A novel curved Gaussian Mixture Model and its application in motion skill encoding

The purpose of this paper is to present a novel curved Gaussian Mixture Model (CGMM) and to study the application of it in motion skill encoding. Primarily, Gaussian mixture model (GMM) has been widely applied on many occasions when a probability density function is needed to approximate a complex probability distribution. However, GMM cannot efficiently approach highly non-linear distributions. Thus, the proposed novel CGMM, as a weighted mixture of curved Gaussian models (CGM), is structured with non-linear transfers, which reshapes the flat GMM into a geo-metrically curved one. As a consequence, CGMM has more freedoms and flexibilities than the flat GMM so a CGMM requires fewer number of components in fitting highly non-linear motion trajectories. Moreover, we derive a dedicated iterative parameter estimation algorithm for the CGMM based on maximum likelihood estimation (MLE) theory. To evaluate the performance of the CGMM and its parameter estimation algorithm, a series of quantitative experiments are carried out. We first test the model performance in the data fitting task with the generated synthetic data. Then a motion skill encoding test is carried out on a human motion trajectory dataset built by a Virtual Reality (VR) based motion tracking system. The empirical results support that CGMM outperforms state-of-the-arts in the model performance test. Meanwhile, CGMM has a significant improvement in encoding high dimensional non-linear trajectory data compared to the GMM in motion skill encoding test with its dedicated parameter estimation algorithm.