# Linear Discriminant Analysis (LDA) A wrapper function for the various LDA implementations available in this package. Generates class predictions for `TestData`. ```r 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`. ## Returns 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. ## Examples ```r 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) ``` ## 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.

LDA function