# Graph Fused Lasso (FGSG)

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### Description

Given A = {a_1,…,a_n}, the response y, and a set of edges E, this function aims to solves

min 1/2||Ax-y||^2 + λ_1||x||_1 + λ_2 ∑_{(i,j) in E}w_(i,j)|x_i-r_(i,j)x_j|

where w_(i,j) is the weight of the edge (i,j), and r_(i,j) is the sign of the correlation between features a_i and a_j. The weight and sign can be specified in Rwt: w=|Rwt|, and r=sign(Rwt).

### Usage

 1 2 3 4 gflasso(A, y, tp, s1, s2, RmaxIter = 100, RaMaxIter = 1000, Rrho = 5, Rtau = 0.15, Rwt = rep(1, length(tp)), Rtol = 0.001, RaTol = 0.001, x0 = rep(0, ncol(A))) 

### Arguments

 A A The data matrix of size n \times p, each row corresponds to one sample. y y The response vector of length n. tp tp The edges vector of length 2*g (eg. (1,2,3,4) means an edge between 1 and 2, and an edge between 3 and 4, g=2 is the number of edges). s1 s1 The l_1 regularization parameter, s1 >=0. s2 s2 Tge grouping penatly parameter, s2 >=0. RmaxIter RmaxIter The maximum number of iterations in DC programming (default 100). RaMaxIter RaMaxIter The maximum number of iterations in ADMM (default 1000). Rrho Rrho The dual update length ofor ADMM (default 5). Rtau Rtau The tuning parameter for non-convex penalty (default 0.15). Rwt Rwt The weight and signs of edges (default rep(1,g)). Rtol Rtol The tolerance for convergence in DC programming (default 1e-3). RaTol RaTol The tolerance for convergence in ADMM (default 1e-3). x0 x0 The returned weight vector (default rep(0,p)).

### Value

Returned value x0 is the solution to the optimizaiton problem.

Yiwen Sun

### References

S.Kim and E.Xing. Statisctical estimation of correlated genome associations to a quantitative trait network. PLoS genetics, 5(8):e1000587, 2009

### Examples

 1 2 3 4 A<-matrix(rnorm(25),5,5) y<-rnorm(5) tp<-c(1,2,2,3,3,4,4,5) gflasso(A,y,tp,0,0) 

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