数学建模之因子分析（FA）

Python中街区普查案例代码（FA）

1. import pandas as pd 2. import numpy as np 3. import matplotlib.pyplot as plt 4. from sklearn.preprocessing import StandardScaler 5. import matplotlib 6. 7. LA_data = pd.read_csv("LA.Neighborhoods.csv") 8. LA_data 9. # 新增人口密度，去掉人口量、面积、经度和维度 10. LA_data["density"] = LA_data["Population"]/LA_data["Area"] 11. LA_data_final = LA_data.drop(["Population","Area","Longitude","Latitude"],axis=1) 12. LA_data_final_feat = LA_data_final.drop(['LA.Nbhd'],axis=1) 13. LA_data_final_feat 14. 15. #数据标准化 16. f = StandardScaler().fit_transform(LA_data_final_feat) # 数据标准化 17. f = pd.DataFrame(f) 18. 19. #计算巴特利特P值 20. from factor_analyzer.factor_analyzer import calculate_bartlett_sphericity 21. chi_square_value,P_value = calculate_bartlett_sphericity(f) 22. chi_square_value,P_value 23. #计算KMO 24. from factor_analyzer.factor_analyzer import calculate_kmo 25. kom_all,kmo_model = calculate_kmo(f) 26. kom_all,kmo_model 27. 28. from factor_analyzer import FactorAnalyzer 29. fa = FactorAnalyzer(LA_data_final_feat.shape[1]+1,rotation=None) 30. fa.fit(LA_data_final_feat) 31. ev,v = fa.get_eigenvalues() # 计算特征值和特征向量 32. var = fa.get_factor_variance()#给出方差贡献率 33. print('\n相关矩阵特征值：', ev) 34. matplotlib.rcParams["font.family"] = "SimHei" 35. plt.figure(figsize=(8, 6.5)) 36. plt.scatter(range(1, f.shape[1]+1), ev) 37. plt.plot(range(1, f.shape[1]+1), ev) 38. plt.title('碎石图', fontdict={'weight': 'normal', 'size': 25}) 39. plt.xlabel('因子', fontdict={'weight': 'normal', 'size': 15}) 40. plt.ylabel('特征值', fontdict={'weight': 'normal', 'size': 15}) 41. plt.grid() 42. plt.show() 43. 44. print('\n方差贡献率：', var) 45. matplotlib.rcParams["font.family"] = "SimHei" 46. plt.figure(figsize=(8, 6.5)) 47. plt.scatter(range(1, f.shape[1]+1), var[2]) 48. plt.plot(range(1, f.shape[1]+1), var[2]) 49. plt.title('方差贡献率', fontdict={'weight': 'normal', 'size': 25}) 50. plt.xlabel('因子', fontdict={'weight': 'normal', 'size': 15}) 51. plt.ylabel('特征值', fontdict={'weight': 'normal', 'size': 15}) 52. plt.grid() 53. plt.show() 54. 55. fa = FactorAnalyzer(4,rotation="varimax") 56. fa.fit(LA_data_final_feat) 57. df_loading = pd.DataFrame(fa.loadings_,index=LA_data_final_feat.columns.tolist()) 58. # 输出载荷矩阵 59. df_loading 60. 61. # 对系数矩阵进行可视化 62. import seaborn as sns 63. df_cm = pd.DataFrame(np.abs(fa.loadings_),index=df_loading.index) 64. plt.figure(figsize = (8,8)) 65. ax = sns.heatmap(df_cm, annot=True, cmap="BuPu") 66. # 设置y轴的字体的大小 67. ax.yaxis.set_tick_params(labelsize=12) 68. plt.title('Factor Analysis', fontsize='xx-large') 69. # Set y-axis label 70. plt.ylabel('Sepal Width', fontsize='xx-large') 71. #plt.savefig('factorAnalysis.png', dpi=200) 72. 73. #计算因子得分 74. LA_data_trans = pd.DataFrame(fa.transform(LA_data_final_feat),index=LA_data_final["LA.Nbhd"]) 75. LA_data_trans 76. 77. #以散点图的形式呈现 78. matplotlib.rcParams["font.family"] = "SimHei" 79. matplotlib.rcParams['axes.unicode_minus']=False 80. plt.figure(figsize = (10,4),dpi = 80) 81. plt.subplot(1,2,1) 82. plt.scatter(LA_data_trans.loc[:,0],LA_data_trans.loc[:,1]) 83. plt.title("Scree Plot") 84. plt.xlabel("Factor1") 85. plt.ylabel("Factor2") 86. plt.grid()