例 8.1 给定如表 8.1 所示训练数据．假设弱分类器由 x < v 或 x > v 产生，
阈值v 使该分类器在训练数据集上分类误差率最低．试用 AdaBoost 算法学习一个
强分类器．
表 8.1 训练数据表
序号 1 2 3 4 5 6 7 8 9 10
x 0 1 2 3 4 5 6 7 8 9
y 1 1 1 –1 –1 –1 1 1 1 –1
import math x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] y = [1, 1, 1, -1, -1, -1, 1, 1, 1, -1] # 初始化权值分布 w0 = [0.1 for i in range(0, 10)] # first split point 2.5 F1 = [1 if xi < 2.5 else -1 for xi in x] e1 = [w0[i] if F1[i] != y[i] else 0 for i in range(0, 10)] e1 = sum(e1) # 错误率 a1 = 0.5 * math.log((1 - e1) / e1) Z = [0.1 * math.exp(-a1 * F1[i] * y[i]) for i in range(0, 10)] Zs = sum(Z) w1 = [z / Zs for z in Z] # 根椐错误率调整后的权值分布 # second split point 8.5 F2 = [1 if xi < 8.5 else -1 for xi in x] e2 = [w1[i] if F2[i] != y[i] else 0 for i in range(0, 10)] e2 = sum(e2) a2 = 0.5 * math.log((1 - e2) / e2) Z = [w1[i] * math.exp(-a2 * F2[i] * y[i]) for i in range(0, 10)] Zs = sum(Z) w2 = [z / Zs for z in Z] # third split point 5.5 F3 = [-1 if xi < 5.5 else 1 for xi in x] e3 = [w2[i] if F3[i] != y[i] else 0 for i in range(0, 10)] e3 = sum(e3) a3 = 0.5 * math.log((1 - e3) / e3) Z = [w2[i] * math.exp(-a3 * F3[i] * y[i]) for i in range(0, 10)] Zs = sum(Z) w3 = [z / Zs for z in Z] # final split function G3 = [a1 * F1[i] + a2 * F2[i] + a3 * F3[i] for i in range(0, 10)] G3 = [1 if g > 0 else -1 for g in G3] print(G3)
