PCA + kmeans

先记录一下PCA实战需要用到的安装包(arch下,python2环境)

python2-scikit-learn

python2-numpy

python2-pandas

python2-matplotlib

python2-seaborn

pandas.DataFrame

pandas 数据结构介绍

几个和科学计算数据分析有关的重要的python库:Numpy、Matplotlib ,pandas

(之前数字图像处理课程都接触过了orz)

其中matplotlib 主要用于图像绘制

sklearn 是用于机器学习的python 模块

Seaborn也是用于图像绘制

str.fomat() 是 python2语法

format中的变量会按照str中{} 出现的顺序替换

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sklearn.datasets import fetch_mldata
from sklearn.decomposition import PCA
import seaborn as sns
mnist = fetch_mldata("MNIST original")

X = mnist.data / 255.0
y = mnist.target

#print X.shape, y.shape


feat_cols = [ 'pixel'+str(i) for i in range(X.shape[1]) ]
df = pd.DataFrame(X,columns=feat_cols) # transform into some pandas DS named DataFrame
df['label'] = y  # add a column named 'label',valued by variable y
df['label'] = df['label'].apply(lambda i: str(i))  # df.apply (some funciton)
X, y = None, None
#print 'Size of the dataframe: {}' .format(df.shape)   # str.format() , '{}' is replaced by some value 

# Plot the graph
#print df

#rndperm = np.random.permutation(df.shape[0])
#plt.gray()
#fig = plt.figure( figsize=(16,7) )
#for i in range(0,30):
#    ax = fig.add_subplot(3,10,i+1, title='Digit: ' + str(df.loc[rndperm[i],'label']) )
#    ax.matshow(df.loc[rndperm[i],feat_cols].values.reshape((28,28)).astype(float))
#plt.show()

#print df

n_components_pca = 3
pca = PCA(n_components=n_components_pca)
pca_result = pca.fit_transform(df[feat_cols].values)

print 'kkkkk?'
df['pca-one'] = pca_result[:,0]
df['pca-two'] = pca_result[:,1] 
df['pca-three'] = pca_result[:,2]

print 'Explained variation per principal component: {}'.format(pca.explained_variance_ratio_)


pca_var_explained_df = pd.DataFrame({'principal component':np.arange(1,n_components_pca+1),
                                    'variance_explained':pca.explained_variance_ratio_})
print pca_var_explained_df.sum()


ax = sns.barplot(x='principal component',
                 y='variance_explained',
                 data=pca_var_explained_df,
                 palette="Set1")
ax.set_title('PCA - Variance explained')
plt.show()

PCA+kmeans 时间对比:

代码:

import time
import numpy as np
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA  
vec_num=120
data = np.random.rand(10000, vec_num) #生成一个随机数据，样本大小为10000, 特征数为120
#print (data)

t0 = time.clock()
estimator = KMeans(n_clusters=4)#构造聚类器
estimator.fit(data)#聚类
print ("kmeans time:",time.clock()-t0)
inertia = estimator.inertia_ # 某种度量,比如距离平方和,用来check k-means算法的效果
print ("sum:",inertia/vec_num)

com_num=10
pca=PCA(n_components=com_num)
newdata = pca.fit_transform(data)
t0 = time.clock()
estimator.fit(newdata)
print("kmeans time after PCA:",time.clock()-t0)
inertia = estimator.inertia_
print ("sum after PCA",inertia/com_num)