Chapter 116 · Solutions
Association Rule Mining · Solutions
Five challenges, each verified in code.
Chapter 116 · Practice Challenges, Solved¶
Five market-basket exercises, worked in mlxtend on the Chapter 116 grocery transactions.
In [1]:
import numpy as np, pandas as pd, matplotlib.pyplot as plt
import seaborn as sns # seaborn = high-level statistical plots (heatmaps, pairplots, count/bar plots)
from matplotlib.colors import ListedColormap
EM="#4338ca"; DEEP="#3730a3"; LIGHT="#c7d2fe"; INK="#1a2138"; GRID="#e6e9f2"; RED="#ef4444"; AMBER="#d97706"; GREEN="#059669"; BLUE="#2563eb"; PUR="#9333ea"; GREY="#94a3b8"; SLATE="#475569"; ORG="#4338ca"; CYAN="#0891b2"
plt.rcParams.update({"figure.facecolor":"white","axes.facecolor":"white","figure.dpi":110,"font.size":11,
"axes.edgecolor":GRID,"axes.grid":True,"grid.color":GRID,"axes.axisbelow":True,"axes.spines.top":False,
"axes.spines.right":False,"axes.titlesize":12,"axes.titleweight":"bold","legend.frameon":False})
sns.set_style("whitegrid")
BASE="https://raw.githubusercontent.com/johnfisher-ai/Statistics-Data-Science-AI-Visual-Book/main/data/"
In [2]:
from mlxtend.frequent_patterns import apriori, fpgrowth, association_rules
try: df = pd.read_excel('../../data/association-rule-mining--baskets.xlsx', sheet_name='Data')
except FileNotFoundError: df = pd.read_excel(BASE + 'association-rule-mining--baskets.xlsx', sheet_name='Data')
basket = df.assign(v=1).pivot_table(index='transaction_id', columns='item', values='v', fill_value=0).astype(bool)
print('basket matrix:', basket.shape)
basket matrix: (900, 25)
CHALLENGE 1
Most frequent item
Build the basket matrix and report the item with the highest support.
In [3]:
support = basket.mean().sort_values(ascending=False)
print(support.head(5).round(3).to_string())
print('most frequent item:', support.idxmax(), '(support %.2f)' % support.max())
item bread 0.334 jam 0.187 cereal 0.172 butter 0.170 bacon 0.167 most frequent item: bread (support 0.33)
Solution. Bread has the highest support (in about a third of baskets), the popular staple every rule must be compared against.
CHALLENGE 2
Frequent itemsets
Run Apriori at min_support = 0.05 and count the frequent itemsets.
In [4]:
freq = apriori(basket, min_support=0.05, use_colnames=True)
print('frequent itemsets at 5% support:', len(freq))
print(freq['itemsets'].apply(len).value_counts().sort_index().to_string())
frequent itemsets at 5% support: 54 itemsets 1 25 2 20 3 8 4 1
Solution. A higher support threshold keeps fewer, more reliable itemsets, tune it to trade coverage against trustworthiness.
CHALLENGE 3
Top rule by lift
Mine rules and report the single highest-lift rule.
In [5]:
freq = apriori(basket, min_support=0.03, use_colnames=True)
rules = association_rules(freq, metric='lift', min_threshold=1.0)
rules['A'] = rules['antecedents'].apply(lambda s: ', '.join(sorted(s)))
rules['B'] = rules['consequents'].apply(lambda s: ', '.join(sorted(s)))
best = rules.sort_values('lift', ascending=False).iloc[0]
print('top rule: %s -> %s | support %.3f, confidence %.3f, lift %.2f' % (best.A, best.B, best.support, best.confidence, best.lift))
top rule: salsa -> chips, soda | support 0.092, confidence 0.615, lift 5.70
Solution. The strongest rules link the cookout items (chips, salsa, soda) with lift above 5, buying two of them makes the third far likelier than average.
CHALLENGE 4
Confidence vs lift
Find the lift of bananas -> bread and explain why its high-ish confidence is misleading.
In [6]:
r = rules[(rules.A=='bananas') & (rules.B=='bread')][['support','confidence','lift']]
print(r.round(3).to_string(index=False))
print('bread baseline support = %.2f' % basket['bread'].mean())
print('confidence 0.37 barely beats the 0.33 baseline -> lift ~1.1 -> essentially independent')
support confidence lift 0.047 0.368 1.102 bread baseline support = 0.33 confidence 0.37 barely beats the 0.33 baseline -> lift ~1.1 -> essentially independent
Solution. Bananas do not really drive bread; bread is simply in a third of all baskets, so 37% confidence is almost the baseline. Lift near 1 exposes the coincidence, always judge a rule by lift, not confidence.
CHALLENGE 5
FP-Growth agreement
Confirm FP-Growth returns the same frequent itemsets as Apriori.
In [7]:
a = apriori(basket, min_support=0.03, use_colnames=True)
f = fpgrowth(basket, min_support=0.03, use_colnames=True)
sa = set(frozenset(x) for x in a['itemsets']); sf = set(frozenset(x) for x in f['itemsets'])
print('Apriori itemsets:', len(sa), '| FP-Growth itemsets:', len(sf))
print('identical set of itemsets:', sa == sf)
Apriori itemsets: 61 | FP-Growth itemsets: 61 identical set of itemsets: True
Solution. FP-Growth finds exactly the same frequent itemsets as Apriori but with a compact tree instead of repeated scans, so on large catalogs it is much faster while giving identical rules.
Statistics, Data Science and AI: A Visual Handbook · © 2026 John Fisher