Fit SCAD SVM model

SVM with variable selection (clone selection) using SCAD penalty.

Usage

scadsvc(lambda1 = 0.01, x, y, a = 3.7, tol= 10^(-4), class.weights= NULL,
 seed=123, maxIter=700, verbose=TRUE)

Arguments

lambda1: tuning parameter in SCAD function (default : 0.01)
x: n-by-d data matrix to train (n chips/patients, d clones/genes)
y: vector of class labels -1 or 1\'s (for n chips/patiens )
a: tuning parameter in scad function (default: 3.7)
tol: the cut-off value to be taken as 0
class.weights: a named vector of weights for the different classes, used for asymetric class sizes. Not all factor levels have to be supplied (default weight: 1). All components have to be named. (default: NULL)
seed: seed
maxIter: maximal iteration, default: 700
verbose: verbose, default: TRUE

Value

w: coefficients of the hyperplane.
b: intercept of the hyperplane.
xind: the index of the selected features (genes) in the data matrix.
xqx: internal calculations product \(xqx = 0.5 * x1 * inv_Q * t(x1)\), see code for more details.
fitted: fit of hyperplane f(x) for all _training_ samples with reduced set of features.
index: the index of the resulting support vectors in the data matrix.
type: type of svm, from svm function.
lambda1: optimal lambda1.
gacv: corresponding gacv.
iter: nuber of iterations.

Details

Adopted from Matlab code: http://www4.stat.ncsu.edu/~hzhang/software.html

References

Zhang, H. H., Ahn, J., Lin, X. and Park, C. (2006). Gene selection using support vector machines with nonconvex penalty. Bioinformatics, 22, pp. 88-95.

Author

Axel Benner

Examples



# simulate data
train<-sim.data(n = 200, ng = 100, nsg = 10, corr=FALSE, seed=12)
print(str(train)) 
#> List of 3
#>  $ x   : num [1:100, 1:200] 1.2048 -0.1389 0.864 0.0725 1.4274 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:100] "pos1" "pos2" "pos3" "pos4" ...
#>   .. ..$ : chr [1:200] "1" "2" "3" "4" ...
#>  $ y   : Named num [1:200] 1 1 -1 1 -1 1 1 1 1 -1 ...
#>   ..- attr(*, "names")= chr [1:200] "1" "2" "3" "4" ...
#>  $ seed: num 12
#> NULL
  
# train data  
model <- scadsvc(as.matrix(t(train$x)), y=train$y, lambda=0.01)
#> [1] "start iterations:"
#> [1] "scad converged in 9 iterations"
print(str(model))
#> List of 9
#>  $ w      : Named num [1:92] 0.91 1.225 0.88 0.517 1.14 ...
#>   ..- attr(*, "names")= chr [1:92] "pos1" "pos2" "pos3" "pos4" ...
#>  $ b      : num -0.034
#>  $ xind   : int [1:92] 1 2 3 4 5 6 7 8 9 10 ...
#>  $ index  : int [1:85] 6 19 20 25 40 48 49 54 56 57 ...
#>  $ xqx    : num [1:200, 1:200] 110.635 20.309 -14.916 37.297 0.445 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:200] "1" "2" "3" "4" ...
#>   .. ..$ : chr [1:200] "1" "2" "3" "4" ...
#>  $ fitted : num [1:200] 11.29 4.29 -3.86 8.48 -1.53 ...
#>  $ type   : num 0
#>  $ lambda1: num 0.01
#>  $ iter   : num 9
#>  - attr(*, "class")= chr [1:2] "scadsvm" "penSVM"
#> NULL

print(model)
#> 
#> Bias =  -0.03401226
#> Selected Variables=  pos1 pos2 pos3 pos4 pos5 neg1 neg2 neg3 neg4 neg5 bal1 bal2 bal3 bal5 bal6 bal7 bal9 bal10 bal11 bal12 bal13 bal16 bal17 bal18 bal19 bal20 bal21 bal22 bal23 bal24 bal25 bal26 bal27 bal28 bal29 bal30 bal31 bal32 bal33 bal34 bal35 bal36 bal37 bal38 bal39 bal40 bal41 bal42 bal43 bal44 bal46 bal47 bal48 bal49 bal50 bal51 bal52 bal53 bal54 bal55 bal56 bal57 bal58 bal59 bal60 bal61 bal62 bal63 bal64 bal65 bal66 bal67 bal68 bal69 bal70 bal71 bal72 bal73 bal74 bal75 bal76 bal77 bal78 bal79 bal80 bal81 bal83 bal84 bal86 bal87 bal88 bal90
#> Coefficients:
#>          pos1        pos2        pos3        pos4        pos5        neg1 
#>  0.90955973  1.22480258  0.88002752  0.51730723  1.14042067 -0.89468804 
#>        neg2        neg3        neg4        neg5        bal1        bal2 
#> -0.43818371 -0.21293659 -1.20568431 -1.21418360 -0.10118113 -0.70967352 
#>        bal3        bal5        bal6        bal7        bal9       bal10 
#>  0.33599993  0.10692685  0.28609573 -0.17763121 -0.15925854 -0.10510649 
#>       bal11       bal12       bal13       bal16       bal17       bal18 
#>  0.15029201 -0.44111494  0.20725643 -0.14456508  0.26237408 -0.15746206 
#>       bal19       bal20       bal21       bal22       bal23       bal24 
#> -0.15935625 -0.84453378  0.16942347  0.21879871  0.59584989  0.19418889 
#>       bal25       bal26       bal27       bal28       bal29       bal30 
#> -0.13213214  0.22527711 -0.58930416  0.09744356  0.31787684  0.45157157 
#>       bal31       bal32       bal33       bal34       bal35       bal36 
#>  0.15652711  0.06947663 -0.23303939 -0.54624676 -0.46293890  0.26960990 
#>       bal37       bal38       bal39       bal40       bal41       bal42 
#> -0.21485272  0.07748583 -0.16545216 -0.11277902  0.24936357 -0.37451411 
#>       bal43       bal44       bal46       bal47       bal48       bal49 
#>  0.23639990 -0.39446194  0.05374167  0.44266113 -0.05646721  0.36357278 
#>       bal50       bal51       bal52       bal53       bal54       bal55 
#>  0.39470649  0.21314700 -0.38577263 -0.49098664 -0.13996122 -0.32732887 
#>       bal56       bal57       bal58       bal59       bal60       bal61 
#> -0.57940948  0.27219758  0.04980174 -0.05760230  0.53541416  0.70985471 
#>       bal62       bal63       bal64       bal65       bal66       bal67 
#>  0.11326483  0.41113190 -0.13657480 -0.46424269  0.07664674  0.51321755 
#>       bal68       bal69       bal70       bal71       bal72       bal73 
#>  0.08138307  0.21317335  0.04040227 -0.35703858 -0.60339800  0.09918741 
#>       bal74       bal75       bal76       bal77       bal78       bal79 
#>  0.29333203 -0.06383283  0.05024979 -0.23317950 -0.54833937 -0.32259635 
#>       bal80       bal81       bal83       bal84       bal86       bal87 
#>  0.67043232 -0.11032972  0.18739860  0.28849419 -0.32534129  0.45262742 
#>       bal88       bal90 
#>  0.26339260 -0.28394962 
#>