Maximal Itemsets via the FP-Max Algorithm

Function implementing FP-Max to extract maximal itemsets for association rule mining

from mlxtend.frequent_patterns import fpmax

Overview

The Apriori algorithm is among the first and most popular algorithms for frequent itemset generation (frequent itemsets are then used for association rule mining). However, the runtime of Apriori can be quite small, especially for datasets with a large number of unique items, as the runtime grows exponentially depending on the number of unique items.

In contrast to Apriori, FP-Growth is a frequent pattern generation algorithm that inserts items into a pattern search tree, which allows it to have a linear increase in runtime with respect to the number of unique items or entries.

FP-Max is a variant of FP-Growth, which focuses on obtaining maximal itemsets. An itemset X is said to maximal if X is frequent and there exists no frequent super-pattern containing X. In other words, a frequent pattern X cannot be sub-pattern of larger frequent pattern to qualify for the definition maximal itemset.

References

Example 1 -- Maximal Itemsets

The fpmax function expects data in a one-hot 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 fpmax

fpmax(df, min_support=0.6)
support itemsets
0 0.6 (5, 6)
1 0.6 (8, 3, 5)
2 0.6 (10, 5)

By default, fpmax 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:

fpmax(df, min_support=0.6, use_colnames=True)
support itemsets
0 0.6 (Kidney Beans, Milk)
1 0.6 (Eggs, Onion, Kidney Beans)
2 0.6 (Yogurt, Kidney Beans)

More Examples

Please note that since the fpmax function is a drop-in replacement for fpgrowth and apriori, it comes with the same set of function arguments and return arguments. Thus, for more examples, please see the apriori documentation.

API

fpmax(df, min_support=0.5, use_colnames=False, max_len=None, verbose=0)

Get maximal frequent itemsets from a one-hot DataFrame

Parameters

    Apple  Bananas  Beer  Chicken  Milk  Rice
    0      1        0     1        1     0     1
    1      1        0     1        0     0     1
    2      1        0     1        0     0     0
    3      1        1     0        0     0     0
    4      0        0     1        1     1     1
    5      0        0     1        0     1     1
    6      0        0     1        0     1     0
    7      1        1     0        0     0     0

Returns

pandas DataFrame with columns ['support', 'itemsets'] of all maximal 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 built-in 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).