Python【图解】样本不均衡问题及采样策略

样本不均衡的影响

from sklearn.datasets import make_blobs
import numpy as np, matplotlib.pyplot as mp
from sklearn.linear_model import LogisticRegression

# 负样本:正样本 = 1:1
X, Y = make_blobs(centers=2, cluster_std=2, random_state=0)
# 负样本:正样本 = 5:1
X0 = np.concatenate([X if i < 1 else X[Y == 0] for i in range(5)])
Y0 = np.concatenate((Y, np.zeros(200, np.int32)))
# 负样本:正样本 = 1:5
X1 = np.concatenate([X if i < 1 else X[Y == 1] for i in range(5)])
Y1 = np.concatenate((Y, np.ones(200, np.int32)))

for i, (Xi, Yi) in enumerate([(X, Y), (X0, Y0), (X1, Y1)]):
    # 建模
    model = LogisticRegression()
    model.fit(Xi, Yi)
    # 参数
    k = model.coef_[0]  # coefficient
    b = model.intercept_[0]  # bias
    # 可视化
    mp.subplot(1, 3, i + 1)
    x1, x2 = Xi[:, 0], Xi[:, 1]
    mp.scatter(x1, x2, c=Yi, alpha=.2)  # 原始样本点
    x = np.array([x1.min(), x1.max()])
    y = (-b - k[0] * x) / k[1]  # 决策边界
    mp.plot(x, y)
mp.show()

如图示：样本不均衡时，决策边界不在中间

imblearn实施采样

from sklearn.datasets import make_blobs
import numpy as np, matplotlib.pyplot as mp
from sklearn.linear_model import LogisticRegression
from imblearn import over_sampling, under_sampling  # pip install imblearn

# 负样本:正样本 = 1:1
X, Y = make_blobs(centers=2, cluster_std=2, random_state=0)
# 负样本:正样本 = 5:1
X0 = np.concatenate([X if i < 1 else X[Y == 0] for i in range(5)])
Y0 = np.concatenate((Y, np.zeros(200, np.int32)))
# 负样本:正样本 = 1:5
X1 = np.concatenate([X if i < 1 else X[Y == 1] for i in range(5)])
Y1 = np.concatenate((Y, np.ones(200, np.int32)))
# 下采样
X0u, Y0u = under_sampling.RandomUnderSampler().fit_sample(X0, Y0)
# 上采样
X1o, Y1o = over_sampling.RandomOverSampler().fit_sample(X1, Y1)
# 样本集
samples = [('zero:one = 1:1', X, Y), ('zero:one = 5:1', X0, Y0), ('zero:one = 1:5', X1, Y1),
           ('zero:one = 1:1', X, Y), ('Under Sampling', X0u, Y0u), ('Over Sampling', X1o, Y1o)]

for i, (title, Xi, Yi) in enumerate(samples):
    # 建模
    model = LogisticRegression()
    model.fit(Xi, Yi)
    # 参数
    k = model.coef_[0]  # coefficient
    b = model.intercept_[0]  # bias
    # 可视化
    mp.subplot(2, 3, i + 1)
    mp.title(title)
    mp.xticks(())
    mp.yticks(())
    x1, x2 = Xi[:, 0], Xi[:, 1]
    mp.scatter(x1, x2, c=Yi, alpha=.2)  # 原始样本点
    x = np.array([x1.min(), x1.max()])
    y = (-b - k[0] * x) / k[1]  # 决策边界
    mp.plot(x, y)
mp.show()

实施采样策略后，决策边界偏离度减少