【题目】

1.现有我国大陆30个省、直辖市、自治区的经济发展状况数据集如表所示，包括8项经济指标：国民生产总值（A1）；居民消费水平（A2）；固定资产投资（A3）；职工平均工资（A4）；货物周转量（A5）；居民消费指数（A6）；商品零售价格指数（A7）；工业总产值（A8），试用基本PCA方法将这8项经济指标融合成3项综合指标。

【要求】

1.写出PCA完成降维的主要步骤；

2.详细写出题目降维的计算过程；

3.请大家在博客中直接完成或在作业本上完成后拍照上传。

我国大陆经济发展状况数据
　 A1 A2 A3 A4 A5 A6 A7 A8
北京 1394.89 2505 519.01 8144 373.9 117.3 112.6 843.43
天津 920.11 2720 345.46 6501 342.8 115.2 110.6 582.51
河北 2849.52 1258 704.87 4839 2033.3 115.2 115.8 1234.85
山西 1092.48 1250 290.9 4721 717.3 116.9 115.6 697.25
内蒙古 832.88 1387 250.23 4134 781.7 117.5 116.8 419.39
辽宁 2793.37 2397 387.99 4911 1371.1 116.1 114 1840.55
吉林 1129.2 1872 320.45 4430 497.4 115.2 114.2 762.47
黑龙江 2014.53 2334 435.73 4145 824.8 116.1 114.3 1240.37
上海 2462.57 5343 996.48 9279 207.4 118.7 113 1642.95
江苏 5155.25 1926 1434.95 5934 1025.5 115.8 114.3 2026.64
浙江 3524.79 2249 1006.39 6619 754.4 116.6 113.5 916.59
安徽 2003.58 1254 474 4609 908.3 114.8 112.7 824.14
福建 2160.52 2320 553.97 5857 609.3 115.2 114.4 433.67
江西 1205.1 1182 282.84 4211 411.7 116.9 115.9 571.84
山东 5002.34 1527 1229.55 5145 1196.6 117.6 114.2 2207.69
河南 3002.74 1034 670.35 4344 1574.4 116.5 114.9 1367.92
湖北 2391.42 1527 571.68 4685 849 120 116.6 1220.72
湖南 2195.7 1408 422.61 4797 1011.8 119 115.5 843.83
广东 5381.72 2699 1639.83 8250 656.5 114 111.6 1396.35
广西 1606.15 1314 382.59 5150 556 118.4 116.4 554.97
海南 364.17 1814 198.35 5340 232.1 113.5 111.3 64.33
四川 3534 1261 822.54 4645 902.3 118.5 117 1431.81
贵州 630.07 942 150.84 4475 301.1 121.4 117.2 324.72
云南 1206.68 1261 334 5149 310.4 121.3 118.1 716.65
西藏 55.98 1110 17.87 7382 4.2 117.3 114.9 5.57
陕西 1000.03 1208 300.27 4396 500.9 119 117 600.98
甘肃 553.35 1007 114.81 5493 507 119.8 116.5 468.79
青海 165.31 1445 47.76 5753 61.6 118 116.3 105.8
宁夏 169.75 1355 61.98 5079 121.8 117.1 115.3 114.4
新疆 834.57 1469 376.95 5348 339 119.7 116.7 428.76 
import pandas as pd

import openpyxl

import numpy as np

data = pd.read_excel("D:\User\ROG\jupyter_root_directory\data/我国大陆经济发展状况数据.xlsx",header=None,engine='openpyxl')

data = data [2:]

data = data[[1,2,3,4,5,6,7,8]]

