apriori: Frequent itemsets via the Apriori algorithm
Apriori function to extract frequent itemsets for association rule mining
from mlxtend.frequent_patterns import apriori
Overview
Apriori is a popular algorithm [1] for extracting frequent itemsets with applications in association rule learning. The apriori algorithm has been designed to operate on databases containing transactions, such as purchases by customers of a store. An itemset is considered as "frequent" if it meets a userspecified support threshold. For instance, if the support threshold is set to 0.5 (50%), a frequent itemset is defined as a set of items that occur together in at least 50% of all transactions in the database.
References
[1] Agrawal, Rakesh, and Ramakrishnan Srikant. "Fast algorithms for mining association rules." Proc. 20th int. conf. very large data bases, VLDB. Vol. 1215. 1994.
Related
Example 1  Generating Frequent Itemsets
The apriori
function expects data in a onehot encoded pandas DataFrame.
Suppose we have the following transaction data:
dataset = [['Milk', 'Onion', 'Nutmeg', 'Kidney Beans', 'Eggs', 'Yogurt'],
['Dill', 'Onion', 'Nutmeg', 'Kidney Beans', 'Eggs', 'Yogurt'],
['Milk', 'Apple', 'Kidney Beans', 'Eggs'],
['Milk', 'Unicorn', 'Corn', 'Kidney Beans', 'Yogurt'],
['Corn', 'Onion', 'Onion', 'Kidney Beans', 'Ice cream', 'Eggs']]
We can transform it into the right format via the TransactionEncoder
as follows:
import pandas as pd
from mlxtend.preprocessing import TransactionEncoder
te = TransactionEncoder()
te_ary = te.fit(dataset).transform(dataset)
df = pd.DataFrame(te_ary, columns=te.columns_)
df
Apple  Corn  Dill  Eggs  Ice cream  Kidney Beans  Milk  Nutmeg  Onion  Unicorn  Yogurt  

0  False  False  False  True  False  True  True  True  True  False  True 
1  False  False  True  True  False  True  False  True  True  False  True 
2  True  False  False  True  False  True  True  False  False  False  False 
3  False  True  False  False  False  True  True  False  False  True  True 
4  False  True  False  True  True  True  False  False  True  False  False 
Now, let us return the items and itemsets with at least 60% support:
from mlxtend.frequent_patterns import apriori
apriori(df, min_support=0.6)
support  itemsets  

0  0.8  (3) 
1  1.0  (5) 
2  0.6  (6) 
3  0.6  (8) 
4  0.6  (10) 
5  0.8  (3, 5) 
6  0.6  (8, 3) 
7  0.6  (5, 6) 
8  0.6  (8, 5) 
9  0.6  (10, 5) 
10  0.6  (8, 3, 5) 
By default, apriori
returns the column indices of the items, which may be useful in downstream operations such as association rule mining. For better readability, we can set use_colnames=True
to convert these integer values into the respective item names:
apriori(df, min_support=0.6, use_colnames=True)
support  itemsets  

0  0.8  (Eggs) 
1  1.0  (Kidney Beans) 
2  0.6  (Milk) 
3  0.6  (Onion) 
4  0.6  (Yogurt) 
5  0.8  (Eggs, Kidney Beans) 
6  0.6  (Eggs, Onion) 
7  0.6  (Kidney Beans, Milk) 
8  0.6  (Kidney Beans, Onion) 
9  0.6  (Yogurt, Kidney Beans) 
10  0.6  (Kidney Beans, Eggs, Onion) 
Example 2  Selecting and Filtering Results
The advantage of working with pandas DataFrames
is that we can use its convenient features to filter the results. For instance, let's assume we are only interested in itemsets of length 2 that have a support of at least 80 percent. First, we create the frequent itemsets via apriori
and add a new column that stores the length of each itemset:
frequent_itemsets = apriori(df, min_support=0.6, use_colnames=True)
frequent_itemsets['length'] = frequent_itemsets['itemsets'].apply(lambda x: len(x))
frequent_itemsets
support  itemsets  length  

0  0.8  (Eggs)  1 
1  1.0  (Kidney Beans)  1 
2  0.6  (Milk)  1 
3  0.6  (Onion)  1 
4  0.6  (Yogurt)  1 
5  0.8  (Eggs, Kidney Beans)  2 
6  0.6  (Eggs, Onion)  2 
7  0.6  (Kidney Beans, Milk)  2 
8  0.6  (Kidney Beans, Onion)  2 
9  0.6  (Yogurt, Kidney Beans)  2 
10  0.6  (Kidney Beans, Eggs, Onion)  3 
Then, we can select the results that satisfy our desired criteria as follows:
frequent_itemsets[ (frequent_itemsets['length'] == 2) &
(frequent_itemsets['support'] >= 0.8) ]
support  itemsets  length  

