.. _dpa-apriori-frequent-itemsets-via-the-apriori-algorithm:

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Apriori: Frequent Itemsets via the Apriori Algorithm
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**Stage 3 · 🛒 Market Basket & Association Rules**  ·  Lesson 20 of 56  ·  *intermediate*

:doc:`◀ Previous · How Association Rules Are Discovered: Concepts, Scale, Measures, and the Apriori Approach <19-how-association-rules-are-discovered-concepts-scale-measures-and-the-apriori-approach>`   ·   :doc:`Next · association_rules: Generating Association Rules from Frequent Itemsets (mlxtend) ▶ <21-association-rules-generating-association-rules-from-frequent-itemsets-mlxtend>`   ·   :doc:`↑ Section <index>`


.. important::

   **✨ AI-generated content.** This page was written with the assistance of an
   AI language model and is provided as a learning aid. Despite careful
   review, it may still contain mistakes, omissions, or out-of-date
   information. Whether you are new to the topic, a team lead, or a senior
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   reference: read it critically and independently verify anything you act on
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Prior knowledge
-----------------

The **Apriori algorithm**, introduced by Agrawal and Srikant in **1994**, is the classic method for
finding all **frequent itemsets** — the groups of items whose support clears a chosen **minimum**. Its
name comes from the *a priori* (prior) knowledge it exploits: it uses the frequent itemsets already
found at one size to decide what is worth checking at the next.

The level-wise search
-----------------------

The algorithm walks the itemsets **level by level**, from small to large, applying downward closure at
every step. The key move is **candidate generation**: a :math:`k`-item candidate is formed only if
**all** of its :math:`(k{-}1)`-item subsets are already known to be frequent. Any candidate with an
infrequent subset is discarded **before** its support is ever counted — that is where the saving comes
from.

One level at a time
---------------------

Concretely, each level repeats three steps:

1. **Generate** candidate :math:`k`-itemsets by combining frequent :math:`(k{-}1)`-itemsets, then **prune** those with any infrequent subset;
2. **Count** each surviving candidate's support with a single **scan** of the transaction database;
3. **Keep** those meeting minimum support as the frequent :math:`k`-itemsets.

Start with frequent single items (:math:`k = 1`) and repeat, increasing :math:`k`, until no new
candidates survive. The cost is that dense data can still spawn many candidates and repeated database
scans — Apriori is simple and correct, not always the fastest.

Then the rules
----------------

Apriori delivers frequent **itemsets**; turning them into **rules** is the easy second half. For each
frequent itemset, split it into an antecedent and consequent every way possible and keep the splits
whose **confidence** (or **lift**) clears a threshold. Because both sides come from a frequent itemset,
the rule's support is already known — which is exactly what the next lesson automates in Python.

.. hint::

   **Related lessons:** :doc:`How Association Rules Are Discovered: Concepts, Scale, Measures, and the Apriori Approach <19-how-association-rules-are-discovered-concepts-scale-measures-and-the-apriori-approach>`  ·  :doc:`association_rules: Generating Association Rules from Frequent Itemsets (mlxtend) <21-association-rules-generating-association-rules-from-frequent-itemsets-mlxtend>`  ·  :doc:`Understanding Market Baskets and Ideal Customers <17-understanding-market-baskets-and-ideal-customers>`  ·  :doc:`Cross-Selling <22-cross-selling>`

.. seealso::

   **Source article** Adapted (context, re-expressed) in our own words from: `https://insightful-data-lab.com/2026/01/14/apriori-frequent-itemsets-via-the-apriori-algorithm/ <https://insightful-data-lab.com/2026/01/14/apriori-frequent-itemsets-via-the-apriori-algorithm/>`__ (insightful-data-lab.com).

.. tags:: purpose: reference, topic: data analysis, topic: data preparation, level: intermediate