  Sparse principal component analysis (SPCA) has emerged as a powerful
technique for modern data analysis, providing improved interpretation of
low-rank structures by identifying localized spatial structures in the data and
disambiguating between distinct time scales. We demonstrate a robust and
scalable SPCA algorithm by formulating it as a value-function optimization
problem. This viewpoint leads to a flexible and computationally efficient
algorithm. Further, we can leverage randomized methods from linear algebra to
extend the approach to the large-scale (big data) setting. Our proposed
innovation also allows for a robust SPCA formulation which obtains meaningful
sparse principal components in spite of grossly corrupted input data. The
proposed algorithms are demonstrated using both synthetic and real world data,
and show exceptional computational efficiency and diagnostic performance.
