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python - ValueError：形状（5,5）和（20，）未对齐：5（dim 1）！= 20（dim 0）

问题描述

我正在计算 LDA 的特征值和特征向量。在获得内部散点矩阵值 (SW) 后，我反转我的矩阵，以便我可以将其乘以类之间的散点值或 Sb，但是当我尝试通过将其乘以 Sb 来计算逆 Sw 值时，我得到标题中描述的错误。

这是我的实际 InvSw 值：

[[ 1.04681227e-02, 
  -8.88438953e-03, 
  -1.49760770e-03, 
  -1.40836916e-04,
   5.62586740e-04],
 [-8.88438953e-03,  
   2.51997617e-02, 
  -1.29503509e-02, 
  -1.58583123e-03,
  -1.93338715e-03],
 [-1.49760770e-03, 
  -1.29503509e-02,  
   1.96652733e-01, 
  -1.26808048e-01,
  -5.57741506e-02],
 [-1.40836916e-04,
  -1.58583123e-03, 
  -1.26808048e-01,  
   2.72992280e-01,
  -1.45652927e-01],
 [ 5.62586740e-04, 
  -1.93338715e-03, 
  -5.57741506e-02, 
  -1.45652927e-01,
   2.04121963e-01]]

我的 Sb 值：

[1.29960e+02, 4.09600e+01, 4.00000e-02, 9.24160e+02, 1.00000e+00, 5.10760e+02,
 7.95240e+02, 8.50084e+03, 7.84000e+00, 5.21284e+03, 1.96000e+02, 1.63840e+02,
 3.38560e+02, 1.96000e+00, 3.68640e+02, 3.60000e-01, 4.00000e-02, 2.50000e+01,
 3.38560e+02, 3.53440e+02]

我如何尝试乘法：

invSw_by_Sb = np.dot(invSw, Sb)

整个代码：

c_A_array = [[ 31,  25,  17,  62,  26,  23, 193, 143,  37,  29, 220, 216, 175, 195, 207, 198, 190, 222, 178, 214],
 [ 31,  26,  19,  59,  25,  23, 193, 140,  37,  29, 220, 216, 174, 195, 207, 198, 190, 220, 178, 214],
 [ 31,  23,  17,  67,  23,  22, 195, 147,  38,  31, 222, 215, 182, 195, 213, 198, 185, 221, 178, 207],
 [ 31,  23,  19,  67,  23,  23, 194, 144,  37,  31, 222, 218, 179, 198, 216, 198, 186, 221, 179, 207],
 [ 31,  28,  17,  65,  23,  22, 193, 142,  36,  31, 222, 217, 177, 195, 216, 196, 182, 220, 174, 207]]

c_B_array = [[ 16,  24,  33,  43,  43,  58, 163,  76,  57, 105, 205, 200, 193, 188, 186, 193, 182, 227, 193, 227],
 [  9,  13,  22,  36,  13,  49, 163,  39,  33, 105, 204, 200, 193, 191, 188, 193, 183, 224, 194, 227],
 [ 23,  17,  10,  28,  21,  40, 166,  46,  28, 102, 208, 206, 196, 198, 195, 202, 190, 225, 196, 229],
 [ 25,  19,  11,  30,  23,  39, 166,  46,  26,  99, 208, 206, 199, 196, 198, 201, 189, 227, 198, 231],
 [ 25,  20,  12,  31,  25,  40, 169,  48,  27, 101, 211, 206, 198, 198, 196, 202, 190, 226, 198, 229]]

c_A_array = np.asarray(c_A_array)
c_B_array = np.asarray(c_B_array)


c_1_mean = c_A_array.mean(axis=0)
c_2_mean = c_B_array.mean(axis=0)

S1_c1 = np.cov(c_A_array)
S2_c2 = np.cov(c_B_array)
Sw = S1_c1 + S2_c2 


Sb = (c_1_mean - c_2_mean) * (c_1_mean - c_2_mean)
invSw = np.linalg.inv(Sw)
invSw_by_Sb = np.dot(invSw, Sb)
[V, D] = np.linalg.eig(invSw_by_Sb)

标签： pythonpython-3.xnumpymachine-learningstatistics

解决方案

您正在为 np.cov 和 np.mean 使用不同的维度。如果您想使用 np.mean(..., axis=0)，那么您还应该更改 cov 的维度，如下所示：

c_1_mean = c_A_array.mean(axis=0)
c_2_mean = c_B_array.mean(axis=0)
S1_c1 = np.cov(c_A_array.T)
S2_c2 = np.cov(c_B_array.T)
Sw = S1_c1 + S2_c2

此外，您的 Sb 应该是协方差矩阵：

Sb = (c_1_mean - c_2_mean) * (c_1_mean - c_2_mean).reshape([-1, 1])

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