Maximal Data Piling

Eric Bridgeford

2018-02-05

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

MDP

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.mdp(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.mdp(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.mdp(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")