We have briefly described how to plot the figures in the Analysis on Entity Embeddings section.

RotatE:
Each dimension of entity embeddings is a complex number---(re, im). Thus, we can regard the embeddings of an entity as a group of 2D points and plot them on a 2D plane.

HAKE:
HAKE maps entities into the polar coordinate system. Therefore, we can also plot the entity embeddings generated by HAKE on a 2D plane based on their polar coordinates. We use the logarithmic scale to better display the differences between entity embeddings.
The figures in the paper are plotted using matlab. The skeleton of the corresponding python code is as follows.

import numpy as np
import matplotlib.pyplot as plt
import os

"""
model_path
embedding_range
head_id 
tail_id 
"""
entity_embedding = np.load(os.path.join(model_path, 'entity_embedding.npy'))

head = entity_embedding[head_id]
tail = entity_embedding[tail_id]

phase_head, mod_head = np.split(head, 2)
phase_tail, mod_tail = np.split(tail, 2)

mod_head = np.log(np.abs(mod_head))  * np.sign(mod_head)
mod_tail = np.log(np.abs(mod_tail))  * np.sign(mod_tail)

phase_head = phase_head / embedding_range * np.pi
phase_tail = phase_tail / embedding_range * np.pi

x_head, y_head = mod_head * np.cos(phase_head), mod_head * np.sin(phase_head)
x_tail, y_tail = mod_tail * np.cos(phase_tail), mod_tail * np.sin(phase_tail)

plt.scatter(x_head, y_head)
plt.scatter(x_tail, y_tail)
plt.axis('equal')
plt.show()

About the 2D plane. #2

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