参考代码
结合自己的理解，添加注释。

代码

1. 导入相关的库

import numpy as np
import pandas as pd
import matplotlib
from matplotlib import pyplot as plt

2. 导入数据，进行数据处理和特征工程
   得到数据集 D = { ( x i , y i ) } i = 1 m , y i ∈ { 0 , 1 } D=\{ (x_i,y_i) \}_{i=1}^m, y_i \in \{0,1\} D={(xi​,yi​)}i=1m​,yi​∈{0,1}

# 1.数据处理，特征工程
data_path = 'watermelon3_0_Ch.csv'
data = pd.read_csv(data_path).values
# 按照数据集3.0α，强制转换数据类型
X = data[:,7:9].astype(float)
y = data[:,9]
y[y=='是'] = 1
y[y=='否'] = 0
y = y.astype(int)

3. 计算西瓜书60页中的$X_i、{\mu }_i、{\Sigma }_i$

# 将X的数据根据label值分成X0和X1
pos = y == 1
neg = y == 0
X0 = X[neg]
X1 = X[pos]# 计算u0，u1 keepdims保持原数据维数
u0 = X0.mean(0, keepdims=True)
u1 = X1.mean(0, keepdims=True)# 计算sigma0，sigma1
sigma0 = np.dot((X0-u0).T,X0-u0)
sigma1 = np.dot((X1-u1).T,X1-u1)

4. 根据式3.33计算类内散度矩阵
   $$S_w={\Sigma }_0+{\Sigma }_1=\sum _{x\in X_0}(x-{\mu }_0)(x-{\mu }_0{)}^T+\sum _{x\in X_1}(x-{\mu }_1)(x-{\mu }_1{)}^T$$
   根据式3.39计算$w$
   $$w=S_w^{-1}({\mu }_0-{\mu }_1)$$

# 计算类内散度矩阵 with-class scatter matrix
sw = sigma0 + sigma1# numpy.linalg.inv() 函数来计算矩阵的逆
w = np.dot(np.linalg.inv(sw),(u0-u1).T).reshape(1,-1)

5. 画出样本点和得到的直线

fig, ax = plt.subplots()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.spines['left'].set_position(('data', 0))
ax.spines['bottom'].set_position(('data', 0))plt.scatter(X1[:, 0], X1[:, 1], c='k', marker='o', label='good')
plt.scatter(X0[:, 0], X0[:, 1], c='r', marker='x', label='bad')plt.xlabel('密度', labelpad=1)
plt.ylabel('含糖量')
plt.legend(loc='upper right')x_tmp = np.linspace(-0.05, 0.15)
y_tmp = x_tmp * w[0, 1] / w[0, 0]
plt.plot(x_tmp, y_tmp, '#808080', linewidth=1)

得到下图

6. 计算每个样本点在直线上的投影
   计算的理解参考这篇文章

# 求w这个向量的 单位向量 wu
# np.linalg.norm()默认求2 范数，表示向量中各个元素平方和 的 1/2 次方，L2 范数又称 Euclidean 范数或者 Frobenius 范数。
wu = w / np.linalg.norm(w)# 正负样本点
# 求负样本的投影点，并连线
X0_project = np.dot(X0, np.dot(wu.T, wu))
plt.scatter(X0_project[:, 0], X0_project[:, 1], c='r', s=15)
for i in range(X0.shape[0]):plt.plot([X0[i, 0], X0_project[i, 0]], [X0[i, 1], X0_project[i, 1]], '--r', linewidth=1)# 求正样本的投影点，并连线
X1_project = np.dot(X1, np.dot(wu.T, wu))
plt.scatter(X1_project[:, 0], X1_project[:, 1], c='k', s=15)
for i in range(X1.shape[0]):plt.plot([X1[i, 0], X1_project[i, 0]], [X1[i, 1], X1_project[i, 1]], '--k', linewidth=1)

得到下图

将上述代码封装成类，如下：

class LDA(object):def fit(self, X_, y_, plot_=False):pos = y_ == 1neg = y_ == 0X0 = X_[neg]X1 = X_[pos]u0 = X0.mean(0, keepdims=True)  # (1, n)u1 = X1.mean(0, keepdims=True)sw = np.dot((X0 - u0).T, X0 - u0) + np.dot((X1 - u1).T, X1 - u1)w = np.dot(np.linalg.inv(sw), (u0 - u1).T).reshape(1, -1)  # (1, n)if plot_:# 设置字体为楷体plt.rcParams['axes.unicode_minus']=False #用来正常显示负号plt.rcParams['font.sans-serif'] = ['KaiTi']fig, ax = plt.subplots()ax.spines['right'].set_color('none')ax.spines['top'].set_color('none')ax.spines['left'].set_position(('data', 0))ax.spines['bottom'].set_position(('data', 0))plt.scatter(X1[:, 0], X1[:, 1], c='k', marker='o', label='good')plt.scatter(X0[:, 0], X0[:, 1], c='r', marker='x', label='bad')plt.xlabel('密度', labelpad=1)plt.ylabel('含糖量')plt.legend(loc='upper right')x_tmp = np.linspace(-0.05, 0.15)y_tmp = x_tmp * w[0, 1] / w[0, 0]plt.plot(x_tmp, y_tmp, '#808080', linewidth=1)wu = w / np.linalg.norm(w)# 正负样板店X0_project = np.dot(X0, np.dot(wu.T, wu))plt.scatter(X0_project[:, 0], X0_project[:, 1], c='r', s=15)for i in range(X0.shape[0]):plt.plot([X0[i, 0], X0_project[i, 0]], [X0[i, 1], X0_project[i, 1]], '--r', linewidth=1)X1_project = np.dot(X1, np.dot(wu.T, wu))plt.scatter(X1_project[:, 0], X1_project[:, 1], c='k', s=15)for i in range(X1.shape[0]):plt.plot([X1[i, 0], X1_project[i, 0]], [X1[i, 1], X1_project[i, 1]], '--k', linewidth=1)# 中心点的投影u0_project = np.dot(u0, np.dot(wu.T, wu))plt.scatter(u0_project[:, 0], u0_project[:, 1], c='#FF4500', s=60)u1_project = np.dot(u1, np.dot(wu.T, wu))plt.scatter(u1_project[:, 0], u1_project[:, 1], c='#696969', s=60)ax.annotate(r'u0 投影点',xy=(u0_project[:, 0], u0_project[:, 1]),xytext=(u0_project[:, 0] - 0.2, u0_project[:, 1] - 0.1),size=13,va="center", ha="left",arrowprops=dict(arrowstyle="->",color="k",))ax.annotate(r'u1 投影点',xy=(u1_project[:, 0], u1_project[:, 1]),xytext=(u1_project[:, 0] - 0.1, u1_project[:, 1] + 0.1),size=13,va="center", ha="left",arrowprops=dict(arrowstyle="->",color="k",))plt.axis("equal")  # 两坐标轴的单位刻度长度保存一致plt.show()self.w = wself.u0 = u0self.u1 = u1return selfdef predict(self, X):project = np.dot(X, self.w.T)wu0 = np.dot(self.w, self.u0.T)wu1 = np.dot(self.w, self.u1.T)return (np.abs(project - wu1) < np.abs(project - wu0)).astype(int)