PCA应用（鸢尾花分类）
关于pca的推导能够点击此处
数据来源：http://archive.ics.uci.edu/ml/datasets/Irisweb
数听说明：花萼长 花萼宽 花瓣长 花瓣宽 类型dom
类型一共有三种，各自都是线性可分的。svg
咱们先利用PCA将数据降维获得下面的分类
以后咱们利用EC特征升维和Logistic回归将特征进行分类，获得下图
训练结果：
测试
import pandas as pd
import numpy as np
from sklearn.decomposition import PCA
from sklearn.feature_selection import SelectKBest, SelectPercentile, chi2
from sklearn.linear_model import LogisticRegressionCV
from sklearn import metrics
from sklearn.model_selection import train_test_split
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.manifold import TSNE
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
def extend(a, b):
return 1.05*a-0.05*b, 1.05*b-0.05*a
if __name__ == '__main__':
stype = 'pca'
pd.set_option('display.width', 200)
data = pd.read_csv('iris.data', header=None)
#print(data)
columns = np.array(['花萼长度', '花萼宽度', '花瓣长度', '花瓣宽度', '类型'])
data.rename(columns=dict(list(zip(np.arange(5), columns))), inplace=True) # 给每一列的数据标记名字
#print(data)
data['类型'] = pd.Categorical(data['类型']).codes # 将种类的类型用0 1 2 3来代替
x = data[columns[:-1]] # 保存待降维的4个要素
y = data[columns[-1]]
if stype == 'pca':
pca = PCA(n_components=2, whiten=True, random_state=0)
x = pca.fit_transform(x) # 将训练 标准化，降维，归一化后的获得的组分1，2赋给x
print(x)
print('各方向方差：', pca.explained_variance_)
print('方差所占比例：', pca.explained_variance_ratio_)
x1_label, x2_label = '组分1', '组分2'
title = 'PCA'
else:
fs = SelectKBest(chi2, k=2)
# fs = SelectPercentile(chi2, percentile=60)
fs.fit(x, y)
idx = fs.get_support(indices=True)
print('fs.get_support() = ', idx)
x = x[columns[idx]]
x = x.values # 为下面使用方便，DataFrame转换成ndarray
x1_label, x2_label = columns[idx]
title = '鸢尾花数据特征选择'
#print(x[:5])
cm_light = mpl.colors.ListedColormap(['#77E0A0', '#FF8080', '#A0A0FF'])
cm_dark = mpl.colors.ListedColormap(['g', 'r', 'b'])
mpl.rcParams['font.sans-serif'] = 'SimHei'
mpl.rcParams['axes.unicode_minus'] = False
plt.figure(facecolor='w')
plt.scatter(x[:, 0], x[:, 1], s=30, c=y, marker='o', cmap=cm_dark)
plt.grid(b=True, ls=':', color='k')
plt.xlabel(x1_label, fontsize=12)
plt.ylabel(x2_label, fontsize=12)
plt.title(title, fontsize=15)
# plt.savefig('1.png')
plt.show()
#
x, x_test, y, y_test = train_test_split(x, y, train_size=0.7)
model = Pipeline([
('poly', PolynomialFeatures(degree=2, include_bias=True)),
('lr', LogisticRegressionCV(Cs=np.logspace(-3, 4, 8), cv=5, fit_intercept=False))
])
model.fit(x, y)
print('最优参数：', model.get_params('lr')['lr'].C_)
y_hat = model.predict(x)
print('训练集精确度：', metrics.accuracy_score(y, y_hat))
y_test_hat = model.predict(x_test)
print('测试集精确度：', metrics.accuracy_score(y_test, y_test_hat))
N, M = 500, 500 # 横纵各采样多少个值
x1_min, x1_max = extend(x[:, 0].min(), x[:, 0].max()) # 第0列的范围
x2_min, x2_max = extend(x[:, 1].min(), x[:, 1].max()) # 第1列的范围
t1 = np.linspace(x1_min, x1_max, N)
t2 = np.linspace(x2_min, x2_max, M)
x1, x2 = np.meshgrid(t1, t2) # 生成网格采样点
x_show = np.stack((x1.flat, x2.flat), axis=1) # 测试点
y_hat = model.predict(x_show) # 预测值
y_hat = y_hat.reshape(x1.shape) # 使之与输入的形状相同
plt.figure(facecolor='w')
plt.pcolormesh(x1, x2, y_hat, cmap=cm_light) # 预测值的显示
plt.scatter(x[:, 0], x[:, 1], s=30, c=y, edgecolors='k', cmap=cm_dark) # 样本的显示
plt.xlabel(x1_label, fontsize=12)
plt.ylabel(x2_label, fontsize=12)
plt.xlim(x1_min, x1_max)
plt.ylim(x2_min, x2_max)
plt.grid(b=True, ls=':', color='k')
# 画各类图
# a = mpl.patches.Wedge(((x1_min+x1_max)/2, (x2_min+x2_max)/2), 1.5, 0, 360, width=0.5, alpha=0.5, color='r')
# plt.gca().add_patch(a)
patchs = [mpatches.Patch(color='#77E0A0', label='Iris-setosa'),
mpatches.Patch(color='#FF8080', label='Iris-versicolor'),
mpatches.Patch(color='#A0A0FF', label='Iris-virginica')]
plt.legend(handles=patchs, fancybox=True, framealpha=0.8, loc='lower right')
plt.title('鸢尾花Logistic回归分类效果', fontsize=15)
plt.show()