modeling. There are four learning algorithms for GPDMs: maximizing a posterior (MAP), fixing the kernel hyperparameters α _ (Fix.α _ ), balanced GPDM (B-GPDM) and two-stage MAP (T.MAP), which are designed for model training with complete data. When data are incomplete, GPDMs reconstruct the missing data using a function of the latent variables before parameter updates, which, however, may cause cumulative errors. In this paper, we present four new algorithms (MAP+, Fix.α + , B-GPDM+ and T.MAP+) for learning GPDMs with incomplete training data and a new conditional model (CM+) for recovering incomplete test data. Our methods adopt the Bayesian framework and can fully and properly use the partially observed data. We conduct experiments on incomplete motion capture data (walk, run, swing and multiple-walker) and make comparisons with the existing four algorithms as well as k-NN, spline interpolation and VGPDS. Our methods perform much better on both training with incomplete data and recovering incomplete test data.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space.

Two main themes are the use of switching linear models (e.g.,