Genera un insieme di dati bidimensionale a distribuzione uniforme.

L’obiettivo di questa lezione è creare un insieme di dati che useremo per illustrare i principi di base delle support vector machine. In questo esercizio faremo il primo passo: creare un insieme di dati bidimensionale, a distribuzione uniforme, contenente 600 punti dati.

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Support Vector Machines in R

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Istruzioni dell'esercizio

Imposta il numero di punti dati, n.
Genera un dataframe df con due variabili a distribuzione uniforme, x1 e x2, nell’intervallo (0, 1).

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

#set seed
set.seed(42)

#set number of data points. 
n <- ___

#Generate data frame with two uniformly distributed predictors lying between 0 and 1.
df <- data.frame(x1 = ___, 
                 x2 = ___)

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Questo esercizio fa parte del corso

Support Vector Machines in R

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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: Contenuto di zucchero nelle bibite Exercise 2: Visualizzare un insieme di dati sul contenuto di zucchero Exercise 3: Identificare i confini decisionali Exercise 4: Trova il separatore a margine massimo Exercise 5: Visualizza il separatore a margine massimo Exercise 6: Generare un insieme di dati linearmente separabile Exercise 7: Genera un insieme di dati bidimensionale a distribuzione uniforme.

Esercizio in corso

Exercise 8: Crea un confine decisionale Exercise 9: Introduci un margine nell'insieme di dati

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