This thesis is concerned with Local Discriminant Basis (LDB) algorithm, its properties, optimization and applications in feature extraction and classification. LDB algorithm targets features extraction from redundant dictionaries such as wavelet packets or local trigonometric bases at low computational complexity.As the main contribution of this thesis, an optimization process is introduced to further improve the accuracy of the overall scheme in applications when a region of interest can be specified by the experts in the field of application (based on LDB selected features) to further characterize signal classes in smaller regions. Audio signal and textured image classifications are practical applications that are studied in this thesis to test the efficiency of optimally weighted local discriminant basis algorithm (OLDB) as a feature extraction scheme. Various properties of the algorithm such as noise behavior and stability analysis are studied from an engineering perspective. The implementation aspects of the algorithm in one dimension are reviewed as well as in two dimensions that serve as implementation guidelines.