Using SVD to plot word vector to measure similarity

Question

This is the code I am using to calculate a word co-occurrence matrix for immediate neighbor counts. I found the following code on the net, which uses 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])

In the last line of code, the first element of U is used as an x-coordinate and the second element of U is used as a y-coordinate to project the words, to see the similarity. What is the intuition behind this approach? Why they are taking the 1st and 2nd elements in each row (each row represents each word) as x and y to represent a word? Please help.

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()

In the plot, pan axes towards left and you will see all the words.