outlierensembles

Let us add some anomalies inside an ring.

set.seed(1)
r1 <-runif(803)
r2 <-rnorm(803, mean=5)
theta = 2*pi*r1;
R1 <- 2
R2 <- 2
dist = r2+R2;
x =  dist * cos(theta)
y =  dist * sin(theta)

X <- data.frame(
    x1 = x,
    x2 = y
)
labs <- c(rep(0,800), rep(1,3))
nn <- dim(X)[1]
knn_auc <- lof_auc <- cof_auc <- rep(0, 10)
mu <-  0
z <- cbind(rnorm(3,mu, sd=0.2), rnorm(3,0, sd=0.2))
X[801:803, 1:2] <- z
ggplot(X, aes(x1, x2)) + geom_point()

Let us find outliers using DDoutlier R package and use the IRT ensemble to construct an ensemble score.

y1 <- DDoutlier::KNN_AGG(X,  k_min=10, k_max=20)
y2 <- DDoutlier::LOF(X, k=10)
y3 <- DDoutlier::COF(X, k=10)
y4 <- DDoutlier::INFLO(X, k=10)
y5 <- DDoutlier::KDEOS(X, k_min=10, k_max=20)
y6 <- DDoutlier::LDF(X, k=10)
y7 <- DDoutlier::LDOF(X, k=10)
Y <- cbind.data.frame(y1, y2, y3, y4, y5, y6, y7)
ens1 <- irt_ensemble(Y)
df <- cbind.data.frame(X, ens1$scores)
colnames(df)[3] <- "IRT"
ggplot(df, aes(x1, x2)) + geom_point(aes(color=IRT))  +  scale_color_gradient(low="yellow", high="red")

Then we do the greedy ensemble.

ens2 <- greedy_ensemble(Y)
df <- cbind.data.frame(X, ens2$scores)
colnames(df)[3] <- "Greedy"
ggplot(df, aes(x1, x2)) + geom_point(aes(color=Greedy)) +  scale_color_gradient(low="yellow", high="red")

We do the ICWA ensemble next.

ens3 <- icwa_ensemble(Y)
df <- cbind.data.frame(X, ens3)
colnames(df)[3] <- "ICWA"
ggplot(df, aes(x1, x2)) + geom_point(aes(color=ICWA)) +  scale_color_gradient(low="yellow", high="red")

Next, we use the maximum scores to build the ensemble.

ens4 <- max_ensemble(Y)
df <- cbind.data.frame(X, ens4)
colnames(df)[3] <- "Max"
ggplot(df, aes(x1, x2)) + geom_point(aes(color=Max)) +  scale_color_gradient(low="yellow", high="red")

Then, we use the a threshold sum to construct the ensemble.

ens5 <- threshold_ensemble(Y)
df <- cbind.data.frame(X, ens5)
colnames(df)[3] <- "Threshold"
ggplot(df, aes(x1, x2)) + geom_point(aes(color=Threshold)) +  scale_color_gradient(low="yellow", high="red")

Finally, we use the mean values as the ensemble score.

ens6 <- average_ensemble(Y)
df <- cbind.data.frame(X, ens6)
colnames(df)[3] <- "Average"
ggplot(df, aes(x1, x2)) + geom_point(aes(color=Average)) +  scale_color_gradient(low="yellow", high="red")