Create a dataset that we'll use to illustrate key principles of SVMs.
Dataset has two variables and a linear decision boundary.
Generating a two-dimensional dataset using runif()
Generate a two variable dataset with 200 points
Variables x1 and x2 uniformly distributed in (0,1).
# Preliminaries...
# Set required number of data points
n <- 200
# Set seed to ensure reproducibility
set.seed(42)
# Generate dataframe with two predictors x1 and x2 in (0,1)
df <- data.frame(x1 = runif(n),
x2 = runif(n))
Creating two classes
Create two classes, separated by the straight line decision boundary x1 = x2
Line passes through (0, 0) and makes a 45 degree angle with horizontal
Class variable y = -1 for points below line and y = 1 for points above it
# Classify points as -1 or +1
df$y <- factor(ifelse(df$x1 - df$x2 > 0, -1, 1),
levels = c(-1, 1))
Visualizing dataset using ggplot
Create 2 dimensional scatter plot with x1 on the x axis and x2 on the y-axis
Distinguish classes by color (below line = red; above line = blue)
Decision boundary is line x1 = x2: passes through (0, 0) and has slope = 1
library(ggplot2)
# Build plot
p <- ggplot(data = df, aes(x = x1, y = x2, color = y)) +
geom_point() +
scale_color_manual(values = c("-1" = "red", "1" = "blue")) +
geom_abline(slope = 1, intercept = 0)
# Display it
p
Introducing a margin
To create a margin we need to remove points that lie close to the boundary
Remove points that have x1 and x2 values that differ by less than a specified value
# Create a margin of 0.05 in dataset
delta <- 0.05
# Retain only those points that lie outside the margin
df1 <- df[abs(df$x1 - df$x2) > delta, ]
# Check number of data points remaining
nrow(df1)
# Replot dataset with margin (code is exactly same as before)
p <- ggplot(data = df1, aes(x = x1, y = x2, color = y)) +
geom_point() +
scale_color_manual(values = c("red", "blue")) +
geom_abline(slope = 1, intercept = 0)
# Display plot
p
Plotting the margin boundaries
The margin boundaries are:
parallel to the decision boundary (slope = 1).
located delta units on either side of it (delta = 0.05).
p <- p +
geom_abline(slope = 1, intercept = delta, linetype = "dashed") +
geom_abline(slope = 1, intercept = -delta, linetype = "dashed")
p
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