Mining association rules between sets of items in large databases
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Mining Association Rules between Sets of Items in Large Databases. presented by Zhuang Wang. Outline. Introduction Formal Model Apriori Algorithm Experiments Summary. Introduction. Association rule:

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Presentation Transcript

Outline Databases

  • Introduction

  • Formal Model

  • Apriori Algorithm

  • Experiments

  • Summary

Introduction Databases

  • Association rule:

    - Association rules are used to discover elements that co-occur frequently within a dataset consisting of multiple independent selections of elements (such as purchasing transactions), and to discover rules.

  • Applications:

    - Questions such as "if a customer purchases product A, how likely is he to purchase product B?" and "What products will a customer buy if he buys products C and D?" are answered by association-finding algorithms.(market basket analysis)

Formal model
Formal Model Databases

  • Let I = I_1, I_2,. . ., I_n be a set of items.

    Let T be a database of transactions.

    Each transaction t in T is represented as a subset of I .

    Let X be a subset of I.

  • Support and Confidence:

    By an association rule, we mean an implication of the form X  I_k, where X is a set of some items in I, and I_k is a single item in I that is not present in X.

    support: probability that a transaction contains X and I_k.

    P(X ,I_k)

    confidence: conditional probability that a transaction having X also contains I_k.

    P(l_k | X)

Support and confidence example
Support and Confidence - Example Databases

  • Let minimum support 50%, and minimum confidence 50%, we have

    • A  C (50%, 66.6%)

    • C  A (50%, 100%)

Apriori algorithm
Apriori Algorithm Databases

  • To find subsets which are common to at least a minimum confidence of the itemsets.

  • Using a "bottom up" approach, where frequent itemsets (the sets of items that follows minimum support) are extended one item at a time (a step known as candidate generation), and groups of candidates are tested against the data.

  • The algorithm terminates when no further successful extensions are found.

  • Generating from each large itemset, rules that use items from the large itemset

Find frequent itemsets example
Find DatabasesFrequent Itemsets - Example

Database D



Scan D




Scan D



Scan D

Experiments Databases

  • We experimented with the rule mining algorithm using

    the sales data obtained from a large retailing company.

  • There are a total of 46,873 customer transactions in

    this data. Each transaction contains the department

    numbers from which a customer bought an item in

    a visit.

  • There are a total of 63 departments. The

    algorithm finds if there is an association between

    departments in the customer purchasing behavior.

  • The following rules were found for a minimum support of 1% and minimum condence of 50%.

  • [Tires]  [Automotive Services] (98.80, 5.79)

  • [Auto Accessories], [Tires]  [Automotive Services] (98.29, 1.47)

  • [Auto Accessories]  [Automotive Services] (79.51, 11.81)

  • [Automotive Services]  [Auto Accessories] (71.60, 11.81)

  • [Home Laundry Appliances]  [Maintenance Agreement Sales] (66.55, 1.25)

  • [Children's Hardlines]  [Infants and Children's wear] (66.15, 4.24)

  • [Men's Furnishing]  [Men's Sportswear] (54.86, 5.21)

Summary and minimum condence of 50%.

  • Apriori, while historically significant, suffers from a number of inefficiencies or trade-offs, which have spawned other algorithms.

  • Hash tables: uses a hash tree to store candidate itemsets. This hash tree has item sets at the leaves and at internal nodes

  • Partitioning: Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB

  • Sampling: mining on a subset of given data, need a lower support threshold + a method to determine the completeness.

Reference and minimum condence of 50%.

  • R. Agrawal, T. Imielinski, A. Swami: “Mining Associations between Sets of Items in Massive Databases”, Proc. of the ACM SIGMOD Int'l Conference on Management of Data, Washington D.C., May 1993, 207-216.