A quick benchmark for computing a metric based on the cosine distance

cosine_distance_metric_benchmark.py

from math import sqrt, acos
import numpy as np

def make_test_arrays(N, norm=True):  
    X = np.random.rand(N)
    Y = np.random.rand(N)
    if norm:
        X /= np.linalg.norm(X)
        Y /= np.linalg.norm(Y)
    return X, Y

def euclidean_dist(X, Y):
    XY = X - Y
    return sqrt(XY.dot(XY))

def cosine_dist(X, Y):
    """Not a metric in general"""
    X = X / np.linalg.norm(X)
    Y = Y / np.linalg.norm(Y)
    return 1 - X.dot(Y)

def cosine_dist_spherical(X, Y):
    """Assumes that X, Y are L2 normalized,
    this is a metric, equal to euclidean_dist/2
    """
    return 1 - X.dot(Y)

def arccosine_dist_spherical(X, Y):
    """Assumes that X, Y are L2 normalized, just to check
    the acos overhead"""
    return acos(X.dot(Y))


X, Y = make_test_arrays(10000, norm=True)

%timeit euclidean_dist(X, Y)
%timeit cosine_dist(X, Y)
%timeit cosine_dist_spherical(X, Y)
%timeit arccosine_dist_spherical(X, Y)
## Returns
# 100000 loops, best of 3: 11 µs per loop
# The slowest run took 5.40 times longer than the fastest. This could mean that an intermediate result is being cached.
# 10000 loops, best of 3: 43.6 µs per loop
# The slowest run took 18.30 times longer than the fastest. This could mean that an intermediate result is being cached.
# 100000 loops, best of 3: 4.73 µs per loop
# The slowest run took 5.81 times longer than the fastest. This could mean that an intermediate result is being cached.
# 100000 loops, best of 3: 4.41 µs per loop