FGSG (version 1.0.2)

ncTL: Non Convex Truncated L1 Feature Grouping and Selection (FGSG)

Description

Given $A = {a_1,\dots,a_n}$, the response $y$, and a set of edges $E$, this function aims to solves $$min 1/2||Ax-y||^2 + \lambda_1 \sum\limits_i(J_\tau(|x_i|)) + \lambda_2 \sum_{(i,j)\in E} w_(i,j)|x_i-r_{(i,j)}x_j|$$ where $J_\tau(x)=min(x/\tau,1)$ is a surrogate of the L0 norm, $w_(i,j)$ 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

ncTL(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.

References

S.Yang, L.Yuan, Y.Lai, X.Shen, P.Wonka, and J.Ye. Feature grouping and selection over an undirected graph. KDD, 2012.

Examples

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