# Data Piling

#### Eric Bridgeford

#### 2020-06-25

    require(lolR)

    ## Loading required package: lolR

    require(ggplot2)

    ## Loading required package: ggplot2

    require(MASS)

    ## Loading required package: MASS

    n=400
    d=30
    r=3

Data for this notebook will be `n=400` examples of `d=30` dimensions.

# DP

## Stacked Cigar Simulation

We first visualize the first `2` dimensions:

    testdat <- lol.sims.cigar(n, d)
    X <- testdat$X
    Y <- testdat$Y

    data <- data.frame(x1=X[,1], x2=X[,2], y=Y)
    data$y <- factor(data$y)
    ggplot(data, aes(x=x1, y=x2, color=y)) +
      geom_point() +
      xlab("x1") +
      ylab("x2") +
      ggtitle("Simulated Data")

Projecting with MDP to `K-1=1` dimension and visualizing:

    result <- lol.project.dp(X, Y)

    data <- data.frame(x1=result$Xr[,1], y=Y)
    data$y <- factor(data$y)
    ggplot(data, aes(x=x1, y=y, color=y)) +
      geom_point() +
      xlab("x1") +
      ylab("Class") +
      ggtitle("Projected Data using MDP")

## Trunk Simulation

We visualize the first `2` dimensions:

    testdat <- lol.sims.rtrunk(n, d)
    X <- testdat$X
    Y <- testdat$Y

    data <- data.frame(x1=X[,1], x2=X[,2], y=Y)
    data$y <- factor(data$y)
    ggplot(data, aes(x=x1, y=x2, color=y)) +
      geom_point() +
      xlab("x1") +
      ylab("x2") +
      ggtitle("Simulated Data")

Projecting with MDP to `K-1=1` dimensions and visualizing:

    result <- lol.project.dp(X, Y)

    data <- data.frame(x1=result$Xr[,1], y=Y)
    data$y <- factor(data$y)
    ggplot(data, aes(x=x1, y=y, color=y)) +
      geom_point() +
      xlab("x1") +
      ylab("Class") +
      ggtitle("Projected Data using MDP")

## Rotated Trunk Simulation

We visualize the first `2` dimensions:

    testdat <- lol.sims.rtrunk(n, d, rotate=TRUE)
    X <- testdat$X
    Y <- testdat$Y

    data <- data.frame(x1=X[,1], x2=X[,2], y=Y)
    data$y <- factor(data$y)
    ggplot(data, aes(x=x1, y=x2, color=y)) +
      geom_point() +
      xlab("x1") +
      ylab("x2") +
      ggtitle("Simulated Data")

Projecting with MDP to `K-1=1` dimensions and visualizing:

    result <- lol.project.dp(X, Y)

    data <- data.frame(x1=result$Xr[,1], y=Y)
    data$y <- factor(data$y)
    ggplot(data, aes(x=x1, y=y, color=y)) +
      geom_point() +
      xlab("x1") +
      ylab("Class") +
      ggtitle("Projected Data using MDP")