L1 regularization can also be used for feature selection[0] and hence dimensionality reduction. I've in found practice that the speed of this can compare favorably even to fast implementations[1] of svd.

[0] Feature selection, L1 vs. L2 regularization, and rotational invariance, Andrew Y. Ng. In Proceedings of the Twenty-first International Conference on Machine Learning, 2004. http://ai.stanford.edu/~ang/papers/icml04-l1l2.pdf

[1]"Augmented Implicitly Restarted Lanczos Bidiagonalization Methods", J. Baglama and L. Reichel, SIAM J. Sci. Comput. 2005.