Human Body Tracking with Rank Priors for Continuous Non-Linear Dimensionality Reduction Diploma Thesis
چکیده
Non-linear dimensionality reduction methods are powerful techniques to deal with high-dimensional datasets. However, they often are susceptible to local minima and perform poorly when initialized far from the global optimum, even when the intrinsic dimensionality is known a priori. In this work a prior over the dimensionality of the latent space is introduced, which allows for simultaneously optimizing both the latent space and its intrinsic dimensionality. Ad-hoc initialization schemes are unnecessary with this approach; the latent space is initialized to the observation space and the latent dimensionality is automatically inferred using an optimization scheme that drops dimensions in a continuous fashion. The prior is applied to various tasks involving probabilistic non-linear dimensionality reduction, and it is shown that this method can outperform graph-based dimensionality reduction techniques as well as previously suggested ad-hoc initialization strategies. Results are reported for artificial datasets which cause problems to nearest neighbor-based spectral methods and for a real-world example, where the task consists of tracking a person performing activities in a kitchen scenario.