biClassify (version 1.3)

LDA: Linear Discriminant Analysis (LDA)

Description

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

Generates class predictions for TestData.

Usage

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

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 determines which version of LDA to use. Must be either "Full", "Compressed", "Subsampled", "Projected", or "fastRandomFisher". Default is "Full".

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.

type

A string of characters determining the type of compression matrix used. The accepted values are Rademacher, Gaussian, and Count.

Value

A list containing

Predictions

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

Dvec

(px1) Discriminant vector used to predict the class labels.

Details

Function which handles all implementations of LDA.

References

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

Ye, Haishan, Yujun Li, Cheng Chen, and Zhihua Zhang. ``Fast Fisher discriminant analysis with randomized algorithms.'' Pattern Recognition 72 (2017): 82-92.

Examples

# NOT RUN {
TrainData <- LDA_Data$TrainData
TrainCat <- LDA_Data$TrainCat
TestData <- LDA_Data$TestData
plot(TrainData[,2]~TrainData[,1], col = c("blue","orange")[as.factor(TrainCat)])

#----- Full LDA -------
LDA(TrainData = TrainData,
    TrainCat = TrainCat,
    TestData = TestData,
    Method = "Full",
    gamma = 1E-5)
  
#----- Compressed LDA -------  
 m1 <- 700
 m2 <- 300
 s <- 0.01
 LDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Compressed",
     Mode = "Research",
     m1 = m1,
     m2 = m2,
     s = s,
     gamma = 1E-5)
     
 LDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Compressed",
     Mode = "Automatic",
     gamma = 1E-5)
 
 #----- Sub-sampled LDA ------
 m1 <- 700
 m2 <- 300
 LDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Subsampled",
     Mode = "Research",
     m1 = m1,
     m2 = m2,
     gamma = 1E-5)
 
  LDA(TrainData = TrainData,
     TrainCat = TrainCat,
     TestData = TestData,
     Method = "Subsampled",
     Mode = "Automatic",
     gamma = 1E-5)
     
 #----- Projected LDA ------
  m1 <- 700
  m2 <- 300
  s <- 0.01
  LDA(TrainData = TrainData,
      TrainCat = TrainCat,
      TestData = TestData,
      Method = "Projected",
      Mode = "Research",
      m1 = m1, 
      m2 = m2, 
      s = s,
      gamma = 1E-5)
      
   LDA(TrainData = TrainData,
      TrainCat = TrainCat,
      TestData = TestData,
      Method = "Projected",
      Mode = "Automatic",
      gamma = 1E-5)
      
 #----- Fast Random Fisher ------    
  m <- 1000 
  s <- 0.01
  LDA(TrainData = TrainData,
      TrainCat = TrainCat,
      TestData = TestData,
      Method = "fastRandomFisher",
      Mode = "Research",
      m = m, 
      s = s,
      gamma = 1E-5)
      
   LDA(TrainData = TrainData,
      TrainCat = TrainCat,
      TestData = TestData,
      Method = "fastRandomFisher",
      Mode = "Automatic",
      gamma = 1E-5)  
# }