LDA忽略n U组件？

Question

当我试图使用Scikit Learn中的LDA时，它始终只提供一个组件，即使我要求更多：

>>> from sklearn.lda import LDA
>>> x = np.random.randn(5,5)
>>> y = [True, False, True, False, True]
>>> for i in range(1,6):
...     lda = LDA(n_components=i)
...     model = lda.fit(x,y)
...     model.transform(x)

给予

/Users/orthogonal/virtualenvs/osxml/lib/python2.7/site-packages/sklearn/lda.py:161: UserWarning: Variables are collinear
  warnings.warn("Variables are collinear")
array([[-0.12635305],
       [-1.09293574],
       [ 1.83978459],
       [-0.37521856],
       [-0.24527725]])
array([[-0.12635305],
       [-1.09293574],
       [ 1.83978459],
       [-0.37521856],
       [-0.24527725]])
array([[-0.12635305],
       [-1.09293574],
       [ 1.83978459],
       [-0.37521856],
       [-0.24527725]])
array([[-0.12635305],
       [-1.09293574],
       [ 1.83978459],
       [-0.37521856],
       [-0.24527725]])
array([[-0.12635305],
       [-1.09293574],
       [ 1.83978459],
       [-0.37521856],
       [-0.24527725]])

如你所见，它每次只打印出一个维度。这是为什么？这和变量共线有关系吗？

另外，当我使用Scikit Learn的PCA时，它会给我想要的。

>>> from sklearn.decomposition import PCA
>>> for i in range(1,6):
...     pca = PCA(n_components=i)
...     model = pca.fit(x)
...     model.transform(x)
... 
array([[ 0.83688322],
       [ 0.79565477],
       [-2.4373344 ],
       [ 0.72500848],
       [ 0.07978792]])
array([[ 0.83688322, -1.56459039],
       [ 0.79565477,  0.84710518],
       [-2.4373344 , -0.35548589],
       [ 0.72500848, -0.49079647],
       [ 0.07978792,  1.56376757]])
array([[ 0.83688322, -1.56459039, -0.3353066 ],
       [ 0.79565477,  0.84710518, -1.21454498],
       [-2.4373344 , -0.35548589, -0.16684946],
       [ 0.72500848, -0.49079647,  1.09006296],
       [ 0.07978792,  1.56376757,  0.62663807]])
array([[ 0.83688322, -1.56459039, -0.3353066 ,  0.22196922],
       [ 0.79565477,  0.84710518, -1.21454498, -0.15961993],
       [-2.4373344 , -0.35548589, -0.16684946, -0.04114339],
       [ 0.72500848, -0.49079647,  1.09006296, -0.2438673 ],
       [ 0.07978792,  1.56376757,  0.62663807,  0.2226614 ]])
array([[  8.36883220e-01,  -1.56459039e+00,  -3.35306597e-01,
          2.21969223e-01,  -1.66533454e-16],
       [  7.95654771e-01,   8.47105182e-01,  -1.21454498e+00,
         -1.59619933e-01,   3.33066907e-16],
       [ -2.43733440e+00,  -3.55485895e-01,  -1.66849458e-01,
         -4.11433949e-02,   0.00000000e+00],
       [  7.25008484e-01,  -4.90796471e-01,   1.09006296e+00,
         -2.43867297e-01,  -1.38777878e-16],
       [  7.97879229e-02,   1.56376757e+00,   6.26638070e-01,
          2.22661402e-01,   2.22044605e-16]])