# lol.sims.qdtoep: Quadratic Discriminant Toeplitz Simulation In lolR: Linear Optimal Low-Rank Projection

## Description

A function for simulating data generalizing the Toeplitz setting, where each class has a different covariance matrix. This results in a Quadratic Discriminant.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```lol.sims.qdtoep( n, d, rotate = FALSE, priors = NULL, D1 = 10, b = 0.4, rho = 0.5 ) ```

## Arguments

 `n` the number of samples of the simulated data. `d` the dimensionality of the simulated data. `rotate` whether to apply a random rotation to the mean and covariance. With random rotataion matrix `Q`, `mu = Q*mu`, and `S = Q*S*Q`. Defaults to `FALSE`. `priors` the priors for each class. If `NULL`, class priors are all equal. If not null, should be `|priors| = K`, a length `K` vector for `K` classes. Defaults to `NULL`. `D1` the dimensionality for the non-equal covariance terms. Defaults to `10`. `b` a scaling parameter for the means. Defaults to `0.4`. `rho` the scaling of the covariance terms, should be < 1. Defaults to `0.5`.

## Value

A list of class `simulation` with the following:

 `X` `[n, d]` the `n` data points in `d` dimensions as a matrix. `Y` `[n]` the `n` labels as an array. `mus` `[d, K]` the `K` class means in `d` dimensions. `Sigmas` `[d, d, K]` the `K` class covariance matrices in `d` dimensions. `priors` `[K]` the priors for each of the `K` classes. `simtype` The name of the simulation. `params` Any extraneous parameters the simulation was created with.

## Details

For more details see the help vignette: `vignette("sims", package = "lolR")`

Eric Bridgeford

## Examples

 ```1 2 3``` ```library(lolR) data <- lol.sims.qdtoep(n=200, d=30) # 200 examples of 30 dimensions X <- data\$X; Y <- data\$Y ```

lolR documentation built on July 8, 2020, 7:35 p.m.