raptMake {expandFunctions}

Define a Random Affine Projection Transformation (RAPT) object

Description

Create a Random Affine Projection Transformation (RAPT) object. Such objects use random affine projection transformation to the resulting matrix. This allows RAPT objects serve as a basis for a large number of kinds of expansions.

Usage

raptMake(p, q, Wdist = rnorm, WdistOpt = NULL, bDist = runif,
  bDistOpt = list(min = 0, max = 0))

Arguments

p

Number of input features (columns of X).

q

Number of output features,

Wdist

W distribution function. Coefficients for the random projection matrix W are drawn from this distribution. The default is rnorm.

WdistOpt

List of optional parameters for Wdist. If this is NULL (default), then only defaults of the distribution are used.

bDist

b distribution function. Coefficients for the offset vector b are drawn from this distribution. The default is runif.

bDistOpt

List of optional parameters for bDist. If this is NULL then only defaults of the distribution are used. The default is bDistOpt=list(min=0,max=0), which results in b = 0, with no offset.

Details

This initializes a eRAPTobj, which holds all the parameters needed to perform a random projection transformation expansion (RAPT).

An RAPT of X is defined as

X W + b

where

X is the input matrix

W is a matrix of coefficients drawn from Wdist with options WdistOpt

b is a column matrix of coefficients drawn from bDist with options bDistOpt

If there is a need for multiple W or b distributions, then make multiple raptObj. This makes each raptObj fairly simple, while allowing arbitrary complexity through multiple expansion and composition.

A simple way to get a linear feature, in addition to the RAPT features, is to simply cbind the original matrix X in with the raptObj matrix.

Value

An expand object, which defines the following fields: W Input weighting matrix b Input offset matrix

Examples

raptObj <- raptMake(21,210,bDistOpt=list(min=-pi,max=+pi))