Linear predictive models estimation based on the LIBLINEAR C/C++ Library.

LiblineaR allows the estimation of predictive linear models for classification and regression, such as L1- or L2-regularized logistic regression, L1- or L2-regularized L2-loss support vector classification, L2-regularized L1-loss support vector classification and multi-class support vector classification. It also supports L2-regularized support vector regression (with L1- or L2-loss). The estimation of the models is particularly fast as compared to other libraries. The implementation is based on the LIBLINEAR C/C++ library for machine learning.

LiblineaR(
  data,
  target,
  type = 0,
  cost = 1,
  epsilon = 0.01,
  svr_eps = NULL,
  bias = 1,
  wi = NULL,
  cross = 0,
  verbose = FALSE,
  findC = FALSE,
  useInitC = TRUE,
  ...
)

Arguments

data

a nxp data matrix. Each row stands for an example (sample, point) and each column stands for a dimension (feature, variable). Sparse matrices of class matrix.csr, matrix.csc and matrix.coo from package SparseM are accepted. Sparse matrices of class dgCMatrix, dgRMatrix or dgTMatrix from package Matrix are also accepted. Note that C code at the core of LiblineaR package corresponds to a row-based sparse format. Hence, dgCMatrix, dgTMatrix, matrix.csc and matrix.csr inputs are first transformed into matrix.csr or dgRMatrix formats, which requires small extra computation time.

target

a response vector for prediction tasks with one value for each of the n rows of data. For classification, the values correspond to class labels and can be a 1xn matrix, a simple vector or a factor. For regression, the values correspond to the values to predict, and can be a 1xn matrix or a simple vector.

type

LiblineaR can produce 10 types of (generalized) linear models, by combining several types of loss functions and regularization schemes. The regularization can be L1 or L2, and the losses can be the regular L2-loss for SVM (hinge loss), L1-loss for SVM, or the logistic loss for logistic regression. The default value for type is 0. See details below. Valid options are:

for multi-class classification

0 – L2-regularized logistic regression (primal)
1 – L2-regularized L2-loss support vector classification (dual)
2 – L2-regularized L2-loss support vector classification (primal)
3 – L2-regularized L1-loss support vector classification (dual)
4 – support vector classification by Crammer and Singer
5 – L1-regularized L2-loss support vector classification
6 – L1-regularized logistic regression
7 – L2-regularized logistic regression (dual)

for regression

11 – L2-regularized L2-loss support vector regression (primal)
12 – L2-regularized L2-loss support vector regression (dual)
13 – L2-regularized L1-loss support vector regression (dual)

cost

cost of constraints violation (default: 1). Rules the trade-off between regularization and correct classification on data. It can be seen as the inverse of a regularization constant. See information on the 'C' constant in details below. A usually good baseline heuristics to tune this constant is provided by the heuristicC function of this package.

epsilon

set tolerance of termination criterion for optimization. If NULL, the LIBLINEAR defaults are used, which are:

if type is 0, 2, 5 or 6: epsilon=0.01
if type is 1, 3, 4, 7, 12 or 13: epsilon=0.1

The meaning of epsilon is as follows:

if type is 0 or 2:: \(|f'(w)|_{2} \le \code{epsilon} \times \min (pos,neg) / l \times |f'(w_{0})|_{2}\), where f is the primal function and pos/neg are # of positive/negative data (default 0.01)
if type is 11:: \(|f'(w)|_{2} \le \code{epsilon} \times |f'(w_{0})|_{2},\) where f is the primal function (default 0.001)
if type is 1, 3, 4 or 7:: Dual maximal violation \(\le \code{epsilon}\) (default 0.1)
if type is 5 or 6:: \(|f'(w)|_\infty \le \code{epsilon}\times \min(pos,neg)/l\ |f'(w_{0})|_\infty,\) where f is the primal function (default 0.01)
if type is 12 or 13:: \(|f'(\alpha)|_1 \le \code{epsilon}\times |f'(\alpha_{0})|_1,\) where f is the dual function (default 0.1)

svr_eps

set tolerance margin (epsilon) in regression loss function of SVR. Not used for classification methods.

bias

if bias > 0, instance data becomes [data; bias]; if <= 0, no bias term added (default 1).

