Principal Component Analysis Based on L1-Norm Maximization from TPami

Traditional Principal Component Analysis (PCA) based on L2-norm maximization is sensitive to outliers. In contrast, PCA based on L1-norm maximization offers stronger robustness and effectively resists outlier interference. This method achieves feature extraction by optimizing an L1-norm objective function, with the core mechanism involving iterative solution of weight vectors to maximize the variance of projected data under the L1-norm framework. Compared to conventional PCA, this approach has higher computational complexity but demonstrates superior performance for noisy datasets, particularly excelling in image processing and bioinformatics applications. During implementation, special attention should be paid to initialization strategies and convergence condition settings. The author-provided code typically includes efficient iterative optimization algorithms that employ coordinate descent or weighted median computations to solve the L1-norm optimization problem. Key implementation aspects include: - Proper initialization of projection vectors to ensure convergence - Setting appropriate tolerance thresholds for iteration termination - Handling sign fluctuations in the optimization process - Efficient computation of L1-norm projections through weighted schemes The algorithm structure generally involves iteratively updating projection directions while maximizing the L1-norm variance, making it particularly valuable for real-world applications containing significant noise or outlier contamination.