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Add mutual information metric to association_rules #1182

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Add mutual information metric to association_rules #1182

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17 changes: 17 additions & 0 deletions mlxtend/frequent_patterns/association_rules.py
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Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@
"jaccard",
"certainty",
"kulczynski",
"mutual_information",
]


Expand Down Expand Up @@ -142,6 +143,19 @@ def kulczynski_helper(sAC, sA, sC, disAC, disA, disC, dis_int, dis_int_):
kulczynski = (conf_AC + conf_CA) / 2
return kulczynski

def mutual_information_metric_helper(
sAC, sA, sC, disAC, disA, disC, dis_int, dis_int_
):
with np.errstate(divide="ignore", invalid="ignore"):
numerator = sAC
denominator = sA * sC
mi = np.where(
(numerator > 0) & (denominator > 0),
np.log2(numerator / denominator),
-np.inf,
)
return mi

def conviction_helper(conf, sC):
conviction = np.empty(conf.shape, dtype=float)
if not len(conviction.shape):
Expand Down Expand Up @@ -223,6 +237,9 @@ def certainty_metric_helper(sAC, sA, sC, disAC, disA, disC, dis_int, dis_int_):
"kulczynski": lambda sAC, sA, sC, _, __, ____, _____, ______: kulczynski_helper(
sAC, sA, sC, disAC, disA, disC, dis_int, dis_int_
),
"mutual_information": lambda sAC, sA, sC, _, __, ____, _____, ______: mutual_information_metric_helper(
sAC, sA, sC, disAC, disA, disC, dis_int, dis_int_
),
}

# check for metric compliance
Expand Down
80 changes: 70 additions & 10 deletions mlxtend/frequent_patterns/tests/test_association_rules.py
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Original file line number Diff line number Diff line change
Expand Up @@ -50,6 +50,7 @@
"jaccard",
"certainty",
"kulczynski",
"mutual_information",
]


Expand All @@ -65,15 +66,15 @@ def test_default():

expect = pd.DataFrame(
[
[(8,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
[(6,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
[(8, 3), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
[(8, 5), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 1.0, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875],
[(8,), (3, 5), 0.6, 0.8, 0.6, 1.0, 1.25, 1.0, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875],
[(3,), (5,), 0.8, 1.0, 0.8, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.8, 0.0, 0.9],
[(5,), (3,), 1.0, 0.8, 0.8, 0.8, 1.0, 1.0, 0.0, 1.0, 0.0, 0.8, 0.0, 0.9],
[(10,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8],
[(8,), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 1.0, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875],
[(8,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8, 0.0],
[(6,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8, 0.0],
[(8, 3), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8, 0.0],
[(8, 5), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 1.0, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875, 0.0],
[(8,), (3, 5), 0.6, 0.8, 0.6, 1.0, 1.25, 1.0, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875, 0.0],
[(3,), (5,), 0.8, 1.0, 0.8, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.8, 0.0, 0.9, 0.0],
[(5,), (3,), 1.0, 0.8, 0.8, 0.8, 1.0, 1.0, 0.0, 1.0, 0.0, 0.8, 0.0, 0.9, 0.0],
[(10,), (5,), 0.6, 1.0, 0.6, 1.0, 1.0, 1.0, 0.0, np.inf, 0, 0.6, 0.0, 0.8, 0.0],
[(8,), (3,), 0.6, 0.8, 0.6, 1.0, 1.25, 1.0, 0.12, np.inf, 0.5, 0.75, 1.0, 0.875, 0.0],
],

columns=columns_ordered,
Expand Down Expand Up @@ -120,6 +121,7 @@ def test_nullability():
0.667,
0,
0.833,
0.0,
],
[
(10, 5),
Expand All @@ -136,6 +138,7 @@ def test_nullability():
0.667,
0.0,
0.833,
0.0,
],
[
(10,),
Expand All @@ -152,6 +155,7 @@ def test_nullability():
0.615,
0.0,
0.833,
0.415,
],
[
(10,),
Expand All @@ -168,6 +172,7 @@ def test_nullability():
0.615,
0.0,
0.833,
0.415,
],
[
(10,),
Expand All @@ -184,6 +189,7 @@ def test_nullability():
0.615,
0,
0.833,
-0.169,
],
[
(3, 5),
Expand All @@ -200,6 +206,7 @@ def test_nullability():
0.615,
-0.333,
0.833,
-0.169,
],
[
(3,),
Expand All @@ -216,6 +223,7 @@ def test_nullability():
0.667,
0.0,
0.833,
0.0,
],
[
(3,),
Expand All @@ -232,6 +240,7 @@ def test_nullability():
0.615,
-0.333,
0.833,
-0.169,
],
[(3,), (5,), 1.0, 1.0, 1.0, 1.0, 1.0, 0.8, 0.0, np.inf, 0, 1.0, 0, 1.0],
[
Expand All @@ -249,6 +258,7 @@ def test_nullability():
0.667,
0,
0.833,
0.0,
],
[
(5,),
Expand All @@ -265,8 +275,25 @@ def test_nullability():
0.615,
-0.333,
0.833,
-0.169,
],
[
(5,),
(3,),
1.0,
1.0,
1.0,
1.0,
1.0,
0.8,
0.0,
np.inf,
0,
1.0,
0.0,
1.0,
0.0,
],
[(5,), (3,), 1.0, 1.0, 1.0, 1.0, 1.0, 0.8, 0.0, np.inf, 0, 1.0, 0.0, 1.0],
],
columns=columns_ordered,
)
Expand Down Expand Up @@ -335,6 +362,7 @@ def test_empty_result():
"jaccard",
"certainty",
"kulczynski",
"mutual_information",
]
)
res_df = association_rules(df_freq_items, len(df), min_threshold=2)
Expand Down Expand Up @@ -540,3 +568,35 @@ def test_with_empty_dataframe():
df_freq = df_freq_items_with_colnames.iloc[:0]
with pytest.raises(ValueError):
association_rules(df_freq, len(df))


def test_mutual_information_metric():
"""Test mutual_information metric returns correct values."""
import math

res_df = association_rules(
df_freq_items_with_colnames,
len(df),
metric="mutual_information",
min_threshold=-100,
)
assert "mutual_information" in res_df.columns

# Eggs -> Kidney Beans: sAC=0.6, sA=0.8, sC=1.0
# MI = log2(0.6 / (0.8 * 1.0)) = log2(0.75) approx -0.415
rule = res_df[
res_df["antecedents"].apply(lambda x: x == frozenset({"Eggs"}))
& res_df["consequents"].apply(lambda x: x == frozenset({"Kidney Beans"}))
]
assert len(rule) == 1
expected_mi = math.log2(0.6 / (0.8 * 1.0))
assert abs(rule["mutual_information"].values[0] - expected_mi) < 1e-6

# Milk -> Kidney Beans: sAC=0.6, sA=0.6, sC=1.0
# MI = log2(0.6 / (0.6 * 1.0)) = log2(1) = 0
milk_rule = res_df[
res_df["antecedents"].apply(lambda x: x == frozenset({"Milk"}))
& res_df["consequents"].apply(lambda x: x == frozenset({"Kidney Beans"}))
]
assert len(milk_rule) == 1
assert abs(milk_rule["mutual_information"].values[0]) < 1e-6
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