Association Rule Mining

Association rule learning is a method for discovering interesting relations between variables in large databases. It is intended to identify strong rules discovered in databases using different measures of interestingness.

For example, the rule association-rule-miningfound in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy hamburger meat. Such information can be used as the basis for decisions about marketing activities such as, e.g., promotional pricing or product placements. In addition to the above example from market basket analysis association rules are employed today in many application areas including Web usage mining, intrusion detection, Continuous production, and bioinformatics.

Association rule mining is primarily focused on finding frequent co-occurring associations among a collection of items. It is sometimes referred to as “Market Basket Analysis”, since that was the original application area of association mining. The goal is to find associations of items that occur together more often than you would expect from a random sampling of all possibilities.

An association rule has two parts, an antecedent (if) and a consequent (then). An antecedent is an item found in the data. A consequent is an item that is found in combination with the antecedent.

Association rules are created by analyzing data for frequent if/then patterns and using the criteria support and confidence to identify the most important relationships. Support is an indication of how frequently the items appear in the database. Confidence indicates the number of times the if/then statements have been found to be true.

In data mining, association rules are useful for analyzing and predicting customer behavior. They play an important part in shopping basket data analysis, product clustering, catalog design and store layout.


How association rules work. The usefulness of this technique to address unique data mining problems is best illustrated in a simple example. Suppose we are collecting data at the check-out cash registers at a large book store. Each customer transaction is logged in a database, and consists of the titles of the books purchased by the respective customer, perhaps additional magazine titles and other gift items that were purchased, and so on. Hence, each record in the database will represent one customer (transaction), and may consist of a single book purchased by that customer, or it may consist of many (perhaps hundreds of) different items that were purchased, arranged in an arbitrary order depending on the order in which the different items (books, magazines, and so on) came down the conveyor belt at the cash register. The purpose of the analysis is to find associations between the items that were purchased, i.e., to derive association rules that identify the items and co-occurrences of different items that appear with the greatest (co-)frequencies. For example, we want to learn which books are likely to be purchased by a customer who we know already purchased (or is about to purchase) a particular book. This type of information could then quickly be used to suggest to the customer those additional titles. You may already be “familiar” with the results of these types of analyses if you are a customer of various on-line (Web-based) retail businesses; many times when making a purchase on-line, the vendor will suggest similar items (to the ones purchased by you) at the time of “check-out”, based on some rules such as “customers who buy book title A are also likely to purchase book title B,” and so on.

Sequence Analysis. Sequence analysis is concerned with a subsequent purchase of a product or products given a previous buy. For instance, buying an extended warranty is more likely to follow (in that specific sequential order) the purchase of a TV or other electric appliances. Sequence rules, however, are not always that obvious, and sequence analysis helps you to extract such rules no matter how hidden they may be in your market basket data. There is a wide range of applications for sequence analysis in many areas of industry including customer shopping patterns, phone call patterns, the fluctuation of the stock market, DNA sequence, and Web log streams.

Link Analysis. Once extracted, rules about associations or the sequences of items as they occur in a transaction database can be extremely useful for numerous applications. Obviously, in retailing or marketing, knowledge of purchase “patterns” can help with the direct marketing of special offers to the “right” or “ready” customers (i.e., those who, according to the rules, are most likely to purchase specific items given their observed past consumption patterns). However, transaction databases occur in many areas of business, such as banking. In fact, the term “link analysis” is often used when these techniques – for extracting sequential or non-sequential association rules – are applied to organize complex “evidence.” It is easy to see how the “transactions” or “shopping basket” metaphor can be applied to situations where individuals engage in certain actions, open accounts, contact other specific individuals, and so on. Applying the technologies described here to such databases may quickly extract patterns and associations between individuals and actions and, hence, for example, reveal the patterns and structure of some clandestine illegal network.

Unique data analysis requirements. Crosstabulation tables, and in particular Multiple Response tables can be used to analyze data of this kind. However, in cases when the number of different items (categories) in the data is very large (and not known ahead of time), and when the “factorial degree” of important association rules is not known ahead of time, then these tabulation facilities may be too cumbersome to use, or simply not applicable: Consider once more the simple “bookstore-example” discussed earlier. First, the number of book titles is practically unlimited. In other words, if we would make a table where each book title would represent one dimension, and the purchase of that book (yes/no) would be the classes or categories for each dimension, then the complete crosstabulation table would be huge and sparse (consisting mostly of empty cells). Alternatively, we could construct all possible two-way tables from all items available in the store; this would allow us to detect two-way associations (association rules) between items. However, the number of tables that would have to be constructed would again be huge, most of the two-way tables would be sparse, and worse, if there were any three-way association rules “hiding” in the data, we would miss them completely. The a-priori algorithm implemented in Association Rules will not only automatically detect the relationships (“cross-tabulation tables”) that are important (i.e., cross-tabulation tables that are not sparse, not containing mostly zero’s), but also determine the factorial degree of the tables that contain the important association rules.