wi

a named vector of weights for the different classes, used for asymmetric class sizes. Not all factor levels have to be supplied (default weight: 1). All components have to be named according to the corresponding class label. Not used in regression mode.

cross

if an integer value k>0 is specified, a k-fold cross validation on data is performed to assess the quality of the model via a measure of the accuracy. Note that this metric might not be appropriate if classes are largely unbalanced. Default is 0.

verbose

if TRUE, information are printed. Default is FALSE.

findC

if findC is TRUE runs a cross-validation of cross folds to find the best cost (C) value (works only for type 0 and 2). Cross validation is conducted many times under parameters C = start_C, 2*start_C, 4*start_C, 8*start_C, ..., and finds the best one with the highest cross validation accuracy. The procedure stops when the models of all folds become stable or C reaches the maximal value of 1024.

useInitC

if useInitC is TRUE (default) cost is used as the smallest start_C value of the search range (findC has to be TRUE). If useInitC is FALSE, then the procedure calculates a small enough start_C.

...

for backwards compatibility, parameter labels may be provided instead of target. A warning will then be issued, or an error if both are present. Other extra parameters are ignored.

Value

If cross>0, the average accuracy (classification) or mean square error (regression) computed over cross runs of cross-validation is returned.

Otherwise, an object of class "LiblineaR" containing the fitted model is returned, including:

TypeDetail: A string decsribing the type of model fitted, as determined by type.
Type: An integer corresponding to type.
W: A matrix with the model weights. If bias >0, W contains p+1 columns, the last being the bias term. The columns are named according to the names of data, if provided, or "Wx" where "x" ranges from 1 to the number of dimensions. The bias term is named "Bias".If the number of classes is 2, or if in regression mode rather than classification, the matrix only has one row. If the number of classes is k>2 (classification), it has k rows. Each row i corresponds then to a linear model discriminating between class i and all the other classes. If there are more than 2 classes, rows are named according to the class i which is opposed to the other classes.
Bias: The value of bias
ClassNames: A vector containing the class names. This entry is not returned in case of regression models.

Details

For details for the implementation of LIBLINEAR, see the README file of the original c/c++ LIBLINEAR library at https://www.csie.ntu.edu.tw/~cjlin/liblinear/.

Note

Classification models usually perform better if each dimension of the data is first centered and scaled.

References

For more information on LIBLINEAR itself, refer to:
R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin.
LIBLINEAR: A Library for Large Linear Classification,
Journal of Machine Learning Research 9(2008), 1871-1874.
https://www.csie.ntu.edu.tw/~cjlin/liblinear/

Author

Thibault Helleputte thibault.helleputte@dnalytics.com and
Jerome Paul jerome.paul@dnalytics.com and Pierre Gramme.
Based on C/C++-code by Chih-Chung Chang and Chih-Jen Lin

Examples

data(iris)
attach(iris)

x=iris[,1:4]
y=factor(iris[,5])
train=sample(1:dim(iris)[1],100)

xTrain=x[train,]
xTest=x[-train,]
yTrain=y[train]
yTest=y[-train]

# Center and scale data
s=scale(xTrain,center=TRUE,scale=TRUE)

# Find the best model with the best cost parameter via 10-fold cross-validations
tryTypes=c(1:6)
tryCosts=c(1000,0.001)
bestCost=NA
bestAcc=0
bestType=NA

for(ty in tryTypes){
  for(co in tryCosts){
    acc=LiblineaR(data=s,target=yTrain,type=ty,cost=co,bias=1,cross=5,verbose=FALSE)
    cat("Results for C=",co," : ",acc," accuracy.\n",sep="")
    if(acc>bestAcc){
      bestCost=co
      bestAcc=acc
      bestType=ty
    }
  }
}
#> Results for C=1000 : 0.94 accuracy.
#> Results for C=0.001 : 0.81 accuracy.
#> Results for C=1000 : 0.97 accuracy.
#> Results for C=0.001 : 0.78 accuracy.
#> Results for C=1000 : 0.93 accuracy.
#> Results for C=0.001 : 0.76 accuracy.
#> Results for C=1000 : 0.96 accuracy.
#> Results for C=0.001 : 0.76 accuracy.
#> Results for C=1000 : 0.97 accuracy.
#> Results for C=0.001 : 0.3 accuracy.
#> Results for C=1000 : 0.97 accuracy.
#> Results for C=0.001 : 0.35 accuracy.

