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test_similarities.py
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test_similarities.py
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"""
Module for testing the similarity measures
"""
import random
import numpy as np
import surprise.similarities as sims
n_x = 8
yr_global = {
0: [(0, 3), (1, 3), (2, 3), (5, 1), (6, 1.5), (7, 3)], # noqa
1: [
(0, 4),
(1, 4),
(2, 4),
], # noqa
2: [(2, 5), (3, 2), (4, 3)], # noqa
3: [(1, 1), (2, 4), (3, 2), (4, 3), (5, 3), (6, 3.5), (7, 2)], # noqa
4: [(1, 5), (2, 1), (5, 2), (6, 2.5), (7, 2.5)], # noqa
}
def test_cosine_sim():
"""Tests for the cosine similarity."""
yr = yr_global.copy()
# shuffle every rating list, to ensure the order in which ratings are
# processed does not matter (it's important because it used to be error
# prone when we were using itertools.combinations)
for _, ratings in yr.items():
random.shuffle(ratings)
sim = sims.cosine(n_x, yr, min_support=1)
# check symmetry and bounds (as ratings are > 0, cosine sim must be >= 0)
for xi in range(n_x):
assert sim[xi, xi] == 1
for xj in range(n_x):
assert sim[xi, xj] == sim[xj, xi]
assert 0 <= sim[xi, xj] <= 1
# on common items, users 0, 1 and 2 have the same ratings
assert sim[0, 1] == 1
assert sim[0, 2] == 1
# for vectors with constant ratings (even if they're different constants),
# cosine sim is necessarily 1
assert sim[3, 4] == 1
# pairs of users (0, 3) have no common items
assert sim[0, 3] == 0
assert sim[0, 4] == 0
# check for float point support and computation correctness
dot_product56 = 1 * 1.5 + 3 * 3.5 + 2 * 2.5
assert sim[5, 6] == (
dot_product56
/ ((1**2 + 3**2 + 2**2) * (1.5**2 + 3.5**2 + 2.5**2)) ** 0.5
)
# ensure min_support is taken into account. Only users 1 and 2 have more
# than 4 common ratings.
sim = sims.cosine(n_x, yr, min_support=4)
for i in range(n_x):
for j in range(i + 1, n_x):
if i != 1 and j != 2:
assert sim[i, j] == 0
def test_msd_sim():
"""Tests for the MSD similarity."""
yr = yr_global.copy()
# shuffle every rating list, to ensure the order in which ratings are
# processed does not matter (it's important because it used to be error
# prone when we were using itertools.combinations)
for _, ratings in yr.items():
random.shuffle(ratings)
sim = sims.msd(n_x, yr, min_support=1)
# check symmetry and bounds. MSD sim must be in [0, 1]
for xi in range(n_x):
assert sim[xi, xi] == 1
for xj in range(n_x):
assert sim[xi, xj] == sim[xj, xi]
assert 0 <= sim[xi, xj] <= 1
# on common items, users 0, 1 and 2 have the same ratings
assert sim[0, 1] == 1
assert sim[0, 2] == 1
# msd(3, 4) = mean(1^2, 1^2). sim = (1 / (1 + msd)) = 1 / 2
assert sim[3, 4] == 0.5
# pairs of users (0, 3) have no common items
assert sim[0, 3] == 0
assert sim[0, 4] == 0
# ensure min_support is taken into account. Only users 1 and 2 have more
# than 4 common ratings.
sim = sims.msd(n_x, yr, min_support=4)
for i in range(n_x):
for j in range(i + 1, n_x):
if i != 1 and j != 2:
assert sim[i, j] == 0
def test_pearson_sim():
"""Tests for the pearson similarity."""
yr = yr_global.copy()
# shuffle every rating list, to ensure the order in which ratings are
# processed does not matter (it's important because it used to be error
# prone when we were using itertools.combinations)
for _, ratings in yr.items():
random.shuffle(ratings)
sim = sims.pearson(n_x, yr, min_support=1)
# check symmetry and bounds. -1 <= pearson coeff <= 1
for xi in range(n_x):
assert sim[xi, xi] == 1
for xj in range(n_x):
assert sim[xi, xj] == sim[xj, xi]
assert -1 <= sim[xi, xj] <= 1
# on common items, users 0, 1 and 2 have the same ratings
assert sim[0, 1] == 1
assert sim[0, 2] == 1
# for vectors with constant ratings, pearson sim is necessarily zero (as
# ratings are centered)
assert sim[3, 4] == 0
assert sim[2, 3] == 0
assert sim[2, 4] == 0
# pairs of users (0, 3), have no common items
assert sim[0, 3] == 0
assert sim[0, 4] == 0
# almost same ratings (just with an offset of 0.5)
assert sim[5, 6] == 1
# ratings vary in the same direction
assert sim[2, 5] > 0
# check for float point support and computation correctness
mean6 = (1.5 + 3.5 + 2.5) / 3
var6 = (1.5 - mean6) ** 2 + (3.5 - mean6) ** 2 + (2.5 - mean6) ** 2
mean7 = (3 + 2 + 2.5) / 3
var7 = (3 - mean7) ** 2 + (2 - mean7) ** 2 + (2.5 - mean7) ** 2
num = sum(
[
((1.5 - mean6) * (3 - mean7)),
((3.5 - mean6) * (2 - mean7)),
((2.5 - mean6) * (2.5 - mean7)),
]
)
assert sim[6, 7] == num / (var6 * var7) ** 0.5
# ensure min_support is taken into account. Only users 1 and 2 have more
# than 4 common ratings.
sim = sims.pearson(n_x, yr, min_support=4)
for i in range(n_x):
for j in range(i + 1, n_x):
if i != 1 and j != 2:
assert sim[i, j] == 0
def test_pearson_baseline_sim():
"""Tests for the pearson_baseline similarity."""
yr = yr_global.copy()
# shuffle every rating list, to ensure the order in which ratings are
# processed does not matter (it's important because it used to be error
# prone when we were using itertools.combinations)
for _, ratings in yr.items():
random.shuffle(ratings)
global_mean = 3 # fake
x_biases = np.random.normal(0, 1, n_x) # fake
y_biases = np.random.normal(0, 1, 5) # fake (there are 5 ys)
sim = sims.pearson_baseline(n_x, yr, 1, global_mean, x_biases, y_biases)
# check symmetry and bounds. -1 <= pearson coeff <= 1
for xi in range(n_x):
assert sim[xi, xi] == 1
for xj in range(n_x):
assert sim[xi, xj] == sim[xj, xi]
assert -1 <= sim[xi, xj] <= 1
# Note: as sim now depends on baselines, which depend on both users and
# items ratings, it's now impossible to test assertions such that 'as users
# have the same ratings, they should have a maximal similarity'. Both users
# AND common items should have same ratings.
# pairs of users (0, 3), have no common items
assert sim[0, 3] == 0
assert sim[0, 4] == 0
# ensure min_support is taken into account. Only users 1 and 2 have more
# than 4 common ratings.
sim = sims.pearson_baseline(n_x, yr, 4, global_mean, x_biases, y_biases)
for i in range(n_x):
for j in range(i + 1, n_x):
if i != 1 and j != 2:
assert sim[i, j] == 0