感知机算法中误分类点的计算与可视化求助

问题描述 #

已完成感知机线性分类器的大部分Python代码编写，但在计算误分类点数量并将其可视化的环节遇到困难，需要补全代码实现该功能。原代码如下：

import numpy as np

DATA = np.loadtxt("C:/Users/abish/OneDrive/Desktop/Machine Learning/data_Perceptron.txt")
X = DATA[:, 0:2]
Y = DATA[:, 2]

import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1, figsize=(5, 5))
ax.scatter(X[:, 0], X[:, 1], c=Y)
ax.set_title('ground truth', fontsize=20)
plt.xlabel('X1')
plt.ylabel('X2')
plt.show()


# Add a bias to the X vector
X_bias = np.ones([X.shape[0], 3])
X_bias[:, 1:3] = X
# Initialize weight vector with zeros
w = np.zeros([3, 1])


# Define the activation function  that returns either 1 or 0
def activation(x):
    return 1 if x >= 1 else 0

# A function to calculate the unit vector of our weights vector
def calc_unit_vector(x):
    return x.transpose() / np.sqrt(x.transpose().dot(x))

# A function that returns values that lay on the hyperplane
def calc_hyperplane(X, w):
    return np.ravel([-(w[0] + x * w[1]) / w[2] for x in X])

for _ in range(10):
    for i in range(X_bias.shape[0]):
        y = activation(w.transpose().dot(X_bias[i, :]))
        # Update weights
        w = w + ((Y[i] - y) * X_bias[i, :]).reshape(w.shape[0], 1)

print('w0 = ', w[0])
print('w1 = ', w[1])
print('w2 = ', w[2])

# Calculate the class of the data points with the weight vector
result = [w.transpose().dot(x) for x in X_bias]
result_class = [activation(w.transpose().dot(x)) for x in X_bias]

# Calculate unit vector
w = calc_unit_vector(w).transpose()

fig, ax = plt.subplots(1, 2, figsize=(15, 5))
ax[0].scatter(X[:, 0], X[:, 1], c=Y)
ax[0].set_title('ground truth', fontsize=20)

ax[1].scatter(X[:, 0], X[:, 1], c=result_class)
ax[1].plot([-20, 20], calc_hyperplane([-20, 20], w), lw=3, c='red')
ax[1].set_xlim(ax[0].get_xlim())
ax[1].set_ylim(ax[0].get_ylim())
ax[1].set_yticks([])
ax[1].set_title('Perceptron classification with hyperplane', fontsize=20)
plt.show()

# calculate misclassified points
misclassified =
fig, ax = plt.subplots(1, 1, figsize=(5, 5))
ax.scatter(X[:, 0], X[:, 1], c=misclassified)
ax.set_title('misclassified points', fontsize=20)
plt.xlabel('X1')
plt.ylabel('X2')
plt.show()

解决方案：补全误分类点计算与可视化代码 #

以下是补全后的完整代码，优化了误分类点的识别逻辑和可视化效果：

import numpy as np

DATA = np.loadtxt("C:/Users/abish/OneDrive/Desktop/Machine Learning/data_Perceptron.txt")
X = DATA[:, 0:2]
Y = DATA[:, 2]

import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1, figsize=(5, 5))
ax.scatter(X[:, 0], X[:, 1], c=Y)
ax.set_title('ground truth', fontsize=20)
plt.xlabel('X1')
plt.ylabel('X2')
plt.show()


# Add a bias to the X vector
X_bias = np.ones([X.shape[0], 3])
X_bias[:, 1:3] = X
# Initialize weight vector with zeros
w = np.zeros([3, 1])


# Define the activation function  that returns either 1 or 0
def activation(x):
    return 1 if x >= 1 else 0

# A function to calculate the unit vector of our weights vector
def calc_unit_vector(x):
    return x.transpose() / np.sqrt(x.transpose().dot(x))

# A function that returns values that lay on the hyperplane
def calc_hyperplane(X, w):
    return np.ravel([-(w[0] + x * w[1]) / w[2] for x in X])

for _ in range(10):
    for i in range(X_bias.shape[0]):
        y = activation(w.transpose().dot(X_bias[i, :]))
        # Update weights
        w = w + ((Y[i] - y) * X_bias[i, :]).reshape(w.shape[0], 1)

print('w0 = ', w[0])
print('w1 = ', w[1])
print('w2 = ', w[2])

# Calculate the class of the data points with the weight vector
result = [w.transpose().dot(x) for x in X_bias]
result_class = [activation(w.transpose().dot(x)) for x in X_bias]

# Calculate unit vector
w = calc_unit_vector(w).transpose()

fig, ax = plt.subplots(1, 2, figsize=(15, 5))
ax[0].scatter(X[:, 0], X[:, 1], c=Y)
ax[0].set_title('ground truth', fontsize=20)

ax[1].scatter(X[:, 0], X[:, 1], c=result_class)
ax[1].plot([-20, 20], calc_hyperplane([-20, 20], w), lw=3, c='red')
ax[1].set_xlim(ax[0].get_xlim())
ax[1].set_ylim(ax[0].get_ylim())
ax[1].set_yticks([])
ax[1].set_title('Perceptron classification with hyperplane', fontsize=20)
plt.show()

# ------------------- 补全部分 -------------------
# 将预测结果转为numpy数组，方便与真实标签对比
result_class_np = np.array(result_class)
# 生成误分类标记：1表示误分类，0表示分类正确
misclassified = (result_class_np != Y).astype(int)
# 统计误分类点数量
misclassified_count = np.sum(misclassified)
print(f"误分类点数量：{misclassified_count}")

# 可视化：用红色高亮误分类点，灰色展示正确分类点，叠加分类超平面
fig, ax = plt.subplots(1, 1, figsize=(5, 5))
# 绘制正确分类的点
ax.scatter(X[misclassified == 0, 0], X[misclassified == 0, 1], c='gray', label='正确分类')
# 绘制误分类的点（放大尺寸增强辨识度）
ax.scatter(X[misclassified == 1, 0], X[misclassified == 1, 1], c='red', s=80, label='误分类')
# 绘制分类超平面
ax.plot([-20, 20], calc_hyperplane([-20, 20], w), lw=3, c='blue', label='分类超平面')
ax.set_title('misclassified points', fontsize=20)
plt.xlabel('X1')
plt.ylabel('X2')
ax.legend()
plt.show()

关键逻辑说明 #

• 误分类点识别：通过result_class_np != Y生成布尔数组，直接标记每个样本的分类正误，再转为整数类型便于后续处理。
• 数量统计：利用np.sum()快速统计误分类点的总数。
• 可视化优化：通过分层绘制不同类别的点，并用颜色和尺寸区分正误分类，叠加超平面让结果更直观。

内容的提问来源于stack exchange，提问作者Abishek Phuyal