# softMarginVectorLoss: Soft Margin Vector Loss function for multiclass SVM In bmrm: Bundle Methods for Regularized Risk Minimization Package

## Description

Soft Margin Vector Loss function for multiclass SVM

## Usage

 `1` ```softMarginVectorLoss(x, y, l = 1 - table(seq_along(y), y)) ```

## Arguments

 `x` instance matrix, where x(t,) defines the features of instance t `y` target vector where y(t) is an integer encoding target of x(t,). If it contains NAs, the return function is a non-convex loss for transductive multiclass-SVM. `l` loss matrix. l(t,p(t)) must be the loss for predicting target p(t) instead of y(t) for instance t. By default, the parameter is set to character value "0/1" so that the loss is set to a 0/1 loss matrix.

## Value

a function taking one argument w and computing the loss value and the gradient at point w

## References

Teo et al. A Scalable Modular Convex Solver for Regularized Risk Minimization. KDD 2007

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ``` # -- Build a 2D dataset from iris, and add an intercept x <- cbind(intercept=100,data.matrix(iris[c(1,2)])) y <- iris\$Species # -- build the multiclass SVM model w <- nrbm(softMarginVectorLoss(x,y)) table(predict(w,x),y) # -- Plot the dataset, the decision boundaries, the convergence curve, and the predictions gx <- seq(min(x[,2]),max(x[,2]),length=200) # positions of the probes on x-axis gy <- seq(min(x[,3]),max(x[,3]),length=200) # positions of the probes on y-axis Y <- outer(gx,gy,function(a,b) {predict(w,cbind(100,a,b))}) image(gx,gy,unclass(Y),asp=1,main="dataset & decision boundaries", xlab=colnames(x)[2],ylab=colnames(x)[3]) points(x[,-1],pch=19+as.integer(y)) ```

bmrm documentation built on May 2, 2019, 2:49 p.m.