Support vector machine model for classification

Beijing Institute of Technology | Ming-Jian Li

The following Python code is a companion code for the course on Artificial Intelligence and Simulation Science. It functions to establish a support vector machine classification model to classify the given data.

x
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from sklearn.svm import SVC
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import numpy as np
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import matplotlib.pyplot as plt
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# generate data
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np.random.seed(11)
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mean_1 = [1.8, 0]
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cov_1 = [[0.1, 0], [0, 0.1]]
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mean_2 = [0, 0.4]
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cov_2 = [[0.1, 0], [0, 0.1]]
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X1 = np.random.multivariate_normal(mean_1, cov_1, 50)
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y1 = np.zeros(50)
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X2 = np.random.multivariate_normal(mean_2, cov_2, 50)
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y2 = np.ones(50)
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X = np.concatenate((X1, X2), axis=0)
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y = np.concatenate((y1, y2))
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# support vector classification
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svc = SVC(kernel='linear')
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svc.fit(X, y)
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# Plot data
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plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Set1, edgecolor='k')
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# Plot decision boundary
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w = svc.coef_[0]
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b = svc.intercept_[0]
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x_plot = np.linspace(min(X[:, 0]) - 1, max(X[:, 0]) + 1, 10)
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y_plot = -w[0] / w[1] * x_plot - b / w[1]
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plt.plot(x_plot, y_plot, 'k-', label='Decision Boundary')
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# Plot margin
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margin = 1 / np.linalg.norm(w)
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b_upper = b + margin
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b_lower = b - margin
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y_upper = -(w[0] * x_plot + b_upper) / w[1]
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y_lower = -(w[0] * x_plot + b_lower) / w[1]
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plt.plot(x_plot, y_upper, 'k--', label='Upper Margin')
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plt.plot(x_plot, y_lower, 'k--', label='Lower Margin')
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# Set the x and y limits for the plot
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plt.xlim([min(X[:, 0]) - 1, max(X[:, 0]) + 1])
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plt.ylim([min(X[:, 1]) - 1, max(X[:, 1]) + 1])
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plt.xlabel('Feature 1')
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plt.ylabel('Feature 2')
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plt.legend(loc='upper left')
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plt.title('SVM Decision Boundary with Margin')
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plt.show()
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X_new = np.array([[2, 0.5], [-1.0, -2.0]])
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y_pred = svc.predict(X_new)
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print("Predicted Labels:", y_pred)

The result is as follows: