  This work develops a sparse and outlier-insensitive method to fit a
one-dimensional subspace that can be used as a replacement for eigenvector
methods such as principal component analysis (PCA). The method is insensitive
to outlier observations by formulating procedures as optimization problems that
seek the best-fit line according to the $\ell^1$ norm. It is also capable of
producing sparse principal components by leveraging an additional penalty term
induce sparsity. The algorithm has a worst-case time complexity of $O{(m^2n
\log n)}$ and, under certain conditions, produces a globally optimal solution.
An implementation of this algorithm in the parallel and heterogeneous
environment NVIDIA CUDA is tested on synthetic and real world datasets and
compared to existing methods. The results demonstrate the scalability and
efficiency of the proposed approach.
