  Nowadays, analysing data from different classes or over a temporal grid has
attracted a great deal of interest. As a result, various multiple graphical
models for learning a collection of graphical models simultaneously have been
derived by introducing sparsity in graphs and similarity across multiple
graphs. This paper focuses on the fused multiple graphical Lasso model which
encourages not only shared pattern of sparsity, but also shared values of edges
across different graphs. For solving this model, we develop an efficient
regularized proximal point algorithm, where the subproblem in each iteration of
the algorithm is solved by a superlinearly convergent semismooth Newton method.
To implement the semismooth Newton method, we derive an explicit expression for
the generalized Jacobian of the proximal mapping of the fused multiple
graphical Lasso regularizer. Unlike those widely used first order methods, our
approach has heavily exploited the underlying second order information through
the semismooth Newton method. This can not only accelerate the convergence of
the algorithm, but also improve its robustness. The efficiency and robustness
of our proposed algorithm are demonstrated by comparing with some
state-of-the-art methods on both synthetic and real data sets. Supplementary
materials for this article are available online.
