L1L1-norm projection pursuit principal component analysis

We develop a new method of robust principal component analysis based on the L1L1-norm projection pursuit approach. The aim of the paper is threefold. First, we present the underlying mathematical theory and show that it is closely related to the old centroid method of calculating principal components. Second, we present three algorithms to perform the required calculations. Third, we use Benzecri's geometric relative measure of the influence of a point on a principal axis to define cutpoints for the identification of outliers, and iteratively use it to eliminate outliers and obtain robust L1L1-norm projection pursuit principal components. Two examples of well-known data sets are provided.