KOS {biClassify}

Function which generates feature weights, discriminant vector, and class predictions.

Description

Returns a (m x 1) vector of predicted group membership (either 1 or 2) for each data point in X. Uses Data and Cat to train the classifier.

Usage

KOS(TestData = NULL, TrainData, TrainCat, Method = "Full",
  Mode = "Automatic", m1 = NULL, m2 = NULL, Sigma = NULL,
  Gamma = NULL, Lambda = NULL, Epsilon = 1e-05)

Arguments

TestData

(m x p) Matrix of unlabelled data with numeric features to be classified. Cannot have missing values.

TrainData

(n x p) Matrix of training data with numeric features. Cannot have missing values.

TrainCat

(n x 1) Vector of class membership corresponding to Data. Values must be either 1 or 2.

Method

A string of characters which determines which version of KOS to use. Must be either "Full" or "Subsampled". 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.

Sigma

Scalar Gaussian kernel parameter. Default set to NULL and is automatically generated if user-specified value not provided. Must be > 0. User-specified parameters must satisfy hierarchical ordering.

Gamma

Scalar ridge parameter used in kernel optimal scoring. Default set to NULL and is automatically generated if user-specified value not provided. Must be > 0. User-specified parameters must satisfy hierarchical ordering.

Lambda

Scalar sparsity parameter on weight vector. Default set to NULL and is automatically generated by the function if user-specified value not provided. Must be >= 0. When Lambda = 0, SparseKOS defaults to kernel optimal scoring of [Lapanowski and Gaynanova, preprint] without sparse feature selection. User-specified parameters must satisfy hierarchical ordering.

Epsilon

Numerical stability constant with default value 1e-05. Must be > 0 and is typically chosen to be small.

Details

Function which handles classification. Generates feature weight vector and discriminant coefficients vector in sparse kernel optimal scoring. If a matrix X is provided, the function classifies each data point using the generated feature weight vector and discriminant vector. Will use user-supplied parameters Sigma, Gamma, and Lambda if any are given. If any are missing, the function will run SelectParams to generate the other parameters. User-specified values must satisfy hierarchical ordering.

Value

A list of

Predictions

(m x 1) Vector of predicted class labels for the data points in TestData. Only included in non-null value of X is provided.

Weights

(p x 1) Vector of feature weights.

Dvec

(n x 1) Discrimiant coefficients vector.

References

Lapanowski, Alexander F., and Gaynanova, Irina. “Sparse feature selection in kernel discriminant analysis via optimal scoring”, Artificial Intelligence and Statistics, 2019.

Examples

Sigma <- 1.325386  #Set parameter values equal to result of SelectParam.
Gamma <- 0.07531579 #Speeds up example.
Lambda <- 0.002855275

TrainData <- KOS_Data$TrainData
TrainCat <- KOS_Data$TrainCat
TestData <- KOS_Data$TestData
TestCat <- KOS_Data$TestCat

KOS(TestData = TestData, 
    TrainData = TrainData, 
    TrainCat = TrainCat , 
    Sigma = Sigma , 
    Gamma = Gamma , 
    Lambda = Lambda)