Regression with Hyperdimensional Features: Application to Chemometric Calibration

The automatic analysis of data acquired with hyperdimensional sensors is rather challenging since it should be carried out in hyperdimensional feature spaces. The huge size of the feature space involves the so-called curse of dimensionality. This latter is due to the unbalancing between the number of features and the number of samples. In this book, it is proposed to exploit the whole information available in the original hyperdimensional feature space by means of the fusion of multiple regression methods. The development of the proposed multiple regression systems will include three main steps. The first one is related to the partition of the original hyperdimensional feature space into subspaces of reduced dimensionality. The second step consists in training in each of the subspaces obtained in the previous step a regression method. Finally, in the third and final step, the results provided by the different regression methods will be combined in order to produce a global estimate of the physical parameter of interest with an expected higher accuracy with respect to what can be achieved by the classical regression approach based on feature selection.