原文：
http://ihoge.cn/2018/SVM繪圖.html

%matplotlib inline import matplotlib.pyplot as plt import numpy as np class1 = np.array([[1, 1], [1, 3], [2, 1], [1, 2], [2, 2]]) class2 = np.array([[4, 4], [5, 5], [5, 4], [5, 3], [4, 5], [6, 4]]) plt.figure(figsize=(6, 4), dpi=120)plt.title('Decision Boundary')plt.xlim(0, 8) plt.ylim(0, 6) ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.scatter(class1[:, 0], class1[:, 1], marker='o') plt.scatter(class2[:, 0], class2[:, 1], marker='s') plt.plot([1, 5], [5, 1], '-r') plt.arrow(4, 4, -1, -1, shape='full', color='r') plt.plot([3, 3], [0.5, 6], '--b') plt.arrow(4, 4, -1, 0, shape='full', color='b', linestyle='--') plt.annotate(r'margin 1',xy=(3.5, 4), xycoords='data',xytext=(3.1, 4.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'margin 2',xy=(3.5, 3.5), xycoords='data',xytext=(4, 3.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'support vector',xy=(4, 4), xycoords='data',xytext=(5, 4.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'support vector',xy=(2, 2), xycoords='data',xytext=(0.5, 1.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.figure(figsize=(6, 4), dpi=120)plt.title('Support Vector Machine')plt.xlim(0, 8) plt.ylim(0, 6) ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.scatter(class1[:, 0], class1[:, 1], marker='o') plt.scatter(class2[:, 0], class2[:, 1], marker='s') plt.plot([1, 5], [5, 1], '-r') plt.plot([0, 4], [4, 0], '--b', [2, 6], [6, 2], '--b') plt.arrow(4, 4, -1, -1, shape='full', color='b') plt.annotate(r'$w^T x + b = 0$',xy=(5, 1), xycoords='data',xytext=(6, 1), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'$w^T x + b = 1$',xy=(6, 2), xycoords='data',xytext=(7, 2), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'$w^T x + b = -1$',xy=(3.5, 0.5), xycoords='data',xytext=(4.5, 0.2), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'd',xy=(3.5, 3.5), xycoords='data',xytext=(2, 4.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'A',xy=(4, 4), xycoords='data',xytext=(5, 4.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

from sklearn.datasets import make_blobsplt.figure(figsize=(10, 4), dpi=140)# sub plot 1 plt.subplot(1, 2, 1)X, y = make_blobs(n_samples=100, n_features=2, centers=[(1, 1), (2, 2)], random_state=4, shuffle=False,cluster_std=0.4)plt.title('Non-linear Separatable')plt.xlim(0, 3) plt.ylim(0, 3) ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.scatter(X[y==0][:, 0], X[y==0][:, 1], marker='o') plt.scatter(X[y==1][:, 0], X[y==1][:, 1], marker='s') plt.plot([0.5, 2.5], [2.5, 0.5], '-r')# sub plot 2 plt.subplot(1, 2, 2)class1 = np.array([[1, 1], [1, 3], [2, 1], [1, 2], [2, 2], [1.5, 1.5], [1.2, 1.7]]) class2 = np.array([[4, 4], [5, 5], [5, 4], [5, 3], [4, 5], [6, 4], [5.5, 3.5], [4.5, 4.5], [2, 1.5]])plt.title('Slack Variable')plt.xlim(0, 7) plt.ylim(0, 7) ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.scatter(class1[:, 0], class1[:, 1], marker='o') plt.scatter(class2[:, 0], class2[:, 1], marker='s') plt.plot([1, 5], [5, 1], '-r') plt.plot([0, 4], [4, 0], '--b', [2, 6], [6, 2], '--b') plt.arrow(2, 1.5, 2.25, 2.25, shape='full', color='b') plt.annotate(r'violate margin rule.',xy=(2, 1.5), xycoords='data',xytext=(0.2, 0.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'normal sample. $\epsilon = 0$',xy=(4, 5), xycoords='data',xytext=(4.5, 5.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'$\epsilon > 0$',xy=(3, 2.5), xycoords='data',xytext=(3, 1.5), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.figure(figsize=(6, 4), dpi=120)plt.title('Cost')plt.xlim(0, 4) plt.ylim(0, 2) plt.xlabel('$y^{(i)} (w^T x^{(i)} + b)$') plt.ylabel('Cost') ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.plot([0, 1], [1.5, 0], '-r') plt.plot([1, 3], [0.015, 0.015], '-r') plt.annotate(r'$J_i = R \epsilon_i$ for $y^{(i)} (w^T x^{(i)} + b) \geq 1 - \epsilon_i$',xy=(0.7, 0.5), xycoords='data',xytext=(1, 1), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2")) plt.annotate(r'$J_i = 0$ for $y^{(i)} (w^T x^{(i)} + b) \geq 1$',xy=(1.5, 0), xycoords='data',xytext=(1.8, 0.2), fontsize=10,arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.figure(figsize=(10, 4), dpi=144)class1 = np.array([[1, 1], [1, 2], [1, 3], [2, 1], [2, 2], [3, 2], [4, 1], [5, 1]]) class2 = np.array([[2.2, 4], [1.5, 5], [1.8, 4.6], [2.4, 5], [3.2, 5], [3.7, 4], [4.5, 4.5], [5.4, 3]])# sub plot 1 plt.subplot(1, 2, 1)plt.title('Non-linear Separatable in Low Dimension')plt.xlim(0, 6) plt.ylim(0, 6) plt.yticks(()) plt.xlabel('X1') ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none') ax.spines['left'].set_color('none')plt.scatter(class1[:, 0], np.zeros(class1[:, 0].shape[0]) + 0.05, marker='o') plt.scatter(class2[:, 0], np.zeros(class2[:, 0].shape[0]) + 0.05, marker='s')# sub plot 2 plt.subplot(1, 2, 2)plt.title('Linear Separatable in High Dimension')plt.xlim(0, 6) plt.ylim(0, 6) plt.xlabel('X1') plt.ylabel('X2') ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.scatter(class1[:, 0], class1[:, 1], marker='o') plt.scatter(class2[:, 0], class2[:, 1], marker='s') plt.plot([1, 5], [3.8, 2], '-r')

def gaussian_kernel(x, mean, sigma):return np.exp(- (x - mean)**2 / (2 * sigma**2))x = np.linspace(0, 6, 500) mean = 1 sigma1 = 0.1 sigma2 = 0.3plt.figure(figsize=(10, 3), dpi=144)# sub plot 1 plt.subplot(1, 2, 1) plt.title('Gaussian for $\sigma={0}$'.format(sigma1))plt.xlim(0, 2) plt.ylim(0, 1.1) ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.plot(x, gaussian_kernel(x, mean, sigma1), 'r-')# sub plot 2 plt.subplot(1, 2, 2) plt.title('Gaussian for $\sigma={0}$'.format(sigma2))plt.xlim(0, 2) plt.ylim(0, 1.1) ax = plt.gca() # gca 代表當前坐標軸，即 'get current axis' ax.spines['right'].set_color('none') # 隱藏坐標軸 ax.spines['top'].set_color('none')plt.plot(x, gaussian_kernel(x, mean, sigma2), 'r-')

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