WSS-project/P4. Appendix - embeddings in high demensional spaces.ipynb

import numpy as np
import pandas as pd
import random
from numpy.linalg import norm

dimensions = [1, 2, 3] + [10 * i for i in range(1, 10)]
nb_vectors = 10000
trials = 100
k = 1  # by setting k=1 we want to check how often the closest vector to the avarage of 2 random vectors is one of these 2 vectors

result = []
for dimension in dimensions:
    vectors = np.random.normal(0, 1, size=(nb_vectors, dimension))
    successes = 0
    for i in range(trials):
        i1, i2 = random.sample(range(nb_vectors), 2)
        target = (vectors[i1] + vectors[i2]) / 2

        distances = pd.DataFrame(
            enumerate(
                np.dot(target, vectors.transpose())
                / norm(target)
                / norm(vectors.transpose(), axis=0)
            )
        )
        distances = distances.sort_values(by=[1], ascending=False)
        if (i1 in (list(distances[0][:k]))) | (i2 in (list(distances[0][:k]))):
            successes += 1
    result.append(successes / trials)

[
    f"dimensions: {i}, cases when observation is the nearest: {100*round(j,3)}%"
    for i, j in zip(dimensions, result)
]

['dimensions: 1, cases when observation is the nearest: 0.0%',
 'dimensions: 2, cases when observation is the nearest: 0.0%',
 'dimensions: 3, cases when observation is the nearest: 0.0%',
 'dimensions: 10, cases when observation is the nearest: 13.0%',
 'dimensions: 20, cases when observation is the nearest: 61.0%',
 'dimensions: 30, cases when observation is the nearest: 96.0%',
 'dimensions: 40, cases when observation is the nearest: 98.0%',
 'dimensions: 50, cases when observation is the nearest: 100.0%',
 'dimensions: 60, cases when observation is the nearest: 100.0%',
 'dimensions: 70, cases when observation is the nearest: 100.0%',
 'dimensions: 80, cases when observation is the nearest: 100.0%',
 'dimensions: 90, cases when observation is the nearest: 100.0%']