# LOL Simulations

#### Eric Bridgeford

#### 2020-06-25

    require(lolR)
    require(ggplot2)
    require(MASS)
    n <- 1000
    d <- 15

    plot_sim <- function(X, Y, name, d1=1, d2=2) {
      data <- data.frame(x1=X[,d1], x2=X[,d2], y=Y)
      data$y <- factor(data$y)
      ggplot(data, aes(x=x1, y=x2, color=y)) +
        geom_point() +
        xlab("x1") +
        ylab("x2") +
        ggtitle(name)
    }

Below, we visualize the different simulation settings with `n=400` in `d=50` dimensions:

# Trunk, 2 Class

    testdat <- lol.sims.rtrunk(n, d, b=20)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Trunk, 2 Class"))

# Rotated Trunk, 2 Class, non-equal priors

In this simulation, we show the trunk, estimate a rotation matrix to apply to the mean and covariances, and use a non-equal prior with more class 1 than class 2.

    testdat <- lol.sims.rtrunk(n, d, rotate=TRUE, priors=c(0.8, 0.2), b=20)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Rotated Trunk, 2 Class, non-equal priors"))

# Trunk, 3 Class

    testdat <- lol.sims.rtrunk(n, d, b=20, K=3)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Trunk, 3 Class"))

# Mean Difference

    testdat <- lol.sims.mean_diff(n, d)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Mean Difference 2 Class"))

# Toeplitz

    testdat <- lol.sims.toep(n, d)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Toeplitz"))

# QD- Toeplitz

    testdat <- lol.sims.qdtoep(n, d)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "QD-Toeplitz"))

# XOR

    testdat <- lol.sims.xor2(n, d)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "XOR"))

# Cigar

    testdat <- lol.sims.cigar(n, d)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Cigar"))

# Fat Tails

    testdat <- lol.sims.fat_tails(n, d)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Fat Tails"))

# Cross

    testdat <- lol.sims.cross(n, d, a=4, b=.25)
    X <- testdat$X
    Y <- testdat$Y
    print(plot_sim(X, Y, "Cross", d1=7, d2=8))