Principal component analysis (PCA) based on L1norm has drawn growing interest in recent years.It is especially popular in the machine learning and pattern recognition communities for its robustness to outliers.Although optimal algorithms for L1-norm maximization exist, they have very high computational complexity and can be used for evaluation purposes only.In practice, only approximate techniques have been considered so far.Currently, the most popular method is the bit-flipping technique, where the L1-norm maximization is viewed as a combinatorial problem over the binary field.Recently, we proposed exhaustive, but faster algorithm [1] based on two-dimensional Jacobi rotations that also offer high accuracy.In this paper, we develop a novel variant of this method that uses three-dimensional rotations and quaternion algebra.Our experiments show that the proposed approach offers higher accuracy than other approximate algorithms, but at the expense of the additional computational cost.However, for large datasets, the cost is still lower than that of the bit-flipping technique.

Most recently, a link between principal component analysis (PCA) based on L1-norm and independent component analysis (ICA) has been discovered.It was shown that the ICA can actually be performed by L1-PCA under the whitening assumption, inheriting the improved robustness to outliers.In this paper, a novel ICA algorithm based on Jacobi iterative framework is proposed that utilizes the non-differentiable L1-norm criterion as an objective function.We show that such function can be optimized by sequentially applying Jacobi rotations to the whitened data, wherein optimal rotation angles are found using an exhaustive search method.The experiments show that the proposed method provides a superior convergence as compared to FastICA variants.It also outperforms existing methods in terms of source extraction performance for Laplacian distributed sources.Although the proposed approach exploits the exhaustive search method, it offers a lower computational complexity than that of the optimal L1-PCA algorithm.