pcaL1 is a package for the R environment for finding principal components using methods based on the L1 norm. The principal components derived using traditional principal component analysis (PCA) can be interpreted as an optimal solution to several optimization problems involving the L2 norm. Using the L1 norm in these problems provides an alternative that is more robust to outlier observations in moderate-sized datasets. Replacing the L2 norm with the L1 norm in the different optimization problems yields different principal components. The package pcaL1 implements three algorithms: PCA-L1, L1-PCA, and L1-PCA*. Results are presented for test datasets that indicate the conditions under which each method performs best and the computation time required by each implementation.
Virginia Commonwealth University, Richmond, Virginia, April, 2012.