  rdering of regression or classification coefficients occurs in many
real-world applications. Fused Lasso exploits this ordering by explicitly
regularizing the differences between neighboring coefficients through an
$\ell_1$ norm regularizer. However, due to nonseparability and nonsmoothness of
the regularization term, solving the fused Lasso problem is computationally
demanding. Existing solvers can only deal with problems of small or medium
size, or a special case of the fused Lasso problem in which the predictor
matrix is identity matrix. In this paper, we propose an iterative algorithm
based on split Bregman method to solve a class of large-scale fused Lasso
problems, including a generalized fused Lasso and a fused Lasso support vector
classifier. We derive our algorithm using augmented Lagrangian method and prove
its convergence properties. The performance of our method is tested on both
artificial data and real-world applications including proteomic data from mass
spectrometry and genomic data from array CGH. We demonstrate that our method is
many times faster than the existing solvers, and show that it is especially
efficient for large p, small n problems.
