Advanced non linear dimensionality reduction methods for multidimensional time series: applications to human motion analysis

This dissertation contributes to the state of the art in the field of pattern recognition and machine learning by advancing a family of nonlinear dimensionality reduction methods. We start with the automatisation of spectral dimensionality reduction approaches in order to facilitate the usage of these techniques by scientists in various domains wherever there is a need to explore large volumes of multivariate data. Then, we focus on the crucial and open problem of modelling the intrinsic structure of multidimensional time series. Solutions to this outstanding scientific challenge would advance various branches of science from meteorology, biology, engineering to computer vision, wherever time is a key asset of high dimensional data. We introduce two different approaches to this complex problem, which are both derived from the proposed concept of introducing spatio-temporal constraints between time series. The first algorithm allows for an efficient deterministic parameterisation of multidimensional time series spaces, even in the presence of data variations, whereas the second one approximates an underlying distribution of such spaces in a generative manner. We evaluate our original contributions in the area of visual human motion analysis, especially in two major computer vision tasks, i.e. human body pose estimation and human action recognition from video. In particular, we propose two variants of temporally constrained human motion descriptors, which become a foundation of view independent action recognition frameworks, and demonstrate excellent robustness against style, view .and speed variability in recognition of different kinds of motions. Performance analysis confirms the strength and potential of our contributions, which may benefit many domains beyond computer vision.