如何将高维向量可视化为二维平面中的点？答案

【问题标题】：How to visualize high-dimension vectors as points in 2D plane?如何将高维向量可视化为二维平面中的点？
【发布时间】：2021-10-15 01:21:24
【问题描述】：

例如，有如下三个向量。

[ 0.0377,  0.1808,  0.0807, -0.0703,  0.2427, -0.1957, -0.0712, -0.2137,
     -0.0754, -0.1200,  0.1919,  0.0373,  0.0536,  0.0887, -0.1916, -0.1268,
     -0.1910, -0.1411, -0.1282,  0.0274, -0.0781,  0.0138, -0.0654,  0.0491,
      0.0398,  0.1696,  0.0365,  0.2266,  0.1241,  0.0176,  0.0881,  0.2993,
     -0.1425, -0.2535,  0.1801, -0.1188,  0.1251,  0.1840,  0.1112,  0.3172,
      0.0844, -0.1142,  0.0662,  0.0910,  0.0416,  0.2104,  0.0781, -0.0348,
     -0.1488,  0.0129],
 [-0.1302,  0.1581, -0.0897,  0.1024, -0.1133,  0.1076,  0.1595, -0.1047,
      0.0760,  0.1092,  0.0062, -0.1567, -0.1448, -0.0548, -0.1275, -0.0689,
     -0.1293,  0.1024,  0.1615,  0.0869,  0.2906, -0.2056,  0.0442, -0.0595,
     -0.1448,  0.0167, -0.1259, -0.0989,  0.0651, -0.0424,  0.0795, -0.1546,
      0.1330, -0.2284,  0.1672,  0.1847,  0.0841,  0.1771, -0.0101, -0.0681,
      0.1497,  0.1226,  0.1146, -0.2090,  0.3275,  0.0981, -0.3295,  0.0590,
      0.1130, -0.0650],
 [-0.1745, -0.1940, -0.1529, -0.0964,  0.2657, -0.0979,  0.1510, -0.1248,
     -0.1541,  0.1782, -0.1769, -0.2335,  0.2011,  0.1906, -0.1918,  0.1896,
     -0.2183, -0.1543,  0.1816,  0.1684, -0.1318,  0.2285,  0.1784,  0.2260,
     -0.2331,  0.0523,  0.1882,  0.1764, -0.1686,  0.2292]

如何将它们绘制为同一个 2D 平面中的三个点，如下图所示？谢谢！

【问题讨论】：

降维算法从维度 N -> 维度 M 中找到了一个很好的表示。因此，它们要求原始向量都具有相同的形状，而这 3 个不是（前两个是长度 50 , 最后一个是 30)。你确定第三个是正确的吗？
是的，第三个是正确的。所以我也想知道在同一个二维平面上可视化不同维度的向量？

标签： python scikit-learn visualization pca

【解决方案1】：

我使用来自sklearn 的PCA，也许这段代码对你有帮助：

import matplotlib.pyplot as plt
import numpy as np
from sklearn.decomposition import PCA

usa = [ 0.0377,  0.1808,  0.0807, -0.0703,  0.2427, -0.1957, -0.0712, -0.2137,
     -0.0754, -0.1200,  0.1919,  0.0373,  0.0536,  0.0887, -0.1916, -0.1268,
     -0.1910, -0.1411, -0.1282,  0.0274, -0.0781,  0.0138, -0.0654,  0.0491,
      0.0398,  0.1696,  0.0365,  0.2266,  0.1241,  0.0176,  0.0881,  0.2993,
     -0.1425, -0.2535,  0.1801, -0.1188,  0.1251,  0.1840,  0.1112,  0.3172,
      0.0844, -0.1142,  0.0662,  0.0910,  0.0416,  0.2104,  0.0781, -0.0348,
     -0.1488,  0.0129]
obama =  [-0.1302,  0.1581, -0.0897,  0.1024, -0.1133,  0.1076,  0.1595, -0.1047,
      0.0760,  0.1092,  0.0062, -0.1567, -0.1448, -0.0548, -0.1275, -0.0689,
     -0.1293,  0.1024,  0.1615,  0.0869,  0.2906, -0.2056,  0.0442, -0.0595,
     -0.1448,  0.0167, -0.1259, -0.0989,  0.0651, -0.0424,  0.0795, -0.1546,
      0.1330, -0.2284,  0.1672,  0.1847,  0.0841,  0.1771, -0.0101, -0.0681,
      0.1497,  0.1226,  0.1146, -0.2090,  0.3275,  0.0981, -0.3295,  0.0590,
      0.1130, -0.0650]
nationality =  [-0.1745, -0.1940, -0.1529, -0.0964,  0.2657, -0.0979,  0.1510, -0.1248,
     -0.1541,  0.1782, -0.1769, -0.2335,  0.2011,  0.1906, -0.1918,  0.1896,
     -0.2183, -0.1543,  0.1816,  0.1684, -0.1318,  0.2285,  0.1784,  0.2260,
     -0.2331,  0.0523,  0.1882,  0.1764, -0.1686,  0.2292]


pca = PCA(n_components=1)

X = np.array(usa).reshape(2,len(usa)//2)
X = pca.fit_transform(X)

Y = np.array(obama).reshape(2,len(obama)//2)
Y = pca.fit_transform(Y)

Z = np.array(nationality).reshape(2,len(nationality)//2)
Z = pca.fit_transform(Z)



x_coordinates = [X[0][0], Y[0][0], Z[0][0]]
y_coordinates = [X[1][0], Y[1][0], Z[1][0]]
colors = ['r','g','b']
annotations=["U.S.A","Obama","Nationality"]

plt.figure(figsize=(8,6))
plt.scatter(x_coordinates, y_coordinates, marker=",", color=colors,s=300)

for i, label in enumerate(annotations):
    plt.annotate(label, (x_coordinates[i], y_coordinates[i]))
    

plt.show()

输出：

【讨论】：