To summarize, use Association Rules to find rules of the kind If X then (likely) Y where X and Y can be single values, items, words, etc., or conjunctions of values, items, words, etc. (e.g., if (Car=Porsche and Gender=Male and Age<20) then (Risk=High and Insurance=High)). The program can be used to analyze simple categorical variables, dichotomous variables, and/or multiple response variables. The algorithm will determine association rules without requiring the user to specify the number of distinct categories present in the data, or any prior knowledge regarding the maximum factorial degree or complexity of the important associations. In a sense, the algorithm will construct cross-tabulation tables without the need to specify the number of dimensions for the tables, or the number of categories for each dimension. Hence, this technique is particularly well suited for data and text mining of huge databases.


Association rules are usually required to satisfy a user-specified minimum support and a user-specified minimum confidence at the same time. Association rule generation is usually split up into two separate steps

  • A minimum support threshold is applied to find all frequent item-sets in a database.
  • A minimum confidence constraint is applied to these frequent item-sets in order to form rules.

While the second step is straightforward, the first step needs more attention.

Finding all frequent item-sets in a database is difficult since it involves searching all possible item-sets (item combinations). The set of possible item-sets is the power set over I and has size 2^n-1 (excluding the empty set which is not a valid item-set). Although the size of the power-set grows exponentially in the number of items n in I, efficient search is possible using the downward-closure property of support (also called anti-monotonicity) which guarantees that for a frequent itemset, all its subsets are also frequent and thus for an infrequent item-set, all its super-sets must also be infrequent. Exploiting this property, efficient algorithms (e.g., Apriori and Eclat) can find all frequent item-sets.


Algorithms for generating association rules, are

Apriori algorithm – Apriori is the best-known algorithm to mine association rules. It uses a breadth-first search strategy to count the support of itemsets and uses a candidate generation function which exploits the downward closure property of support.

Eclat algorithm – Eclat (stands for Equivalence Class Transformation) is a depth-first search algorithm using set intersection. It is a naturally elegant algorithm suitable for both sequential as well as parallel execution with locality enhancing properties. It was first introduced by Zaki, Parthasarathy, Li and Ogihara in a series of papers written in 1997.

FP-growth algorithm – FP stands for frequent pattern. In the first pass, the algorithm counts occurrence of items (attribute-value pairs) in the dataset, and stores them to ‘header table’. In the second pass, it builds the FP-tree structure by inserting instances. Items in each instance have to be sorted by descending order of their frequency in the dataset, so that the tree can be processed quickly. Items in each instance that do not meet minimum coverage threshold are discarded. If many instances share most frequent items, FP-tree provides high compression close to tree root.

Recursive processing of this compressed version of main dataset grows large item sets directly, instead of generating candidate items and testing them against the entire database. Growth starts from the bottom of the header table (having longest branches), by finding all instances matching given condition. New tree is created, with counts projected from the original tree corresponding to the set of instances that are conditional on the attribute, with each node getting sum of its children counts. Recursive growth ends when no individual items conditional on the attribute meet minimum support threshold, and processing continues on the remaining header items of the original FP-tree.

Context Based Association Rule Mining Algorithm – CBPNARM is the newly developed algorithm which is developed in 2013 to mine association rules on the basis of context. It uses context variable on the basis of which the support of an itemset is changed on the basis of which the rules are finally populated to the rule set.

Node-set-based algorithms – FIN, PrePost and PPV are three algorithms based on node sets. They use nodes in a coding FP-tree to represent itemsets, and employ a depth-first search strategy to discovery frequent itemsets using “intersection” of node sets.

GUHA procedure ASSOC – GUHA is a general method for exploratory data analysis that has theoretical foundations in observational calculi.

The ASSOC procedure is a GUHA method which mines for generalized association rules using fast bitstrings operations. The association rules mined by this method are more general than those output by apriori, for example “items” can be connected both with conjunction and disjunctions and the relation between antecedent and consequent of the rule is not restricted to setting minimum support and confidence as in apriori: an arbitrary combination of supported interest measures can be used.

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