Unsupervised Classification of Array Data Based on the L1-Norm

L1-norm criteria have been the subject a flurry of research in signal processing and machine learning over the last decade, especially due to their ability to exploit the sparsity of latent variables and their robustness in the presence of faulty data. Among such criteria, L1-norm principal component analysis (L1-PCA) has drawn considerable attention, resulting in a variety of optimization algorithms and connections with other data processing techniques such as independent component analysis. The present contribution takes a step forward in the characterization of L1-PCA by exploring its linear discrimination capabilities. A variant of L1-PCA consisting of L1-norm maximization subject to an L2-norm constraint is put forward for unsupervised classification. The discrimination properties of the proposed L1-PCA variant are demonstrated through a number of computer experiments.