The Apriori algorithm

Market Basket Analysis in Python

Isaiah Hull

Visiting Associate Professor of Finance, BI Norwegian Business School

Counting itemsets

$${n \choose k} = \frac{n!}{(n-k)!k!}$$

Item Count	Itemset Size	Combinations
3461	0	1
3461	1	3461
3461	2	5,987,530
3461	3	6,903,622,090
3461	4	5,968,181,296,805

Counting itemsets

$$\sum_{k=0}^{n}{n \choose k} = 2^{n}$$

$n = 3461 \rightarrow 2^{3461}$
$2^{3461}>>10^{82}$
Number of atoms in universe: $10^{82}$.

Reducing the number of itemsets

Not possible to consider all itemsets.
- Not even possible to enumerate them.
How do we remove an itemset without even evaluating it?
- Could set maximum $k$ value.
Apriori algorithm offers alternative.
- Doesn't require enumeration of all itemsets.
- Sensible rule for pruning.

The Apriori principle

Apriori principle.
- Subsets of frequent sets are frequent.
- Retain sets known to be frequent.
- Prune sets not known to be frequent.

Candles = Infrequent
- -> {Candles, Signs} = Infrequent
{Candles, Signs} = Infrequent
- -> {Candles, Signs Boxes} = Infrequent
{Candles, Signs, Boxes} = Infrequent
- -> {Candles, Signs, Boxes, Bags} = Infrequent

Apriori implementation

# Import Apriori algorithm
from mlxtend.frequent_patterns import apriori

# Load one-hot encoded novelty gifts data
onehot = pd.read_csv('datasets/online_retail_onehot.csv')

# Print header.
print(onehot.head())

    50'S CHRISTMAS GIFT BAG LARGE ...  ZINC WILLIE WINKIE  CANDLE STICK  \
0                           False ...              False   
1                           False ...              False   
2                           False ...              False   
3                           False ...              False   
4                           False ...              False

Apriori implementation

# Compute frequent itemsets
frequent_itemsets = apriori(onehot, min_support = 0.0005, 
                            max_len = 4, use_colnames = True)

# Print number of itemsets
print(len(frequent_itemsets))

Apriori implementation

# Print itemsets
print(frequent_itemsets.head())

      support                          itemsets
0     0.000752  ( 50'S CHRISTMAS GIFT BAG LARGE)
1     0.001504              ( DOLLY GIRL BEAKER)
...
1500  0.000752  (PING MICROWAVE APRON, FOOD CONTAINER SET 3 LO...
1501  0.000752  (WOOD 2 DRAWER CABINET WHITE FINISH, FOOD CONT...
...

Let's practice!

Market Basket Analysis in Python