import numpy as np
import matplotlib.pyplot as plt
%config InlineBackend.figure_format = 'retina'

def angle_between(v1, v2):
    cos_theta = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
    return np.arccos(np.clip(cos_theta, -1.0, 1.0)) * 180 / np.pi

v1 = np.array([1, 0])
v2 = np.array([1, 1])

plt.quiver([0, 0], [0, 0], [v1[0], v2[0]], [v1[1], v2[1]], angles='xy', scale_units='xy', scale=1)
plt.xlim(-1, 2)
plt.ylim(-1, 2)

print(f"Angle: {angle_between(v1, v2):.2f}°")

Angle: 45.00°

print(f"Angle: {angle_between(v1, np.array([0, 1])):.2f}°")
plt.quiver([0, 0], [0, 0], [v1[0], 0], [v1[1], 1], angles='xy', scale_units='xy', scale=1)
plt.xlim(-1, 2)
plt.ylim(-1, 2)

Angle: 90.00°

import gensim.downloader as api
from scipy.spatial.distance import cosine

model = api.load("glove-wiki-gigaword-50")  # Small 50D GloVe model

def get_cosine_similarity(word1, word2):
    v1 = model[word1]
    v2 = model[word2]
    return angle_between(v1, v2)

word1 = "king"
v1 = model[word1]

v1

array([ 0.50451 ,  0.68607 , -0.59517 , -0.022801,  0.60046 , -0.13498 ,
       -0.08813 ,  0.47377 , -0.61798 , -0.31012 , -0.076666,  1.493   ,
       -0.034189, -0.98173 ,  0.68229 ,  0.81722 , -0.51874 , -0.31503 ,
       -0.55809 ,  0.66421 ,  0.1961  , -0.13495 , -0.11476 , -0.30344 ,
        0.41177 , -2.223   , -1.0756  , -1.0783  , -0.34354 ,  0.33505 ,
        1.9927  , -0.04234 , -0.64319 ,  0.71125 ,  0.49159 ,  0.16754 ,
        0.34344 , -0.25663 , -0.8523  ,  0.1661  ,  0.40102 ,  1.1685  ,
       -1.0137  , -0.21585 , -0.15155 ,  0.78321 , -0.91241 , -1.6106  ,
       -0.64426 , -0.51042 ], dtype=float32)

word2 = "queen"
v2 = model[word2]
print(v2)

[ 0.37854    1.8233    -1.2648    -0.1043     0.35829    0.60029
 -0.17538    0.83767   -0.056798  -0.75795    0.22681    0.98587
  0.60587   -0.31419    0.28877    0.56013   -0.77456    0.071421
 -0.5741     0.21342    0.57674    0.3868    -0.12574    0.28012
  0.28135   -1.8053    -1.0421    -0.19255   -0.55375   -0.054526
  1.5574     0.39296   -0.2475     0.34251    0.45365    0.16237
  0.52464   -0.070272  -0.83744   -1.0326     0.45946    0.25302
 -0.17837   -0.73398   -0.20025    0.2347    -0.56095   -2.2839
  0.0092753 -0.60284  ]

angle_between(v1, v2)

38.3805515334704

angle_between(model["uncle"], model["aunt"])

40.26145236751397

# Now some dissimilar words
angle_between(model["king"], model["python"])

79.36413285046953

model.most_similar("king")

[('prince', 0.8236179351806641),
 ('queen', 0.7839044332504272),
 ('ii', 0.7746230363845825),
 ('emperor', 0.7736247777938843),
 ('son', 0.766719400882721),
 ('uncle', 0.7627150416374207),
 ('kingdom', 0.7542160749435425),
 ('throne', 0.7539914846420288),
 ('brother', 0.7492411136627197),
 ('ruler', 0.7434254288673401)]

# most dissimilar words to "king"
model.most_similar(negative=["king"])

[('4,835', 0.729358434677124),
 ('rules-based', 0.7123876810073853),
 ('renos', 0.7085371613502502),
 ('meawhile', 0.706490159034729),
 ('nanobiotechnology', 0.6925080418586731),
 ('m-42', 0.6916395425796509),
 ('poligny', 0.6882078051567078),
 ('onyekwe', 0.6877189874649048),
 ('asie', 0.6861312985420227),
 ('metabolomics', 0.682388961315155)]

angle_between(model["king"], model["rules-based"])

135.42952204160463