Global Minimization of Contrast Function with Multiple Random Restarts

To achieve global minimization of the contrast function, multiple random restarts must be performed iteratively. A critical prerequisite involves whitening the input data to ensure an identity covariance matrix. The resulting Wopt matrix transforms the input x to produce independent sources (Wopt*x). Algorithm implementation typically requires: 1. Comparing results from each restart iteration to identify the optimal solution 2. Increasing restart count appropriately to enhance solution accuracy 3. Applying dimensionality reduction techniques to reduce computational complexity and memory usage Key programming considerations include: - Initializing multiple random starting points for optimization routines - Implementing convergence checks for each restart sequence - Maintaining a running comparison of objective function values - Incorporating PCA or similar techniques for data whitening and dimension reduction This task demands careful parameter tuning and methodological patience, but yields high-quality separation results when properly implemented. The core algorithm can be structured with nested loops for restart management and optimization cycles, using matrix operations for efficient whitening and source separation.