Create a decision boundary

The dataset you created in the previous exercise is available to you in the dataframe df (recall that it consists of two uniformly distributed variables x1 and x2, lying between 0 and 1). In this exercise you will add a class variable to that dataset. You will do this by creating a variable y whose value is -1 or +1 depending on whether the point (x1, x2) lies below or above the straight line that passes through the origin and has slope 1.4.

This exercise is part of the course

Support Vector Machines in R

Exercise instructions

Create a new column y in the dataframe df with the following specs:
y = -1 if x2 < 1.4*x1
y = 1 if x2 > 1.4*x1

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

#classify data points depending on location
df$y <- factor(ifelse(df$___ - ___*df$___ < 0, -1, 1), 
    levels = c(-1, 1))

Edit and Run Code

This exercise is part of the course

Support Vector Machines in R

IntermediateSkill Level

4.9+

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This chapter introduces some key concepts of support vector machines through a simple 1-dimensional example. Students are also walked through the creation of a linearly separable dataset that is used in the subsequent chapter.

Exercise 1: Sugar content of soft drinks Exercise 2: Visualizing a sugar content dataset Exercise 3: Identifying decision boundaries Exercise 4: Find the maximal margin separator Exercise 5: Visualize the maximal margin separator Exercise 6: Generating a linearly separable dataset Exercise 7: Generate a 2d uniformly distributed dataset.Exercise 8: Create a decision boundary

Current Exercise

Exercise 9: Introduce a margin in the dataset

Introduces students to the basic concepts of support vector machines by applying the svm algorithm to a dataset that is linearly separable. Key concepts are illustrated through ggplot visualisations that are built from the outputs of the algorithm and the role of the cost parameter is highlighted via a simple example. The chapter closes with a section on how the algorithm deals with multiclass problems.

Exercise 1: Linear Support Vector Machines Exercise 2: Creating training and test datasets Exercise 3: Building a linear SVM classifier Exercise 4: Exploring the model and calculating accuracy Exercise 5: Visualizing Linear SVMs Exercise 6: Visualizing support vectors using ggplot Exercise 7: Visualizing decision & margin bounds using `ggplot2`Exercise 8: Visualizing decision & margin bounds using `plot()`Exercise 9: Tuning linear SVMs Exercise 10: Tuning a linear SVM Exercise 11: Visualizing decision boundaries and margins Exercise 12: When are soft margin classifiers useful?Exercise 13: Multiclass problems Exercise 14: A multiclass classification problem Exercise 15: Iris redux - a more robust accuracy.

Provides an introduction to polynomial kernels via a dataset that is radially separable (i.e. has a circular decision boundary). After demonstrating the inadequacy of linear kernels for this dataset, students will see how a simple transformation renders the problem linearly separable thus motivating an intuitive discussion of the kernel trick. Students will then apply the polynomial kernel to the dataset and tune the resulting classifier.

Exercise 1: Generating a radially separable dataset Exercise 2: Generating a 2d radially separable dataset Exercise 3: Visualizing the dataset Exercise 4: Linear SVMs on radially separable data Exercise 5: Linear SVM for a radially separable dataset Exercise 6: Average accuracy for linear SVM Exercise 7: The kernel trick Exercise 8: Visualizing transformed radially separable data Exercise 9: SVM with polynomial kernel Exercise 10: Tuning SVMs Exercise 11: Using `tune.svm()`Exercise 12: Building and visualizing the tuned model

Builds on the previous three chapters by introducing the highly flexible Radial Basis Function (RBF) kernel. Students will create a "complex" dataset that shows up the limitations of polynomial kernels. Then, following an intuitive motivation for the RBF kernel, students see how it addresses the shortcomings of the other kernels discussed in this course.

Exercise 1: Generating a complex dataset Exercise 2: Generating a complex dataset - part 1 Exercise 3: Generating a complex dataset - part 2 Exercise 4: Visualizing the dataset Exercise 5: Motivating the RBF kernel Exercise 6: Linear SVM for complex dataset Exercise 7: Quadratic SVM for complex dataset Exercise 8: The RBF Kernel Exercise 9: Polynomial SVM on a complex dataset Exercise 10: RBF SVM on a complex dataset Exercise 11: Tuning an RBF kernel SVM