data
  1 2 3 4 5 6 7 8
2 1394.89 2505 519.01 8144 373.9 117.3 112.6 843.43
3 920.11 2720 345.46 6501 342.8 115.2 110.6 582.51
4 2849.52 1258 704.87 4839 2033.3 115.2 115.8 1234.85
5 1092.48 1250 290.9 4721 717.3 116.9 115.6 697.25
6 832.88 1387 250.23 4134 781.7 117.5 116.8 419.39
7 2793.37 2397 387.99 4911 1371.1 116.1 114 1840.55
8 1129.2 1872 320.45 4430 497.4 115.2 114.2 762.47
9 2014.53 2334 435.73 4145 824.8 116.1 114.3 1240.37
10 2462.57 5343 996.48 9279 207.4 118.7 113 1642.95
11 5155.25 1926 1434.95 5934 1025.5 115.8 114.3 2026.64
12 3524.79 2249 1006.39 6619 754.4 116.6 113.5 916.59
13 2003.58 1254 474 4609 908.3 114.8 112.7 824.14
14 2160.52 2320 553.97 5857 609.3 115.2 114.4 433.67
15 1205.1 1182 282.84 4211 411.7 116.9 115.9 571.84
16 5002.34 1527 1229.55 5145 1196.6 117.6 114.2 2207.69
17 3002.74 1034 670.35 4344 1574.4 116.5 114.9 1367.92
18 2391.42 1527 571.68 4685 849 120 116.6 1220.72
19 2195.7 1408 422.61 4797 1011.8 119 115.5 843.83
20 5381.72 2699 1639.83 8250 656.5 114 111.6 1396.35
21 1606.15 1314 382.59 5150 556 118.4 116.4 554.97
22 364.17 1814 198.35 5340 232.1 113.5 111.3 64.33
23 3534 1261 822.54 4645 902.3 118.5 117 1431.81
24 630.07 942 150.84 4475 301.1 121.4 117.2 324.72
25 1206.68 1261 334 5149 310.4 121.3 118.1 716.65
26 55.98 1110 17.87 7382 4.2 117.3 114.9 5.57
27 1000.03 1208 300.27 4396 500.9 119 117 600.98
28 553.35 1007 114.81 5493 507 119.8 116.5 468.79
29 165.31 1445 47.76 5753 61.6 118 116.3 105.8
30 169.75 1355 61.98 5079 121.8 117.1 115.3 114.4
31 834.57 1469 376.95 5348 339 119.7 116.7 428.76 
#减去平均值

sample,feature=data.shape

data = data - np.mean(data)

data
1 2 3 4 5 6 7 8
2 -526.202 759.067 7.50167 2685.17 -292.22 0.0133333 -2.30667 -19.568
3 -1000.98 974.067 -166.048 1042.17 -323.32 -2.08667 -4.30667 -280.488
4 928.428 -487.933 193.362 -619.833 1367.18 -2.08667 0.893333 371.852
5 -828.612 -495.933 -220.608 -737.833 51.18 -0.386667 0.693333 -165.748
6 -1088.21 -358.933 -261.278 -1324.83 115.58 0.213333 1.89333 -443.608
7 872.278 651.067 -123.518 -547.833 704.98 -1.18667 -0.906667 977.552
8 -791.892 126.067 -191.058 -1028.83 -168.72 -2.08667 -0.706667 -100.528
9 93.4377 588.067 -75.7783 -1313.83 158.68 -1.18667 -0.606667 377.372
10 541.478 3597.07 484.972 3820.17 -458.72 1.41333 -1.90667 779.952
11 3234.16 180.067 923.442 475.167 359.38 -1.48667 -0.606667 1163.64
12 1603.7 503.067 494.882 1160.17 88.28 -0.686667 -1.40667 53.592
13 82.4877 -491.933 -37.5083 -849.833 242.18 -2.48667 -2.20667 -38.858
14 239.428 574.067 42.4617 398.167 -56.82 -2.08667 -0.506667 -429.328
15 -715.992 -563.933 -228.668 -1247.83 -254.42 -0.386667 0.993333 -291.158
16 3081.25 -218.933 718.042 -313.833 530.48 0.313333 -0.706667 1344.69
17 1081.65 -711.933 158.842 -1114.83 908.28 -0.786667 -0.00666667 504.922
18 470.328 -218.933 60.1717 -773.833 182.88 2.71333 1.69333 357.722
19 274.608 -337.933 -88.8983 -661.833 345.68 1.71333 0.593333 -19.168
20 3460.63 953.067 1128.32 2791.17 -9.62 -3.28667 -3.30667 533.352
21 -314.942 -431.933 -128.918 -308.833 -110.12 1.11333 1.49333 -308.028
22 -1556.92 68.0667 -313.158 -118.833 -434.02 -3.78667 -3.60667 -798.668
23 1612.91 -484.933 311.032 -813.833 236.18 1.21333 2.09333 568.812
24 -1291.02 -803.933 -360.668 -983.833 -365.02 4.11333 2.29333 -538.278
25 -714.412 -484.933 -177.508 -309.833 -355.72 4.01333 3.19333 -146.348
26 -1865.11 -635.933 -493.638 1923.17 -661.92 0.0133333 -0.00666667 -857.428
27 -921.062 -537.933 -211.238 -1062.83 -165.22 1.71333 2.09333 -262.018
28 -1367.74 -738.933 -396.698 34.1667 -159.12 2.51333 1.59333 -394.208
29 -1755.78 -300.933 -463.748 294.167 -604.52 0.713333 1.39333 -757.198
30 -1751.34 -390.933 -449.528 -379.833 -544.32 -0.186667 0.393333 -748.598
31 -1086.52 -276.933 -134.558 -110.833 -327.12 2.41333 1.79333 -434.238 
S = np.mat(data)

