kernel: Kernel

Grein
02/28/2023

Kernels supported for use in computing inner products.

Usage

  linearKernel(...)

  polynomialKernel(a = NULL, bias = 0, deg = 3, ...)

  rbfKernel(gamma = NULL, ...)

  sigmoidKernel(gamma = NULL, coef0 = 0, ...)

Arguments

`a`

The numeric value for a in the term (a*<x,y> + b)^d. If not specified, (1/(number of features) is used.

`bias`

The numeric value for b in the term (a*<x,y> + b)^d.

`deg`

The integer value for d in the term (a*<x,y> + b)^d.

`gamma`

The numeric value for gamma in the expression tanh(gamma*<x,y> + c). If not specified, 1/(number of features) is used.

`coef0`

The numeric value for c in the expression tanh(gamma*<x,y> + c).

`...`

Additional arguments passed to the Microsoft ML compute engine.

Details

These helper functions specify the kernel that is used for training in relevant algorithms. The kernels that are supported:

linearKernel: linear kernel.

rbfKernel: radial basis function kernel.

polynomialKernel: polynomial kernel.

sigmoidKernel: sigmoid kernel.

Value

A character string defining the kernel.

Author(s)

Microsoft Corporation Microsoft Technical Support

References

Estimating the Support of a High-Dimensional Distribution

New Support Vector Algorithms

Examples


 # Simulate some simple data
 set.seed(7)
 numRows <- 200
 normalData <- data.frame(day = 1:numRows)
 normalData$pageViews = runif(numRows, min = 10, max = 1000) + .5 * normalData$day
 testData <- data.frame(day = 1:numRows)
 # The test data has outliers above 1000
 testData$pageViews = runif(numRows, min = 10, max = 1400) + .5 * testData$day

 train <- function(kernelFunction, args=NULL) {
     model <- rxOneClassSvm(formula = ~pageViews + day, data = normalData,
     kernel = kernelFunction(args))
     scores <- rxPredict(model, data = testData, writeModelVars = TRUE)
     scores$groups = scores$Score > 0
     scores
 }
 display <- function(scores) {
     print(sum(scores$groups))
     rxLinePlot(pageViews ~ day, data = scores, groups = groups, type = "p",
      symbolColors = c("red", "blue"))
 }
 scores <- list()
 scores$rbfKernel <- train(rbfKernel)
 scores$linearKernel <- train(linearKernel)
 scores$polynomialKernel <- train(polynomialKernel, (a = .2))
 scores$sigmoidKernel <- train(sigmoidKernel)
 display(scores$rbfKernel)
 display(scores$linearKernel)
 display(scores$polynomialKernel)
 display(scores$sigmoidKernel)

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