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
from sklearn.cluster import KMeans
from matplotlib import cm
import matplotlib.pyplot as plt
def main():df=pd.read_csv("./data/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_rfig=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.shapeA = 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_denomreturn kmo_valueprint("\nKMO测度:", kmo(df2_corr))# 巴特利特球形检验df2_corr1 = df2_corr.valuesprint("\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.columnseig['eig_value'] = eig_valueeig.sort_values('eig_value', ascending=False, inplace=True)print("\n特征值\n：",eig)eig1=pd.DataFrame(eigvector)eig1.columns = df2_corr.columnseig1.index = df2_corr.columnsprint("\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 = 0j = 0while i < 5:j = 0while j < 15:A[j:, i] = sqrt(eig_value[i]) * eigvector[j, i]j = j + 1i = i + 1a = pd.DataFrame(A)a.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']a.index = df2_corr.columnsprint("\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.columnsprint("\n因子旋转:\n", b)# 因子得分X1 = np.mat(df2_corr)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.columnsprint("\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) / 0.864198fa_t_score = pd.DataFrame(fa_t_score)fa_t_score.columns = ['综合得分']fa_t_score.insert(0, 'ID', range(1, 49))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()