S = S.astype('float16')

# 计算协方差矩阵

X = np.cov(data1.T)

X
array([[ 2.17512816e+06,  3.39017180e+05,  5.64795310e+05,

         3.66799624e+05,  4.18740435e+05, -8.14159678e+02,

        -7.37804742e+02,  7.53426315e+05],

       [ 3.39017180e+05,  7.42673545e+05,  1.47954656e+05,

         8.10174225e+05, -5.98597476e+04, -4.10269647e+02,

        -9.69473039e+02,  1.82942939e+05],

       [ 5.64795310e+05,  1.47954656e+05,  1.62302951e+05,

         2.10470018e+05,  7.98055667e+04, -2.28857444e+02,

        -2.74499481e+02,  1.86527121e+05],

       [ 3.66799624e+05,  8.10174225e+05,  2.10470018e+05,

         1.71571948e+06, -2.14593340e+05, -3.56041630e+02,

        -1.33849453e+03,  7.91434689e+04],

       [ 4.18740435e+05, -5.98597476e+04,  7.98055667e+04,

        -2.14593340e+05,  2.11547288e+05, -2.35784325e+02,

         1.89958719e+01,  1.77085901e+05],

       [-8.14159678e+02, -4.10269647e+02, -2.28857444e+02,

        -3.56041630e+02, -2.35784325e+02,  4.10102506e+00,

         2.93249666e+00, -1.48336671e+02],

       [-7.37804742e+02, -9.69473039e+02, -2.74499481e+02,

        -1.33849453e+03,  1.89958719e+01,  2.93249666e+00,

         3.60350766e+00, -2.13093770e+02],

       [ 7.53426315e+05,  1.82942939e+05,  1.86527121e+05,

         7.91434689e+04,  1.77085901e+05, -1.48336671e+02,

        -2.13093770e+02,  3.41794042e+05]])
#求特征值和特征向量

eig_val, eig_vec = np.linalg.eig(X)

eig_pairs = [(np.abs(eig_val[i]), eig_vec[:, i]) for i in range(feature)]

eig_val
array([3.00989343e+06, 1.90990488e+06, 3.00900997e+05, 8.22843300e+04,

4.08689937e+04, 5.31590865e+03, 4.22552725e+00, 4.17682352e-01])
index = np.argsort(-eig_val)

# 将特征值按从大到小进行排序

np.argsort(eig_val)

