makeGramMatrix

 

 

Description

The makeGramMatrix function returns the N by N matrix containing the dot products of the row vectors in the input {NumMatrix}, known as the Gram matrix. The makeGramMatrix function will only receive a number matrix and always returns a new number Matrix containing the result.

The input argument {NumMatrix} must be an N by M number matrix representing the original independent variable observations (the dependent variable is omitted) in the form of:

x x x x... y

x x x x... y

....

x x x x... y

The output argument will be an N by N number matrix containing the dot products of the row vectors of the original observation matrix X, where: G[r,c] = vectorDotProduct(rowX[r],rowX[c]).

If the optional dependent variable number vector is included, The output argument will be an N by N+1 number matrix containing the dot products of the row vectors of the original observation matrix X, where: G[r,c] = vectorDotProduct(rowX[r],rowX[c]), plus the N+1th column will contain the original dependent values.

When to use

The makeGramMatrix functionis a non-destructive function useful when you want to create a Gram matrix in preparation for dual form regression. See Cristianini, "Support Vector Machines", page 169.

 

Syntax

(makeGramMatrix NumMatrix)



Name Description AIS Types
NumMatrix Matrix containing the original independent observationsNumMatrix


Returns:

A new number Matrix object containing the dot products of the row vectors of the original observation matrix.

 

Examples

Here are a number of links to Lambda coding examples which contain this instruction in various use cases.

Example_NumMatrix_makeGramMatrix_001

This example converts a Number Matrix to a Gram Matrix.

 

Argument Types

Here are the links to the data types of the function arguments.

NumMatrix Vector

Here are also a number of links to functions having arguments with any of these data types.

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