# Pure and Proper Class Cover Catch Digraph Classifier `pcccd_classifier` fits a Pure and Proper Class Cover Catch Digraph (PCCCD) classification model. ```r 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. ## Returns 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 ## 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 c("$X^{\\text{non-target}}\\cap \\bigcup_{i}\n$", "$B_{i} = \\varnothing$") (pure) and c("$X^{\\text{target}}\\subset \\bigcup_{i}\n$", "$B_{i}$") (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. ## Examples ```r 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) ``` ## 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 ## Author(s) Fatih Saglam, saglamf89@gmail.com

pcccd_classifier function