5  0.8  (Eggs, Kidney Beans)  2 
Similarly, using the Pandas API, we can select entries based on the "itemsets" column:
frequent_itemsets[ frequent_itemsets['itemsets'] == {'Onion', 'Eggs'} ]
support  itemsets  length  

6  0.6  (Eggs, Onion)  2 
Frozensets
Note that the entries in the "itemsets" column are of type frozenset
, which is builtin Python type that is similar to a Python set
but immutable, which makes it more efficient for certain query or comparison operations (https://docs.python.org/3.6/library/stdtypes.html#frozenset). Since frozenset
s are sets, the item order does not matter. I.e., the query
frequent_itemsets[ frequent_itemsets['itemsets'] == {'Onion', 'Eggs'} ]
is equivalent to any of the following three
frequent_itemsets[ frequent_itemsets['itemsets'] == {'Eggs', 'Onion'} ]
frequent_itemsets[ frequent_itemsets['itemsets'] == frozenset(('Eggs', 'Onion')) ]
frequent_itemsets[ frequent_itemsets['itemsets'] == frozenset(('Onion', 'Eggs')) ]
Example 3  Working with Sparse Representations
To save memory, you may want to represent your transaction data in the sparse format. This is especially useful if you have lots of products and small transactions.
oht_ary = te.fit(dataset).transform(dataset, sparse=True)
sparse_df = pd.DataFrame.sparse.from_spmatrix(oht_ary, columns=te.columns_)
sparse_df
Apple  Corn  Dill  Eggs  Ice cream  Kidney Beans  Milk  Nutmeg  Onion  Unicorn  Yogurt  

0  False  False  False  True  False  True  True  True  True  False  True 
1  False  False  True  True  False  True  False  True  True  False  True 
2  True  False  False  True  False  True  True  False  False  False  False 
3  False  True  False  False  False  True  True  False  False  True  True 
4  False  True  False  True  True  True  False  False  True  False  False 
apriori(sparse_df, min_support=0.6, use_colnames=True, verbose=1)
Processing 21 combinations  Sampling itemset size 3
support  itemsets  

0  0.8  (Eggs) 
1  1.0  (Kidney Beans) 
2  0.6  (Milk) 
3  0.6  (Onion) 
4  0.6  (Yogurt) 
5  0.8  (Eggs, Kidney Beans) 
6  0.6  (Eggs, Onion) 
7  0.6  (Kidney Beans, Milk) 
8  0.6  (Kidney Beans, Onion) 
9  0.6  (Yogurt, Kidney Beans) 
10  0.6  (Kidney Beans, Eggs, Onion) 
API
apriori(df, min_support=0.5, use_colnames=False, max_len=None, verbose=0, low_memory=False)
Get frequent itemsets from a onehot DataFrame
Parameters

df
: pandas DataFramepandas DataFrame the encoded format. Also supports DataFrames with sparse data; for more info, please see (https://pandas.pydata.org/pandasdocs/stable/ user_guide/sparse.html#sparsedatastructures)
Please note that the old pandas SparseDataFrame format is no longer supported in mlxtend >= 0.17.2.
The allowed values are either 0/1 or True/False. For example,
Apple Bananas Beer Chicken Milk Rice
0 True False True True False True
1 True False True False False True
2 True False True False False False
3 True True False False False False
4 False False True True True True
5 False False True False True True
6 False False True False True False
7 True True False False False False

min_support
: float (default: 0.5)A float between 0 and 1 for minumum support of the itemsets returned. The support is computed as the fraction
transactions_where_item(s)_occur / total_transactions
. 
use_colnames
: bool (default: False)If
True
, uses the DataFrames' column names in the returned DataFrame instead of column indices. 
max_len
: int (default: None)Maximum length of the itemsets generated. If
None
(default) all possible itemsets lengths (under the apriori condition) are evaluated. 
verbose
: int (default: 0)Shows the number of iterations if >= 1 and
low_memory
isTrue
. If=1 and
low_memory
isFalse
, shows the number of combinations. 
low_memory
: bool (default: False)If
True
, uses an iterator to search for combinations abovemin_support
. Note that whilelow_memory=True
should only be used for large dataset if memory resources are limited, because this implementation is approx. 36x slower than the default.
Returns
pandas DataFrame with columns ['support', 'itemsets'] of all itemsets
that are >= min_support
and < than max_len
(if max_len
is not None).
Each itemset in the 'itemsets' column is of type frozenset
,
which is a Python builtin type that behaves similarly to
sets except that it is immutable
(For more info, see
https://docs.python.org/3.6/library/stdtypes.html#frozenset).
Examples
For usage examples, please see https://rasbt.github.io/mlxtend/user_guide/frequent_patterns/apriori/