Contributions to manifold learningapplications to visual data analysis

Resumen

In this thesis, we address two main related problems: (i) graph construction, and (ii) feature extraction through data embedding and dimensionality reduction. For the task of graph construction, we propose a method called Two-Phase Locality-constrained Linear Coding (TPLLC). The proposed approach simultaneously estimates the graph structure and the weights of its edges through sample coding. The key idea is to exploit data self-representativeness property in two phases of Locality-constrained Linear Coding (LLC) where the second phase utilizes adaptive sample pruning and re-weighting. The performance of the resulting graphs is evaluated with three post-graph tasks: label propagation, linear embedding, and Laplacian score based feature selection. For data embedding, the thesis proposes three contributions. Firstly, we use matrix exponential to solve the Small Sample Size (SSS) problem associated with the Local Discriminant Embedding (LDE) method. Secondly, for the Kernel Local Discriminant Embedding (Kernel LDE), we extract two kinds of features (regular and irregular) in order to elicit information from the null space of within-class locality preserving scatter matrix. Thirdly, we propose a parameterless Local Discriminant Embedding method for the task of model-less coarse 3D face pose estimation.Extensive experiments are conducted to tackle the problems of face recognition, object categorization, and model-less 3D face pose estimation. They demonstrate that the proposed algorithms can improve the state-of-the-art results.