SVM lineare per un insieme di dati radialmente separabile

In questo esercizio costruirai due SVM lineari: una con cost = 1 (predefinito) e l’altra con cost = 100, per l’insieme di dati radialmente separabile che hai creato nella prima lezione di questo capitolo. Calcolerai anche le accuratezze su training e test per entrambi i valori di cost. La libreria e1071 è già stata caricata e gli insiemi di dati di training e di test sono stati creati per te e sono disponibili nei data frame trainset e testset.

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Support Vector Machines in R

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#default cost mode;
svm_model_1 <- svm(y ~ ., data = ___, type = "C-classification", cost = ___, kernel = "linear")

#training accuracy
pred_train <- predict(svm_model_1, ___)
mean(pred_train == ___$y)

#test accuracy
pred_test <- predict(svm_model_1, ___)
mean(pred_test == ___$y)

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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: 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 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: Generare un insieme di dati radialmente separabile Exercise 2: Generare un insieme di dati 2D radialmente separabile Exercise 3: Visualizzare l'insieme di dati Exercise 4: SVM lineari su dati radialmente separabili Exercise 5: SVM lineare per un insieme di dati radialmente separabile

Esercizio in corso

Exercise 6: Accuratezza media per SVM lineare Exercise 7: Il kernel trick Exercise 8: Visualizzare i dati radialmente separabili trasformati Exercise 9: SVM con kernel polinomiale Exercise 10: Ottimizzare gli SVM Exercise 11: Uso di `tune.svm()`Exercise 12: Costruire e visualizzare il modello ottimizzato

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