主成分分析提取好的特征

主成分分析

PCA顾名思义，就是找出数据里最主要的方面，用数据里最主要的方面来代替原始数据。具体的，假如我们的数据集是 n维的，共有 m 个数据 (x_{1},x_{2},…,x_{m}) 。我们希望将这 m 个数据的维度从 n 维降到 n’ 维，希望这 m 个 n’ 维的数据集尽可能的代表原始数据集。我们知道数据从 n 维降到 n’ 维肯定会有损失，但是我们希望损失尽可能的小。

成人收入分析

数据集

file = "adult/adult.data"
data = pd.read_csv(file,header = None,names=["Age", "Work-Class", "fnlwgt", "Education",
                                                        "Education-Num", "Marital-Status", "Occupation",
                                                        "Relationship", "Race", "Sex", "Capital-gain",
                                                        "Capital-loss", "Hours-per-week", "Native-Country",
                                                        "Earnings-Raw"])
# drop the blank line
data.dropna(inplace=True)
data.iloc[:5]

data["Hours-per-week"].describe()

data["Education-Num"].median()

data["Work-Class"].unique()

data["LongHours"] = data["Hours-per-week"] > 40
data[:5]

选取好的特征

from sklearn.feature_selection import SelectKBest
from sklearn.feature_selection import chi2

# choose three best features
transformer = SelectKBest(score_func=chi2,k = 3)
Xt_chi2 = transformer.fit_transform(X,y)
print(Xt_chi2[:5])

#the highest is age,capital-gain,capital-loss
print(transformer.scores_)

from scipy.stats import pearsonr
def multivariate_pearsonr(X,y):
    scores,p_values = [],[]
    for column in range(X.shape[1]):
        cur_score,cur_p = pearsonr(X[:,column],y)
        scores.append(cur_score)
        p_values.append(cur_p)
    
    return (np.array(scores),np.array(p_values))

transformer = SelectKBest(score_func=multivariate_pearsonr,k=3)
Xt_pearson = transformer.fit_transform(X,y)
print(Xt_pearson[:5])

# Age,Education-num,Hours-per-week
print(transformer.scores_)

模型建立及评估

from sklearn.tree import DecisionTreeClassifier
from sklearn.cross_validation import cross_val_score
clf = DecisionTreeClassifier(random_state=14)
scores_chi2 = cross_val_score(clf,Xt_chi2,y,scoring="accuracy")
scores_pearson = cross_val_score(clf,Xt_pearson,y,scoring="accuracy")
print("Chi2 performance {0:.1f}%".format(np.mean(scores_chi2)*100))
print("Pearson performance {0:.1f}&".format(np.mean(scores_pearson)*100))

最终chi2结果为0.85，而pearson的结果为0.75。

网站广告分析

数据集

import numpy as np
import pandas as pd
file = "ad-dataset/ad.data"
def convert_num(x):
    try:
        return float(x)
    except ValueError:
        return np.nan

from collections import defaultdict
converters = defaultdict(convert_num)
# set the final column
converters[1558] = lambda x:1. if x.strip() == "ad." else 0.
for column in range(1558):
    converters[column] = convert_num

ads = pd.read_csv(file,header=None,converters=converters)
#ads[2] = pd.to_numeric(ads[2],errors='coerce')
print(ads.shape)
# for column in range(ads.shape[1]-1):
#     ads[column] =  pd.to_numeric(ads[column],errors='coerce').astype('float')
# ads[1558] = ads[1558].apply(lambda x:1. if x.strip() == "ad." else 0.)
ads.dropna(inplace=True)
print(ads.shape)
print(ads[:5])

PCA选取特征

X = ads.drop(1558,axis = 1).values
y = ads[1558]
print(X.shape,y.shape)

from sklearn.decomposition import PCA
pca = PCA(n_components = 5)
Xd = pca.fit_transform(X)
print(Xd[:5])

np.set_printoptions(precision = 3,suppress=True)
pca.explained_variance_ratio_

模型建立及评估

from sklearn.tree import DecisionTreeClassifier
from sklearn.cross_validation import cross_val_score
clf = DecisionTreeClassifier(random_state=14)
scores_pca = cross_val_score(clf,Xd,y,scoring='accuracy')
print("The accuracy is {0:.4f}".format(np.mean(scores_pca)))

%matplotlib inline
from matplotlib import pyplot as plt
# only two:is ad or not
classes = set(y)
colors = ["red","green"]
for cur_class,color in zip(classes,colors):
    mask = (y == cur_class).values
    plt.scatter(Xd[mask,0],Xd[mask,1],marker='o',color=color,label=int(cur_class))
plt.legend()
plt.show()

最终结果准确率为：0.9326