Maximization of L1-norm Using Jacobi Rotations

In recent years, we observe a growing interest in approaches to principal component analysis (PCA) based on L1-norm maximization. Unfortunately, existing L1-PCA algorithms are either computationally expensive or inaccurate. In this paper, we propose to use Jacobi-based rotational framework for solving L1-norm maximization problem. Under this framework, two new suboptimal algorithms are developed: the first one based on exhaustive angle search, and the second one based on a differentiable approximation of the absolute value function. Experimental studies show that the proposed approaches provide high accuracy as compared to the existing suboptimal algorithms. They are also considerably faster than currently the most accurate method based on bit-flipping. Simulation results show that both approaches can be used to perform independent component analysis (ICA) under whitening assumption achieving better robustness to outliers than other methods.