GAMens {GAMens}

Applies the GAMbag, GAMrsm or GAMens ensemble classifier to a data set

Description

Fits the GAMbag, GAMrsm or GAMens ensemble algorithms for binary classification using generalized additive models as base classifiers.

Usage

GAMens(formula, data, rsm_size = 2, autoform = FALSE, iter = 10, df = 4,
  bagging = TRUE, rsm = TRUE, fusion = "avgagg")

Arguments

formula

a formula, as in the gam function. Smoothing splines are supported as nonparametric smoothing terms, and should be indicated by s. See the documentation of s in the gam package for its arguments. The GAMens function also provides the possibility for automatic formula specification. See 'details' for more information.

data

a data frame in which to interpret the variables named in formula.

rsm_size

an integer, the number of variables to use for random feature subsets used in the Random Subspace Method. Default is 2. If rsm=FALSE, the value of rsm_size is ignored.

autoform

if FALSE (default), the model specification in formula is used. If TRUE, the function triggers automatic formula specification. See 'details' for more information.

iter

an integer, the number of base classifiers (GAMs) in the ensemble. Defaults to iter=10 base classifiers.

df

an integer, the number of degrees of freedom (df) used for smoothing spline estimation. Its value is only used when autoform = TRUE. Defaults to df=4. Its value is ignored if a formula is specified and autoform is FALSE.

bagging

enables Bagging if value is TRUE (default). If FALSE, Bagging is disabled. Either bagging, rsm or both should be TRUE

rsm

enables Random Subspace Method (RSM) if value is TRUE (default). If FALSE, RSM is disabled. Either bagging, rsm or both should be TRUE

fusion

specifies the fusion rule for the aggregation of member classifier outputs in the ensemble. Possible values are 'avgagg' (default), 'majvote', 'w.avgagg' or 'w.majvote'.

Details

The GAMens function applies the GAMbag, GAMrsm or GAMens ensemble classifiers (De Bock et al., 2010) to a data set. GAMens is the default with (bagging=TRUE and rsm=TRUE. For GAMbag, rsm should be specified as FALSE. For GAMrsm, bagging should be FALSE.

The GAMens function provides the possibility for automatic formula specification. In this case, dichotomous variables in data are included as linear terms, and other variables are assumed continuous, included as nonparametric terms, and estimated by means of smoothing splines. To enable automatic formula specification, use the generic formula [response variable name]~. in combination with autoform = TRUE. Note that in this case, all variables available in data are used in the model. If a formula other than [response variable name]~. is specified then the autoform option is automatically overridden. If autoform=FALSE and the generic formula [response variable name]~. is specified then the GAMs in the ensemble will not contain nonparametric terms (i.e., will only consist of linear terms).

Four alternative fusion rules for member classifier outputs can be specified. Possible values are 'avgagg' for average aggregation (default), 'majvote' for majority voting, 'w.avgagg' for weighted average aggregation, or 'w.majvote' for weighted majority voting. Weighted approaches are based on member classifier error rates.

Value

An object of class GAMens, which is a list with the following components:

GAMs

the member GAMs in the ensemble.

formula

the formula used tot create the GAMens object.

iter

the ensemble size.

df

number of degrees of freedom (df) used for smoothing spline estimation.

rsm

indicates whether the Random Subspace Method was used to create the GAMens object.

bagging

indicates whether bagging was used to create the GAMens object.

rsm_size

the number of variables used for random feature subsets.

fusion_method

the fusion rule that was used to combine member classifier outputs in the ensemble.

probs

the class membership probabilities, predicted by the ensemble classifier.

class

the class predicted by the ensemble classifier.

samples

an array indicating, for every base classifier in the ensemble, which observations were used for training.

weights

a vector with weights defined as (1 - error rate). Usage depends upon specification of fusion_method.

Author(s)

Koen W. De Bock [e-mail], Kristof Coussement [e-mail] and Dirk Van den Poel [e-mail]

References

De Bock, K.W. and Van den Poel, D. (2012): "Reconciling Performance and Interpretability in Customer Churn Prediction Modeling Using Ensemble Learning Based on Generalized Additive Models". Expert Systems With Applications, Vol 39, 8, pp. 6816–6826.

De Bock, K. W., Coussement, K. and Van den Poel, D. (2010): "Ensemble Classification based on generalized additive models". Computational Statistics & Data Analysis, Vol 54, 6, pp. 1535–1546.

Breiman, L. (1996): "Bagging predictors". Machine Learning, Vol 24, 2, pp. 123–140.

Hastie, T. and Tibshirani, R. (1990): "Generalized Additive Models", Chapman and Hall, London.

Ho, T. K. (1998): "The random subspace method for constructing decision forests". IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 20, 8, pp. 832–844.

See Also

predict.GAMens, GAMens.cv

Examples

## Load data (mlbench library should be loaded)
library(mlbench)
data(Ionosphere)
IonosphereSub<-Ionosphere[,c("V1","V2","V3","V4","V5","Class")]

## Train GAMens using all variables in Ionosphere dataset
Ionosphere.GAMens <- GAMens(Class~., IonosphereSub ,4 , autoform=TRUE,
iter=10 )

## Compare classification performance of GAMens, GAMrsm and GAMbag ensembles,
## using 4 nonparametric terms and 2 linear terms
Ionosphere.GAMens <- GAMens(Class~s(V3,4)+s(V4,4)+s(V5,3)+s(V6,5)+V7+V8,
Ionosphere ,3 , autoform=FALSE, iter=10 )

Ionosphere.GAMrsm <- GAMens(Class~s(V3,4)+s(V4,4)+s(V5,3)+s(V6,5)+V7+V8,
Ionosphere ,3 , autoform=FALSE, iter=10, bagging=FALSE, rsm=TRUE )

Ionosphere.GAMbag <- GAMens(Class~s(V3,4)+s(V4,4)+s(V5,3)+s(V6,5)+V7+V8,
Ionosphere ,3 , autoform=FALSE, iter=10, bagging=TRUE, rsm=FALSE )

## Calculate AUCs (for function colAUC, load caTools library)
library(caTools)
GAMens.auc <- colAUC(Ionosphere.GAMens[[9]], Ionosphere["Class"]=="good",
plotROC=FALSE)
GAMrsm.auc <- colAUC(Ionosphere.GAMrsm[[9]], Ionosphere["Class"]=="good",
plotROC=FALSE)
GAMbag.auc <- colAUC(Ionosphere.GAMbag[[9]], Ionosphere["Class"]=="good",
plotROC=FALSE)