Contributions to High-Dimensional Pattern Recognition
This thesis gathers some contributions to statistical pattern recognition particularly targeted at problems in which the feature vectors are high-dimensional. Three pattern recognition scenarios are addressed, namely pattern classification, regression analysis and score fusion. For each of these, an algorithm for learning a statistical model is presented. In order to address the difficulty that is encountered when the feature vectors are high-dimensional, adequate models and objective functions are defined. The strategy of learning simultaneously a dimensionality reduction function and the pattern recognition model parameters is shown to be quite effective, making it possible to learn the model without discarding any discriminative information. Another topic that is addressed in the thesis is the use of tangent vectors as a way to take better advantage of the available training data. Using this idea, two popular discriminative dimensionality reduction techniques are shown to be effectively improved. For each of the algorithms proposed throughout the thesis, several data sets are used to illustrate the properties and the performance of the approaches. The empirical results show that the proposed techniques perform considerably well, and furthermore the models learned tend to be very computationally efficient.