#进行降维

k = 3

selectVec = np.matrix(eig_vec.T[index[:k]])

finalData = data1 * selectVec.T # (30, 8) * (8, 3) = (30, 3)

finalData.shape

finalData
matrix([[  991.02791011, -2598.05143659,  -442.07545458],

        [ -145.34532529, -1734.65887357,   457.16158882],

        [  557.61661571,  1483.60034716,   -93.14172337],

        [-1197.70506441,   311.50193131,    20.75043138],

        [-1691.41478306,   542.6983315 ,   364.01896739],

        [  925.58426428,   922.66694957,   961.42758107],

        [-1105.78714784,   282.27855119,   652.96927436],

        [ -230.8764751 ,   915.2909667 ,  1154.93539315],

        [ 3479.73362389, -3833.86882421,  1432.59322724],

        [ 3279.28517562,  1443.82207397,  -340.60839295],

        [ 2020.42780485,  -236.33723265,  -368.15435258],

        [ -459.95372537,   899.6555233 ,   -51.4321421 ],

        [  421.88446529,  -480.08094189,   143.32609056],

        [-1424.33703514,   671.74965252,    96.75028233],

        [ 2712.10215068,  2166.91458621,  -234.05003709],

        [  370.55219993,  1915.41058406,  -103.89839129],

        [   75.40542303,   988.63141429,   171.25143746],

        [ -179.38146112,   819.30680274,   -18.32663648],

        [ 4553.43459221,  -648.74796439,  -936.50316474],

        [ -631.0710909 ,   148.57756477,  -260.22529535],

        [-1543.48297854,  -931.20547131,   148.74331019],

        [  963.19113519,  1714.01295905,  -193.78601902],

        [-1924.84798562,   212.88195738,  -181.92664169],

        [ -942.34945313,   -52.02992477,  -208.50404981],

        [-1165.55041791, -2423.78738221, -1276.80765054],

        [-1469.95701957,   456.57292109,    92.47839383],

        [-1461.05431309,  -532.72325834,  -483.85639992],

        [-1662.97477831, -1243.25114115,  -294.80964414],

        [-1974.30737332,  -688.33978176,   -78.22032709],

        [-1139.6165708 ,  -491.32802526,  -129.98141111]])

最新文章

  1. 二叉排序树(BST)创建,删除,查找操作
  2. Html 文档在线编辑器
  3. Console命令详解,让调试js代码变得更简单
  4. arduino 串口实时绘图(以mpu9250为例)
  5. 组件Newtonsoft.Json实现object2json转换
  6. SSRS报表连接超时的问题
  7. 天气预报API获取
  8. 网站实现特定某个地区访问执行跳转(js方法)
  9. ACdrea 1217---Cracking' RSA（高斯消元）
  10. 安装完最小化 RHEL/CentOS 7 后需要做的 30 件事情（五）
  11. [转自小兵的工具箱]C++ Builder 基础
  12. JavaWeb之Servlet：Cookie 和 Session
  13. WordPress Complete Gallery Manager插件‘upload-images.php’任意文件上传漏洞
  14. js基础例子购物车升级版（未优化版）
  15. 用Struts2标签实现Map的迭代
  16. 关于系统弹出错误:429 ， ActiveX 部件不能创建对象 的解决方法
  17. hihoCoder编程练习赛72
  18. Apache Spark技术实战之6 --Standalone部署模式下的临时文件清理
  19. Star sky CodeForces - 835C
  20. js设计模式（二）---策略模式

热门文章

  1. struct device_node *
  2. Vulnhub:Five86-2靶机
  3. RTFormer: Efficient Design for Real-Time Semantic Segmentation with Transformer概述
  4. vue 项目配置自动打压缩包
  5. vue中当数据改变时更新DOM
  6. replace 常用积累
  7. Docker部署Springboot+Vue项目
  8. linux系统下命令行方式创建KVM虚拟机
  9. springcloud 和springboot版本对比
  10. 一条命令删除所有静态路由华为eNSP