PCA-第一个组件上的低可变负载

问题描述 投票:0回答:1

我对40个变量执行PCA,并保持所有组件的最小距离。特征值1(总共5个分量)-STATA给我以下输出:

>pca *all variables*, mineigen(1)


 Component |   Eigenvalue   Difference         Proportion   Cumulative
    -------------+------------------------------------------------------------
           Comp1 |      29.0991      26.3849             0.7275       0.7275
           Comp2 |      2.71421      .672651             0.0679       0.7953
           Comp3 |      2.04156      .803292             0.0510       0.8464
           Comp4 |      1.23826      .201987             0.0310       0.8773
           Comp5 |      1.03628      .170083             0.0259       0.9032


Principal components (eigenvectors) 


    -----------------------------------------------------------------------------
        Variable |    Comp1     Comp2     Comp3     Comp4     Comp5 | Unexplained 
    -------------+--------------------------------------------------+------------
 R_wt1_GLR~13 |   0.0036    0.2762   -0.1522    0.4151    0.3403 |       .4118 
   R_wt7_FO14 |   0.0689    0.0353   -0.2479   -0.2684    0.3559 |       .5124 
    std_GL~24 |   0.1825   -0.0001    0.0000   -0.0959   -0.0131 |       .0191 
    std_GLR~6 |   0.1712    0.0201    0.1849   -0.1215   -0.0321 |      .05681 
    std_GLR~8 |   0.1822    0.0119   -0.0235   -0.0713   -0.0102 |      .02624 
    wt1_GL~13 |   0.0263    0.4621    0.3717    0.0753    0.1531 |      .08684 
    wt1_GL~24 |   0.1819    0.0148    0.0268   -0.0981   -0.0225 |       .0222 
    wt1_GLR~6 |   0.1615    0.0390    0.2516   -0.1209   -0.0765 |      .08364 
    wt1_GLR~8 |   0.1815    0.0138    0.0119   -0.0902   -0.0269 |      .02935 
    wt1_GLR~9 |   0.0192    0.4457    0.3554    0.1194    0.1716 |       .1442 
    wt2_GL~24 |   0.1832   -0.0186   -0.0229    0.0034   -0.0486 |      .01839 
    wt2_GLR~3 |   0.0133    0.4138   -0.1428    0.0898   -0.4108 |       .3035 
    wt2_GLR~5 |   0.1828    0.0111    0.0114   -0.0629   -0.0511 |      .01971 
    wt2_GLR~6 |   0.1758    0.0030    0.1206   -0.0245   -0.0877 |      .06209 
    wt2_GLR~8 |   0.1826   -0.0273   -0.0410    0.0064   -0.0405 |      .02255 
    wt3_GLR~5 |   0.1809    0.0139    0.0323   -0.0957   -0.0601 |      .02963 
    wt3_GLR~6 |   0.1601    0.0576    0.2214   -0.1942   -0.1267 |      .08216 
    wt4_GL~24 |   0.1801    0.0136    0.0055   -0.1630    0.0246 |      .02207 
    wt4_GLR~5 |   0.1823    0.0107    0.0143   -0.0683   -0.0444 |      .02444 
    wt4_GLR~6 |   0.1620    0.0340    0.1740   -0.1918   -0.0349 |       .1246 
    wt5_GL~24 |   0.1793   -0.0337    0.0051    0.0841   -0.0665 |      .04766 
    wt5_GLR~8 |   0.1783   -0.0447    0.0179    0.1118   -0.0840 |      .04559 
    wt7_GL~24 |   0.1823   -0.0213    0.0006   -0.0537    0.0023 |      .02847 
    wt7_GLR~5 |   0.1835   -0.0185   -0.0012   -0.0256   -0.0322 |      .01707 
    wt7_GLR~8 |   0.1815   -0.0169   -0.0189   -0.0773    0.0129 |      .03221 
      wt8_FO9 |   0.0530    0.2385   -0.4929   -0.0310   -0.2132 |       .2196 
    wt8_GLR~8 |   0.1813   -0.0263    0.0131    0.0054   -0.0326 |      .03966 
     wt1_FO10 |  -0.0476   -0.4309    0.1862    0.0542    0.0003 |       .3557 
      wt2_FO4 |   0.1184    0.2212   -0.3360   -0.2154   -0.0222 |       .1705 
     wt2_LM24 |   0.1768   -0.0569   -0.0708    0.1434    0.1202 |      .03092 
      wt2_LM8 |   0.1760   -0.0574   -0.0765    0.1076    0.0800 |      .05662 
     wt4_LM24 |   0.1802   -0.0441   -0.0376    0.1390    0.0486 |      .02063 
      wt4_LM6 |   0.1576   -0.0866    0.0472    0.3475    0.0284 |       .1015 
      wt4_LM8 |   0.1803   -0.0384   -0.0418    0.0807    0.0302 |      .03795 
     wt5_LM24 |   0.1805   -0.0226   -0.0490    0.0956    0.0570 |      .03072 
     wt6_LM24 |   0.1773   -0.0542   -0.0484    0.2013    0.0248 |        .022 
      wt6_LM6 |   0.1606   -0.0935    0.0132    0.3480    0.0376 |      .07385 
     wt7_LM24 |   0.1768   -0.0383   -0.0915    0.1524    0.0798 |      .03353 
      wt7_LM8 |   0.1769   -0.0521   -0.0889    0.1051    0.0278 |      .05139 
     wt8_LM10 |   0.0656    0.0088   -0.0737   -0.2891    0.6266 |       .3532 
    ------------------------------------------------------------------------------

我想知道为什么Comp1上所有变量的负载如此之低(基本上所有<0.2),而对于Comp2,Comp3和Comp5我有4个变量,而对于Comp4有3个变量都都> 0.3。有什么好的解释吗?

感谢您的帮助!

pca
1个回答
0
投票

我不是专家,我只在openCV中使用PCA,但是对我的结果表明,变量之间存在heavy函数关系。

归一化后,第一个分量(仅第一个分量)的特征值保留了原始方差的%72的事实。

(它也比下一个特征向量方向高近11倍。)

这可能意味着其他轴只是在采样噪声,而不是您感兴趣的信号(或信号)...


0
投票

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