Enhance documentation and support count logic in Apriori

machine_learning/apriori_algorithm.py

@@ -1,14 +1,17 @@
 """
-Apriori Algorithm is a Association rule mining technique, also known as market basket
-analysis, aims to discover interesting relationships or associations among a set of
-items in a transactional or relational database.
+Apriori Algorithm — Association Rule Mining Technique
 
-For example, Apriori Algorithm states: "If a customer buys item A and item B, then they
-are likely to buy item C."  This rule suggests a relationship between items A, B, and C,
-indicating that customers who purchased A and B are more likely to also purchase item C.
+The Apriori algorithm is a **classic association rule learning method**, also known as
+**Market Basket Analysis**, used to discover interesting relationships or associations
+among a set of items in a transactional database.
 
-WIKI: https://en.wikipedia.org/wiki/Apriori_algorithm
-Examples: https://www.kaggle.com/code/earthian/apriori-association-rules-mining
+For example:
+"If a customer buys item A and item B, they are likely to buy item C."
+This suggests a relationship between items A, B, and C — indicating that customers
+who purchased A and B are more likely to also purchase C.
+
+📘 WIKI: https://en.wikipedia.org/wiki/Apriori_algorithm  
+📊 Example Notebook: https://www.kaggle.com/code/earthian/apriori-association-rules-mining
 """
 
 from itertools import combinations
@@ -24,76 +27,50 @@
     return [["milk"], ["milk", "butter"], ["milk", "bread"], ["milk", "bread", "chips"]]
 
 
-def prune(itemset: list, candidates: list, length: int) -> list:
-    """
-    Prune candidate itemsets that are not frequent.
-    The goal of pruning is to filter out candidate itemsets that are not frequent.  This
-    is done by checking if all the (k-1) subsets of a candidate itemset are present in
-    the frequent itemsets of the previous iteration (valid subsequences of the frequent
-    itemsets from the previous iteration).
-
-    Prunes candidate itemsets that are not frequent.
-
-    >>> itemset = ['X', 'Y', 'Z']
-    >>> candidates = [['X', 'Y'], ['X', 'Z'], ['Y', 'Z']]
-    >>> prune(itemset, candidates, 2)
-    [['X', 'Y'], ['X', 'Z'], ['Y', 'Z']]
-
-    >>> itemset = ['1', '2', '3', '4']
-    >>> candidates = ['1', '2', '4']
-    >>> prune(itemset, candidates, 3)
-    []
+def get_item_support(data: list[list[str]], candidates: list[list[str]]) -> dict[tuple[str], int]:
     """
-    pruned = []
-    for candidate in candidates:
-        is_subsequence = True
-        for item in candidate:
-            if item not in itemset or itemset.count(item) < length - 1:
-                is_subsequence = False
-                break
-        if is_subsequence:
-            pruned.append(candidate)
-    return pruned
+    Compute the support count for each candidate itemset.
 
+    Args:
+        data: A list of transactions (each transaction is a list of items)
+        candidates: List of candidate itemsets
 
-def apriori(data: list[list[str]], min_support: int) -> list[tuple[list[str], int]]:
+    Returns:
+        Dictionary mapping itemsets to their support count.
     """
-    Returns a list of frequent itemsets and their support counts.
+    support_count = {tuple(sorted(candidate)): 0 for candidate in candidates}
+    for transaction in data:
+        for candidate in candidates:
+            if all(item in transaction for item in candidate):
+                support_count[tuple(sorted(candidate))] += 1
+    return support_count
 
-    >>> data = [['A', 'B', 'C'], ['A', 'B'], ['A', 'C'], ['A', 'D'], ['B', 'C']]
-    >>> apriori(data, 2)
-    [(['A', 'B'], 1), (['A', 'C'], 2), (['B', 'C'], 2)]
 
-    >>> data = [['1', '2', '3'], ['1', '2'], ['1', '3'], ['1', '4'], ['2', '3']]
-    >>> apriori(data, 3)
-    []
+def prune_candidates(prev_freq_itemsets: list[list[str]], k: int) -> list[list[str]]:
     """
-    itemset = [list(transaction) for transaction in data]
-    frequent_itemsets = []
-    length = 1
+    Generate and prune candidate itemsets of size k from previous frequent itemsets.
 
-    while itemset:
-        # Count itemset support
-        counts = [0] * len(itemset)
-        for transaction in data:
-            for j, candidate in enumerate(itemset):
-                if all(item in transaction for item in candidate):
-                    counts[j] += 1
-
-        # Prune infrequent itemsets
-        itemset = [item for i, item in enumerate(itemset) if counts[i] >= min_support]
-
-        # Append frequent itemsets (as a list to maintain order)
-        for i, item in enumerate(itemset):
-            frequent_itemsets.append((sorted(item), counts[i]))
-
-        length += 1
-        itemset = prune(itemset, list(combinations(itemset, length)), length)
+    Args:
+        prev_freq_itemsets: Frequent itemsets of size (k-1)
+        k: Desired size of next candidate itemsets
 
-    return frequent_itemsets
+    Returns:
+        List of pruned candidate itemsets.
+    """
+    candidates = []
+    for i in range(len(prev_freq_itemsets)):
+        for j in range(i + 1, len(prev_freq_itemsets)):
+            l1, l2 = sorted(prev_freq_itemsets[i]), sorted(prev_freq_itemsets[j])
+            if l1[:-1] == l2[:-1]:
+                candidate = sorted(list(set(l1) | set(l2)))
+                # Prune candidates whose subsets are not frequent
+                subsets = list(combinations(candidate, k - 1))
+                if all(list(subset) in prev_freq_itemsets for subset in subsets):
+                    candidates.append(candidate)
+    return candidates
 
 
-if __name__ == "__main__":
+def apriori(data: list[list[str]], min_support: int) -> list[tuple[list[str], int]]:
     """
     Apriori algorithm for finding frequent itemsets.
 
@@ -103,11 +80,46 @@
 
     Returns:
         A list of frequent itemsets along with their support counts.
+
+    Example:
+    >>> data = [['A', 'B', 'C'], ['A', 'B'], ['A', 'C'], ['A', 'D'], ['B', 'C']]
+    >>> apriori(data, 2)
+    [(['A'], 4), (['B'], 3), (['C'], 3), (['A', 'B'], 2), (['A', 'C'], 2), (['B', 'C'], 2)]
     """
-    import doctest
+    # Step 1: Find unique items
+    single_items = sorted({item for transaction in data for item in transaction})
+    current_candidates = [[item] for item in single_items]
+    frequent_itemsets = []
 
+    k = 1
+    while current_candidates:
+        support_count = get_item_support(data, current_candidates)
+        # Keep itemsets meeting minimum support
+        current_freq_itemsets = [
+            list(itemset) for itemset, count in support_count.items() if count >= min_support
+        ]
+        frequent_itemsets.extend(
+            [(list(itemset), count) for itemset, count in support_count.items() if count >= min_support]
+        )
+
+        # Generate next level of candidates
+        k += 1
+        current_candidates = prune_candidates(current_freq_itemsets, k)
+
+    return frequent_itemsets
+
+
+if __name__ == "__main__":
+    """
+    Run Apriori algorithm on the sample dataset with user-defined minimum support.
+    """
+    import doctest
     doctest.testmod()
 
-    # user-defined threshold or minimum support level
-    frequent_itemsets = apriori(data=load_data(), min_support=2)
-    print("\n".join(f"{itemset}: {support}" for itemset, support in frequent_itemsets))
+    transactions = load_data()
+    min_support = 2
+    results = apriori(transactions, min_support)
+
+    print("Frequent Itemsets and Support Counts:\n")
+    for itemset, support in results:
+        print(f"{itemset}: {support}")