In this Master's Thesis, we introduce the methodology Basis-Decomposition Discriminant ICA (BD-DICA), capable of finding the most discriminant Independent Components to characterise a high-dimensional dataset. The algorithm provides for this characterisation for several components with the same structure as the inputs. An adaptation of the algorithm for Feature Extraction is derived in the conclusions of this report. BD-DICA is constructed as a combination of the Basis-Decomposition ICA (BD-ICA), an architecture for ICA used in fMRI data analysis, and the Basis-Decomposition Fisher's Linear Discriminant (BDFLD), a modified version of the classical FLD introduced in this work. BDDICA is originally designed to deal with fMRI Data analysis, in which often we have data of about 10-5- 10-6- dimensions and a much smaller number of instances. BD-DICA finds interesting projections in the data whose output show a high discriminant power while maximising independence among the obtained projectors. Additional strategies based in a high restriction over the search subspace reduce highly the chances of overfitting. Experiments with synthetic data show that the method is robust to noise and that it is capable of successfully finding the discriminant generators of the data. Experiments performed with real fMRI data show that the method offers good results with Resting-State fMRI data. Unfortunately, no conclusive results were obtained for Task-Based fMRI data. A Gradient-Ascend approach to BD-DICA is exposed in detail along the report, including all needed derivatives. In addition, the implementation we used for the experimentation is publicly available running under MATLAB in www.github/qtabs/bddica. Compatibility with Octave is possible with a few adaptations regarding external libraries used by the algorithm.