Python 波士頓房價資料主成分PCA分析降維

import pandas as pd

import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets,metrics
from sklearn.linear_model import linearregression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import standardscaler
from sklearn.decomposition import truncatedsvd
%matplotlib inline

boston = datasets.load_boston()

boston.feature_names

x = boston.data

y = boston.target
scale = standardscaler()
normal_x = scale.fit_transform(x) 
x_train, x_test, y_train, y_test = train_test_split(normal_x, y, test_size=0.1, random_state=42)

# 顯示資料

plt.hist(x_train[:,0], bins=20)
plt.hist(x_train[:,2], bins=20, alpha=0.3)

# pca

n_components = 10
pca = truncatedsvd(n_components=n_components)
x_train_pca = pca.fit_transform(x_train)
x_test_pca = pca.transform(x_test)

components = pca.components_

plt.plot(pca.explained_variance_)
plt.xlabel('component')
plt.ylabel('explained variance')
print("前{}個主成分解釋了資料中%的變化".format(n_components, sum(pca.explained_variance_ratio_)*100))

model = linearregression()

model.fit(x_train_pca, y_train)
print("前{}個pca主成分進行線性回歸的mse是{}".format(n_components,
metrics.mean_squared_error(y_test,model.predict(x_test_pca))))

model = linearregression()

model.fit(x_train, y_train)
print("不進行pca分析線性回歸的mse是{}".format(
metrics.mean_squared_error(y_test,model.predict(x_test))))

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