Question

这是我用来计算直接邻居计数的单词共生矩阵的代码。我在网上找到了以下代码，它使用了SVD。

 import numpy as np
 la = np.linalg
 words = ['I','like','enjoying','deep','learning','NLP','flying','.']
 ### A Co-occurence matrix which counts how many times the word before and after a particular word appears ( ie, like appears after I 2 times)
 arr = np.array([[0,2,1,0,0,0,0,0],[2,0,0,1,0,1,0,0],[1,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,1],[0,1,0,0,0,0,0,1],[0,0,1,0,0,0,0,8],[0,2,1,0,0,0,0,0],[0,0,1,1,1,0,0,0]])
 u, s, v = la.svd(arr, full_matrices=False)
 import matplotlib.pyplot as plt
 for i in xrange(len(words)):
     plt.text(u[i,2], u[i,3], words[i])

在最后一行代码中，U的第一个元素用作x坐标，U的第二个元素用作y坐标以投影单词，以查看相似性。 这种方法背后的直觉是什么？为什么他们将每行中的第1和第2个元素（每行代表每个单词）作为x和y来表示单词？请帮忙。

Answer 1

import numpy as np
import matplotlib.pyplot as plt
la = np.linalg
words = ["I", "like", "enjoy", "deep", "learning", "NLP", "flying", "."]
X = np.array([[0,2,1,0,0,0,0,0], [2,0,0,1,0,1,0,0], [1,0,0,0,0,0,1,0], [0,1,0,0,1,0,0,0], [0,0,0,1,0,0,0,1], [0,1,0,0,0,0,0,1], [0,0,1,0,0,0,0,1], [0,0,0,0,1,1,1,0]])
U, s, Vh = la.svd(X, full_matrices = False)

#plot
for i in range(len(words)):
    plt.text(U[i,0], U[i,1], words[i])
plt.show()

在图中，向左平移轴，您将看到所有单词。

Answer 2

定义SVD的方式，您从s方法获得的la.svd矩阵是一个对角矩阵，包含降序的奇异值。选取u的前两列可确保您选择原始矩阵中最重要的组件。

此过程也称为降维。请阅读here（第11.3.3节）和here。

使用SVD绘制单词矢量来测量相似度

2 个答案: