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from mlxtend.frequent_patterns import aprioriOverviewApriori 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 user-specified 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.
RelatedExample 1 -- Generating Frequent ItemsetsThe apriori 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 pdfrom mlxtend.preprocessing import TransactionEncoderte = 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 aprioriapriori(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 ResultsThe 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 built-in 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 frozensets 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')) ]
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)
APIapriori(df, min_support=0.5, use_colnames=False, max_len=None, verbose=0, low_memory=False)
Get frequent itemsets from a one-hot DataFrame
Parameters
- df : pandas DataFrame
pandas DataFrame the encoded format. Also supportsDataFrames with sparse data; for more info, pleasesee (https://pandas.pydata.org/pandas ... rse-data-structures)
Please note that the old pandas SparseDataFrame formatis no longer supported in mlxtend >= 0.17.2.
The allowed values are either 0/1 or True/False.For example,
- 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 fractiontransactions_where_item(s)_occur / total_transactions.
- use_colnames : bool (default: False)
If True, uses the DataFrames' column names in the returned DataFrameinstead of column indices.
- max_len : int (default: None)
Maximum length of the itemsets generated. If None (default) allpossible itemsets lengths (under the apriori condition) are evaluated.
- verbose : int (default: 0)
Shows the number of iterations if >= 1 and low_memory is True. If
=1 and low_memory is False, shows the number of combinations.
- low_memory : bool (default: False)
If True, uses an iterator to search for combinations abovemin_support.Note that while low_memory=True should only be used for large datasetif memory resources are limited, because this implementation is approx.3-6x slower than the default.
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 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).
Examples
For usage examples, please see https://rasbt.github.io/mlxtend/user_guide/frequent_patterns/apriori/
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