QDA {biClassify}

Quadratic Discriminant Analysis (QDA)

Description

A wrapper function for the various QDA implementations available in this package.

Generates class predictions for TestData.

Usage

QDA(TrainData, TrainCat, TestData, Method = "Full", Mode = "Automatic",
  m1 = NULL, m2 = NULL, m = NULL, s = NULL, gamma = 1e-05)

Arguments

TrainData

A (n x p) numeric matrix without missing values consisting of n training samples each with p features.

TrainCat

A vector of length n consisting of group labels of the n training samples in TrainData. Must consist of 1s and 2s.

TestData

A (m x p) numeric matrix without missing values consisting of m training samples each with p features. The number of features must equal the number of features in TrainData.

Method

A string of characters which determinds which version of QDA to use. Must be either "Full", "Compressed", or "Subsampled".

Mode

A string of characters which determines how the reduced sample paramters will be inputted for each method. Must be either "Research", "Interactive", or "Automatic". Default is "Automatic".

m1

The number of class 1 compressed samples to be generated. Must be a positive integer.

m2

The number of class 2 compressed samples to be generated. Must be a positive integer.

m

The number of total compressed samples to be generated. Must be a positive integer.

s

The sparsity level used in compression. Must satify 0 < s < 1.

gamma

A numeric value for the stabilization amount gamma * I added to the covariance matrixed used in the LDA decision rule. Default amount is 1E-5. Cannot be negative.

Details

Function which handles all implementations of LDA.

Value

Predictions

(m x 1) Vector of predicted class labels for the data points in TestData.

References

Lapanowski, Alexander F., and Gaynanova, Irina. “Compressing large sample data for discriminant analysis” arXiv preprint arXiv:2005.03858 (2020).

Examples

TrainData <- QDA_Data$TrainData
TrainCat <- QDA_Data$TrainCat
TestData <- QDA_Data$TestData
plot(TrainData[,2]~TrainData[,1], col = c("blue","orange")[as.factor(TrainCat)])

#----- Full QDA -------
QDA(TrainData = TrainData,
    TrainCat = TrainCat,
    TestData = TestData,
    Method = "Full",
    gamma = 1E-5)
  
#----- Compressed QDA -------  
 m1 <- 700
 m2 <- 300
 s <- 0.01
 QDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Compressed",
     Mode = "Research",
     m1 = m1,
     m2 = m2,
     s = s,
     gamma = 1E-5)
     
 QDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Compressed",
     Mode = "Automatic",
     gamma = 1E-5)
 
 #----- Sub-sampled QDA ------
 m1 <- 700
 m2 <- 300
 QDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Subsampled",
     Mode = "Research",
     m1 = m1,
     m2 = m2,
     gamma = 1E-5)
     
 QDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Subsampled",
     Mode = "Automatic",
     gamma = 1E-5)