样本类内离散度
S
i
‾
2
\overline{S_i}^2
Si2和总类内离散度
S
w
‾
\overline{S_w}
Sw
而此时类间离散度就成为两类均值差的平方。
计算阈值
y
0
y_0
y0
from sklearn.datasets import make_multilabel_classification
import numpy as np
x, y = make_multilabel_classification(n_samples=20, n_features=2,
n_labels=1, n_classes=1,
random_state=2) # 设置随机数种子，保证每次产生相同的数据。
# 根据类别分个类
index1 = np.array([index for (index, value) in enumerate(y) if value == 0]) # 获取类别1的indexs
index2 = np.array([index for (index, value) in enumerate(y) if value == 1]) # 获取类别2的indexs
c_1 = x[index1] # 类别1的所有数据(x1, x2) in X_1
c_2 = x[index2] # 类别2的所有数据(x1, x2) in X_2
# 2、Fisher算法实现
def cal_cov_and_avg(samples):
"""
给定一个类别的数据，计算协方差矩阵和平均向量
:param samples:
:return:
"""
u1 = np.mean(samples, axis=0)
cov_m = np.zeros((samples.shape[1], samples.shape[1]))
for s in samples:
t = s - u1
cov_m += t*t.reshape(2, 1)
return cov_m, u1
def fisher(c_1, c_2):
"""
fisher算法实现(参考上面的推导公式进行理解)
:param c_1:
:param c_2:
:return:
"""
cov_1, u1 = cal_cov_and_avg(c_1)
cov_2, u2 = cal_cov_and_avg(c_2)
s_w = cov_1 + cov_2 # 总类内离散度矩阵。
u, s, v = np.linalg.svd(s_w) # 下面的参考公式（4-10）
s_w_inv = np.dot(np.dot(v.T, np.linalg.inv(np.diag(s))), u.T)
return np.dot(s_w_inv, u1 - u2)
def judge(sample, w, c_1, c_2):
"""
返回值：ture 属于1；false 属于2
:param sample:
:param w:
:param c_1:
:param c_2:
:return:
"""
u1 = np.mean(c_1, axis=0)
u2 = np.mean(c_2, axis=0)
center_1 = np.dot(w.T, u1) # 参考公式(2-8)
center_2 = np.dot(w.T, u2)
pos = np.dot(w.T, sample) # 新样本进来判断
return abs(pos - center_1) < abs(pos - center_2)
w = fisher(c_1, c_2) # 调用函数，得到参数w
out = judge(c_2[1], w, c_1, c_2) # 判断所属的类别。
print(out)
# 4、绘图功能
plt.scatter(c_1[:, 0], c_1[:, 1], c='red')
plt.scatter(c_2[:, 0], c_2[:, 1], c='blue')
line_x = np.arange(min(np.min(c_1[:, 0]), np.min(c_2[:, 0])),
max(np.max(c_1[:, 0]), np.max(c_2[:, 0])),
step=1)
line_y = -(w[0]*line_x) / w[1]
plt.plot(line_x, line_y, linewidth=3.0, label = 'fisher boundary line ')
plt.legend(loc='upper right')
plt.xlabel('feature 1')
plt.ylabel('feature 2')
plt.show()
参考链接：https://blog.csdn.net/abc13526222160/article/details/90611743