pcccd_classifier {rcccd}

Pure and Proper Class Cover Catch Digraph Classifier

Description

pcccd_classifier fits a Pure and Proper Class Cover Catch Digraph (PCCCD) classification model.

Usage

pcccd_classifier(x, y, proportion = 1)

Arguments

x

feature matrix or dataframe.

y

class factor variable.

proportion

proportion of covered samples. A real number between (0,1]. 1 by default. Smaller numbers results in less dominant samples.

Details

Multiclass framework for PCCCD. PCCCD determines target class dominant points set S and their circular cover area by determining balls B(x^{\text{target}}, r_{i}) with radii r using minimum amount of dominant point which satisfies X^{\text{non-target}}\cap \bigcup_{i} B_{i} = \varnothing (pure) and X^{\text{target}}\subset \bigcup_{i} B_{i} (proper).

This guarantees that balls of target class never covers any non-target samples (pure) and balls cover all target samples (proper).

For detail, please refer to Priebe et al. (2001), Priebe et al. (2003), and Manukyan and Ceyhan (2016).

Note: Much faster than cccd package.

Value

an object of "cccd_classifier" which includes:

i_dominant_list

dominant sample indexes.

x_dominant_list

dominant samples from feature matrix, x

radii_dominant_list

Radiuses of the circle for dominant samples

class_names

class names

k_class

number of classes

proportions

proportions each class covered

Author(s)

Fatih Saglam, [e-mail]

References

Priebe, C. E., DeVinney, J., & Marchette, D. J. (2001). On the distribution of the domination number for random class cover catch digraphs. Statistics & Probability Letters, 55(3), 239–246. https://doi.org/10.1016/s0167-7152(01)00129-8

Priebe, C. E., Marchette, D. J., DeVinney, J., & Socolinsky, D. A. (2003). Classification Using Class Cover Catch Digraphs. Journal of Classification, 20(1), 3–23. https://doi.org/10.1007/s00357-003-0003-7

Manukyan, A., & Ceyhan, E. (2016). Classification of imbalanced data with a geometric digraph family. Journal of Machine Learning Research, 17(1), 6504–6543. https://jmlr.org/papers/volume17/15-604/15-604.pdf

Examples

n <- 1000
x1 <- runif(n, 1, 10)
x2 <- runif(n, 1, 10)
x <- cbind(x1, x2)
y <- as.factor(ifelse(3 < x1 & x1 < 7 & 3 < x2 & x2 < 7, "A", "B"))

m_pcccd <- pcccd_classifier(x = x, y = y)

# dataset
plot(x, col = y, asp = 1)

# dominant samples of first class
x_center <- m_pcccd$x_dominant_list[[1]]

# radii of balls for first class
radii <- m_pcccd$radii_dominant_list[[1]]

# balls
for (i in 1:nrow(x_center)) {
xx <- x_center[i, 1]
yy <- x_center[i, 2]
r <- radii[i]
theta <- seq(0, 2*pi, length.out = 100)
xx <- xx + r*cos(theta)
yy <- yy + r*sin(theta)
lines(xx, yy, type = "l", col = "green")
}

# testing the performance
i_train <- sample(1:n, round(n*0.8))

x_train <- x[i_train,]
y_train <- y[i_train]

x_test <- x[-i_train,]
y_test <- y[-i_train]

m_pcccd <- pcccd_classifier(x = x_train, y = y_train)
pred <- predict(object = m_pcccd, newdata = x_test)

# confusion matrix
table(y_test, pred)

# test accuracy
sum(y_test == pred)/nrow(x_test)