采用因子分析方法，根据48位应聘者的15项指标得分，选出6名最优秀的应聘者##

(1)读入数据，数据标准化

(2)建立相关系数矩阵

(3)进行相关系数矩阵检验——KMO测度和巴特利特球体检验：

KMO值：0.9以上非常好；0.8以上好；0.7一般；0.6差；0.5很差；0.5以下不能接受；巴特利球形检验的值范围在0-1，越接近1，使用因子分析效果越好。

求解特征值及相应特征向量

求公因子个数m,使用前m个特征值的比重大于85%的标准，选出了公共因子是五个

因子载荷阵

因子旋转

因子得分(应试者因子得分)

根据应聘者的五个因子得分，按照贡献率进行加权，得到最终各应试者的综合得分，然后选出前六个得分最高的应聘者。

import pandas as pd
import numpy as np
import math as math
import numpy as np
from numpy import *
from scipy.stats import bartlett
from factor_analyzer import *
import numpy.linalg as nlg#模块包含线性代数的函数。使用这个模块,可以计算逆矩阵、求特征值、解线性方程组以及求解行列式等
from sklearn.cluster import KMeans
from matplotlib import cm
import matplotlib.pyplot as plt
def main():
df=pd.read_csv("C:\Users\xn084037\Desktop\applicant.csv")
# print(df)
df2=df.copy()
print("\n原始数据:\n",df2)
del df2['ID']
# print(df2)
# 皮尔森相关系数
df2_corr=df2.corr()
print("\n相关系数:\n",df2_corr)
#热力图
cmap = cm.Blues
# cmap = cm.hot_r
fig=plt.figure()
ax=fig.add_subplot(111)
map = ax.imshow(df2_corr, interpolation='nearest', cmap=cmap, vmin=0, vmax=1)
plt.title('correlation coefficient--headmap')
ax.set_yticks(range(len(df2_corr.columns)))
ax.set_yticklabels(df2_corr.columns)
ax.set_xticks(range(len(df2_corr)))
ax.set_xticklabels(df2_corr.columns)
plt.colorbar(map)
plt.show()
# KMO测度
def kmo(dataset_corr):
corr_inv = np.linalg.inv(dataset_corr)
nrow_inv_corr, ncol_inv_corr = dataset_corr.shape
A = np.ones((nrow_inv_corr, ncol_inv_corr))
for i in range(0, nrow_inv_corr, 1):
for j in range(i, ncol_inv_corr, 1):
A[i, j] = -(corr_inv[i, j]) / (math.sqrt(corr_inv[i, i] * corr_inv[j, j]))
A[j, i] = A[i, j]
dataset_corr = np.asarray(dataset_corr)
kmo_num = np.sum(np.square(dataset_corr)) - np.sum(np.square(np.diagonal(A)))
kmo_denom = kmo_num + np.sum(np.square(A)) - np.sum(np.square(np.diagonal(A)))
kmo_value = kmo_num / kmo_denom
return kmo_value
print("\nKMO测度:", kmo(df2_corr))
# 巴特利特球形检验
df2_corr1 = df2_corr.values
print("\n巴特利特球形检验:", bartlett(df2_corr1[0], df2_corr1[1], df2_corr1[2], df2_corr1[3], df2_corr1[4],
df2_corr1[5], df2_corr1[6], df2_corr1[7], df2_corr1[8], df2_corr1[9],
df2_corr1[10], df2_corr1[11], df2_corr1[12], df2_corr1[13], df2_corr1[14]))
# 求特征值和特征向量
eig_value, eigvector = nlg.eig(df2_corr) # 求矩阵R的全部特征值，构成向量
eig = pd.DataFrame()
eig['names'] = df2_corr.columns
eig['eig_value'] = eig_value
eig.sort_values('eig_value', ascending=False, inplace=True)
print("\n特征值\n：",eig)
eig1=pd.DataFrame(eigvector)
eig1.columns = df2_corr.columns
eig1.index = df2_corr.columns
print("\n特征向量\n",eig1)
# 求公因子个数m,使用前m个特征值的比重大于85%的标准，选出了公共因子是五个
for m in range(1, 15):
if eig['eig_value'][:m].sum() / eig['eig_value'].sum() >= 0.85:
print("\n公因子个数:", m)
break
# 因子载荷阵
A = np.mat(np.zeros((15, 5)))
i = 0
j = 0
while i < 5:
j = 0
while j < 15:
A[j:, i] = sqrt(eig_value[i]) * eigvector[j, i]
j = j + 1
i = i + 1
a = pd.DataFrame(A)
a.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']
a.index = df2_corr.columns
print("\n因子载荷阵\n", a)
fa = FactorAnalyzer(n_factors=5)
fa.loadings_ = a
# print(fa.loadings_)
print("\n特殊因子方差:\n", fa.get_communalities()) # 特殊因子方差，因子的方差贡献度，反映公共因子对变量的贡献
var = fa.get_factor_variance() # 给出贡献率
print("\n解释的总方差（即贡献率）:\n", var)
# 因子旋转
rotator = Rotator()
b = pd.DataFrame(rotator.fit_transform(fa.loadings_))
b.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']
b.index = df2_corr.columns
print("\n因子旋转:\n", b)
# 因子得分
X1 = np.mat(df2_corr)#生成数组
X1 = nlg.inv(X1)
b = np.mat(b)
factor_score = np.dot(X1, b)
factor_score = pd.DataFrame(factor_score)
factor_score.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']
factor_score.index = df2_corr.columns
print("\n因子得分：\n", factor_score)
fa_t_score = np.dot(np.mat(df2), np.mat(factor_score))
print("\n应试者的五个因子得分：\n",pd.DataFrame(fa_t_score))
# 综合得分
wei = [[0.50092], [0.137087], [0.097055], [0.079860], [0.049277]]
fa_t_score = np.dot(fa_t_score, wei) / 0.864198
fa_t_score = pd.DataFrame(fa_t_score)
fa_t_score.columns = ['综合得分']
fa_t_score.insert(0, 'ID', range(0, 27))
print("\n综合得分：\n", fa_t_score)
print("\n综合得分：\n", fa_t_score.sort_values(by='综合得分', ascending=False).head(6))
plt.figure()
ax1=plt.subplot(111)
X=fa_t_score['ID']
Y=fa_t_score['综合得分']
plt.bar(X,Y,color="#87CEFA")
# plt.bar(X, Y, color="red")
plt.title('result00')
ax1.set_xticks(range(len(fa_t_score)))
ax1.set_xticklabels(fa_t_score.index)
plt.show()
fa_t_score1=pd.DataFrame()
fa_t_score1=fa_t_score.sort_values(by='综合得分',ascending=False).head()
ax2 = plt.subplot(111)
X1 = fa_t_score1['ID']
Y1 = fa_t_score1['综合得分']
plt.bar(X1, Y1, color="#87CEFA")
# plt.bar(X1, Y1, color='red')
plt.title('result01')
plt.show()
if name == 'main':
main()
原文链接：https://www.cnblogs.com/wangshanchuan/p/10820326.html
https ://blog.csdn.net/qq_41081716/article/details/103332472
https://blog.csdn.net/qq_29831163/article/details/88918422?
utm_medium=distribute.pc_relevant.none-task-blog-baidujs-4

[因子分析的步骤]
[1.对原始数据进行标准化处理]
[2．计算相关系数矩阵R ]
[3．计算初等载荷矩阵 ]
[4．选择m （ m≤ p）个主因子，进行因子旋转 ]
[5.计算因子得分，并进行综合评价 ]
[6. 利用综合因子得分公式计算各样本的综合得分]

python-----因子分析