Principal component analysis (PCA) (also called Karhunen Loève transform) has been widely used for dimensionality reduction, denoising, feature selection, subspace detection and other purposes. However, traditional PCA minimizes the sum of squared errors and suffers from both outliers and large feature noises. The L1-norm based PCA (more precisely L1,1 norm) is more robust. Yet, the optimizatio...

The low-rank matrix approximation problem with respect to the component-wise l1-norm (l1LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine learning. Robust PCA aims at recovering a low-rank matrix that was perturbed with sparse noise, with applications for example in foreground-background video separation. Altho...

Recently, some variants of the l1 norm, particularly matrix norms such as the l1,2 and l1,∞ norms, have been widely used in multi-task learning, compressed sensing and other related areas to enforce sparsity via joint regularization. In this paper, we unify the l1,2 and l1,∞ norms by considering a family of l1,q norms for 1 < q ≤ ∞ and study the problem of determining the most appropriate spars...

Given this model, spectral unmixing and endmember detection are the tasks of determining the endmembers and the proportions for every data point in the scene. Several endmember detection and spectral unmixing algorithms have been developed in the literature. However, the majority of these methods do not provide an autonomous way to estimate the number of endmembers and, thus, require the number...