02-15 Logistic回归(鸢尾花分类)

Logistic回归(鸢尾花分类)

导入模块

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from matplotlib.font_manager import FontProperties
from sklearn import datasets
from sklearn.linear_model import LogisticRegression
%matplotlib inline
font = FontProperties(fname='/Library/Fonts/Heiti.ttc')

获取数据

iris_data = datasets.load_iris()
X = iris_data.data[:, [2, 3]]
y = iris_data.target
label_list = ['山鸢尾', '杂色鸢尾', '维吉尼亚鸢尾']

构建决策边界

def plot_decision_regions(X, y, classifier=None):
    marker_list = ['o', 'x', 's']
    color_list = ['r', 'b', 'g']
    cmap = ListedColormap(color_list[:len(np.unique(y))])

    x1_min, x1_max = X[:, 0].min()-1, X[:, 0].max()+1
    x2_min, x2_max = X[:, 1].min()-1, X[:, 1].max()+1
    t1 = np.linspace(x1_min, x1_max, 666)
    t2 = np.linspace(x2_min, x2_max, 666)

    x1, x2 = np.meshgrid(t1, t2)
    y_hat = classifier.predict(np.array([x1.ravel(), x2.ravel()]).T)
    y_hat = y_hat.reshape(x1.shape)
    plt.contourf(x1, x2, y_hat, alpha=0.2, cmap=cmap)
    plt.xlim(x1_min, x1_max)
    plt.ylim(x2_min, x2_max)

    for ind, clas in enumerate(np.unique(y)):
        plt.scatter(X[y == clas, 0], X[y == clas, 1], alpha=0.8, s=50,
                    c=color_list[ind], marker=marker_list[ind], label=label_list[clas])

训练模型

# C与正则化参数λ成反比，即减小参数C增大正则化的强度
# lbfgs使用拟牛顿法优化参数
# 分类方式为OvR（One-vs-Rest）
lr = LogisticRegression(C=100, random_state=1,
                        solver='lbfgs', multi_class='ovr')
lr.fit(X, y)

LogisticRegression(C=100, class_weight=None, dual=False, fit_intercept=True,
          intercept_scaling=1, max_iter=100, multi_class='ovr',
          n_jobs=None, penalty='l2', random_state=1, solver='lbfgs',
          tol=0.0001, verbose=0, warm_start=False)

C参数与权重系数的关系

weights, params = [], []
for c in np.arange(-5, 5):
    lr = LogisticRegression(C=10.**c, random_state=1,
                            solver='lbfgs', multi_class='ovr')
    lr.fit(X, y)
    
    # lr.coef_[1]拿到类别1的权重系数
    weights.append(lr.coef_[1])
    params.append(10.**c)


# 把weights转为numpy数组，即包含两个特征的权重的数组
weights = np.array(weights)
'''
params:
[1e-05, 0.0001, 0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0, 10000.0]
'''
'''
weights:
[[ 2.50572107e-04  6.31528229e-05]
 [ 2.46565843e-03  6.15303747e-04]
 [ 2.13003731e-02  4.74899392e-03]
 [ 9.09176960e-02 -1.80703318e-03]
 [ 1.19168871e-01 -2.19313511e-01]
 [ 8.35644722e-02 -9.08030470e-01]
 [ 1.60682631e-01 -2.15860167e+00]
 [ 5.13026897e-01 -2.99137299e+00]
 [ 1.14643413e+00 -2.79518356e+00]
 [ 1.90317264e+00 -2.26818639e+00]]
'''

plt.plot(params, weights[:, 0], linestyle='--', c='r', label='花瓣长度（cm）')
plt.plot(params, weights[:, 1], c='g', label='花瓣长度（cm）')
plt.xlabel('C')
# 改变x轴的刻度
plt.xscale('log')
plt.ylabel('权重系数', fontproperties=font)
plt.legend(prop=font)
plt.show()

  上图显示了10个不同的逆正则化参数C值拟合逻辑回归模型，此处只收集标签为1（杂色鸢尾）的权重系数。由于数据没有经过处理，所以显示的不太美观，但是总体趋势还是可以看出减小参数C会增大正则化强度，在\(10^{-3}\)的时候权重系数开始收敛为0。

可视化

plot_decision_regions(X, y, classifier=lr)
plt.xlabel('花瓣长度（cm）', fontproperties=font)
plt.ylabel('花瓣宽度（cm）', fontproperties=font)
plt.legend(prop=font)
plt.show()