  Principal component analysis (PCA) is often used to reduce the dimension of
data by selecting a few orthonormal vectors that explain most of the variance
structure of the data. L1 PCA uses the L1 norm to measure error, whereas the
conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the
fitting error of the reconstructed data, we propose an exact reweighted and an
approximate algorithm based on iteratively reweighted least squares. We provide
convergence analyses, and compare their performance against benchmark
algorithms in the literature. The computational experiment shows that the
proposed algorithms consistently perform best.