cat("Best model type is:",bestType,"\n")
#> Best model type is: 2 
cat("Best cost is:",bestCost,"\n")
#> Best cost is: 1000 
cat("Best accuracy is:",bestAcc,"\n")
#> Best accuracy is: 0.97 

# Re-train best model with best cost value.
m=LiblineaR(data=s,target=yTrain,type=bestType,cost=bestCost,bias=1,verbose=FALSE)

# Scale the test data
s2=scale(xTest,attr(s,"scaled:center"),attr(s,"scaled:scale"))

# Make prediction
pr=FALSE
if(bestType==0 || bestType==7) pr=TRUE

p=predict(m,s2,proba=pr,decisionValues=TRUE)

# Display confusion matrix
res=table(p$predictions,yTest)
print(res)
#>             yTest
#>              setosa versicolor virginica
#>   setosa         11          0         0
#>   versicolor      0         18         2
#>   virginica       0          2        17

# Compute Balanced Classification Rate
BCR=mean(c(res[1,1]/sum(res[,1]),res[2,2]/sum(res[,2]),res[3,3]/sum(res[,3])))
print(BCR)
#> [1] 0.9315789

#' #############################################

# Example of the use of a sparse matrix of class matrix.csr :

if(require(SparseM)){

 # Sparsifying the iris dataset:
 iS=apply(iris[,1:4],2,function(a){a[a<quantile(a,probs=c(0.25))]=0;return(a)})
 irisSparse<-as.matrix.csr(iS)

 # Applying a similar methodology as above:
 xTrain=irisSparse[train,]
 xTest=irisSparse[-train,]

 # Re-train best model with best cost value.
 m=LiblineaR(data=xTrain,target=yTrain,type=bestType,cost=bestCost,bias=1,verbose=FALSE)

 # Make prediction
 p=predict(m,xTest,proba=pr,decisionValues=TRUE)

}
#> Loading required package: SparseM

#' #############################################

# Example of the use of a sparse matrix of class dgCMatrix :

if(require(Matrix)){

 # Sparsifying the iris dataset:
 iS=apply(iris[,1:4],2,function(a){a[a<quantile(a,probs=c(0.25))]=0;return(a)})
 irisSparse<-as(iS,"sparseMatrix")

 # Applying a similar methodology as above:
 xTrain=irisSparse[train,]
 xTest=irisSparse[-train,]

 # Re-train best model with best cost value.
 m=LiblineaR(data=xTrain,target=yTrain,type=bestType,cost=bestCost,bias=1,verbose=FALSE)

 # Make prediction
 p=predict(m,xTest,proba=pr,decisionValues=TRUE)

}
#> Loading required package: Matrix
#> 
#> Attaching package: ‘Matrix’
#> The following object is masked from ‘package:SparseM’:
#> 
#>     det
#> 'as(<matrix>, "dgRMatrix")' is deprecated.
#> Use 'as(as(as(., "dMatrix"), "generalMatrix"), "RsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").

#############################################

# Try regression instead, to predict sepal length on the basis of sepal width and petal width:

xTrain=iris[c(1:25,51:75,101:125),2:3]
yTrain=iris[c(1:25,51:75,101:125),1]
xTest=iris[c(26:50,76:100,126:150),2:3]
yTest=iris[c(26:50,76:100,126:150),1]

# Center and scale data
s=scale(xTrain,center=TRUE,scale=TRUE)

# Estimate MSE in cross-vaidation on a train set
MSECross=LiblineaR(data = s, target = yTrain, type = 13, cross = 5, svr_eps=.01)

# Build the model
m=LiblineaR(data = s, target = yTrain, type = 13, cross=0, svr_eps=.01)

# Test it, after test data scaling:
s2=scale(xTest,attr(s,"scaled:center"),attr(s,"scaled:scale"))
pred=predict(m,s2)$predictions
MSETest=mean((yTest-pred)^2)

# Was MSE well estimated?
print(MSETest-MSECross)
#> [1] -0.03077262

# Distribution of errors
print(summary(yTest-pred))
#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#> -0.71905 -0.20916  0.01635  0.02463  0.25683  0.84752