weka的主成分分析返回错误的实例

Question

我用weka做主成分分析，结果肯定是错的。

我的实例如下：

40.4,24.7,7.2,6.1,8.3,8.7,2.442,20
25,12.7,11.2,11,12.9,20.2,3.542,9.1
13.2,3.3,3.9,4.3,4.4,5.5,0.578,3.6
22.3,6.7,5.6,3.7,6,7.4,0.176,7.3
34.3,11.8,7.1,7.1,8,8.9,1.726,27.5
35.6,12.5,16.4,16.7,22.8,29.3,3.017,26.6
22,7.8,9.9,10.2,12.6,17.6,0.847,10.6
48.4,13.4,10.9,9.9,10.9,13.9,1.772,17.8
40.6,19.1,19.8,19,29.7,39.6,2.449,35.8
24.8,8,9.8,8.9,11.9,16.2,0.789,13.7
12.5,9.7,4.2,4.2,4.6,6.5,0.874,3.9
1.8,0.6,0.7,0.7,0.8,1.1,0.056,1
32.3,13.9,9.4,8.3,9.8,13.3,2.126,17.1
38.5,9.1,11.3,9.5,12.2,16.4,1.327,11.6
26.2,10.1,5.6,15.6,7.7,30.1,0.126,25.9

我的java代码如下：

PrincipalComponents pca = new PrincipalComponents();
pca.buildEvaluator(instances);
pca.setVarianceCovered(0.9);
instances=pca.transformedData(instances);
System.out.println(instances);

结果如下：

-0.76617,2.661828,-0.543741,0
-0.970913,0.436367,1.69961,0
2.881824,-0.434979,0.32666,0
2.202041,-0.118079,-0.265614,0
-0.055269,0.917633,-0.825503,0
-3.389144,-0.661234,0.756936,0
0.326235,-0.94073,0.256852,0
-1.020299,0.939242,-0.408135,0
-5.193605,-0.979272,-0.020702,0
0.337214,-0.689053,-0.018816,0
2.413215,0.213961,0.314493,0
4.426397,-0.617956,0.288353,0
-0.373545,0.837791,0.108058,0
-0.347075,-0.059153,0.119701,0
-0.470905,-1.506368,-1.788153,0

但我确信正确的结果如下：

0.76617,2.661828,0.543741,0
0.970913,0.436367,-1.69961,0
-2.881824,-0.434979,-0.32666,0
-2.202041,-0.118079,0.265614,0
0.055269,0.917633,0.825503,0
3.389144,-0.661234,-0.756936,0
-0.326235,-0.94073,-0.256852,0
1.020299,0.939242,0.408135,0
5.193605,-0.979272,0.020702,0
-0.337214,-0.689053,0.018816,0
-2.413215,0.213961,-0.314493,0
-4.426397,-0.617956,-0.288353,0
0.373545,0.837791,-0.108058,0
0.347075,-0.059153,-0.119701,0
0.470905,-1.506368,1.788153,0

第一列和第三列（第一主成分和第三主成分）的符号（正数或负数）相反。

我在stackoverflow上搜索了我的错误线索，但我找不到我的错误，所以有人能找出我的代码或weka代码有问题吗？

Answer 1

主成分分析基于查找数据集的特征向量和特征值，以及eigenvectors are not unique - 或者换句话说，the definition of eigenvector is ambidextrous。

在 PCA 术语中，您可以否定任何主成分的所有 scores，只要您也对 loadings 进行相应的更改。

您从哪里得到“正确结果”？它看起来好像是一个程序或包，只是碰巧使用了与 Weka 不同的约定。