Here is a possible solution to your problem:

Step 1: Data Preprocessing

• Load necessary libraries, including ggplot2 for visualization and mgcv for calculating the area enclosed by the polygon.

library(ggplot2)
library(mgcv)

• Prepare your data. Create a new column that separates red points (class 0) from green points (class 1).

mydata$group = ifelse(mydata[,3] == 0, "red", "green")

Step 2: Data Visualization

• Plot the data with different colors for red and green points.

ggplot(mydata, aes(x=var1, y=var2)) +
    geom_point(aes(color = group), size = 2) +
    scale_color_brewer(palette = "Dark2")

Step 3: Clustering

• Use hierarchical clustering to group points with similar coordinates.

HC = hclust(dist(mydata[mydata$group == "red",1:2]), method="average")

• Select a subset of points that you want to use for the convex hull. For example, take all points in the first cluster.

Grouped3 = which(cutree(HC,3) == 1)

Step 4: Convex Hull

• Calculate the convex hull of the selected points.

CH3 = chull(mydata[which(mydata$group == "red")[Grouped3],1:2])

Step 5: Polygon Creation and Area Calculation

• Create a polygon that encloses all points in the cluster.

boundary = mydata[which(mydata$group == "red")[Grouped3][CH3],1:2]

• Calculate the area enclosed by the polygon.

area_enclosed = sum(in.out(boundary,mydata[which(mydata$group == "green"),1:2]))

Step 6: Visualization and Results

• Plot the convex hull with the points inside the hull colored in red and those outside in green.

ggplot() +
    geom_point(aes(x=var1, y=var2), data = mydata[which(mydata$group == "red"),], size = 2, color = "black") +
    geom_polygon(data = boundary, aes(x=x, y=y), fill = "#FF000033", alpha = 0.5) +
    geom_point(aes(x=var1, y=var2), data = mydata[which(mydata$group == "green") & which(in.out(boundary,mydata[which(mydata$group == "green"),1:2])),], size = 2, color = "red")

• Display the results.

print(paste("Number of points inside the polygon:", sum(in.out(boundary,mydata[which(mydata$group == "green"),1:2]))))

This code follows the steps outlined in your question and uses R to perform the necessary calculations.

Last modified on 2025-02-12