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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html><head><meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"><title>APRIORI algorithm: An efficient implemenation of MSAPRIORI algorithm</title><link href="doxygen.css" rel="stylesheet" type="text/css"></head><body><!-- Generated by Doxygen 1.3.5 --><div class="qindex"><a class="qindexHL" href="index.html">Main Page</a> | <a class="qindex" href="namespaces.html">Namespace List</a> | <a class="qindex" href="annotated.html">Class List</a> | <a class="qindex" href="files.html">File List</a> | <a class="qindex" href="functions.html">Class Members</a> | <a class="qindex" href="globals.html">File Members</a></div><h1>An efficient implemenation of MSAPRIORI algorithm </h1><p>This program is a very efficient implementation of MSAPRIORI algorithm proposed by Bing Liu, Wynne Hsu and Yiming Ma. MSAPRIORI is the most basic and well-known algorithm to find frequent itemsets with multiple minimum supports in a transactional database.<p><h2>Frequent Itemset Mining problem</h2><p>A <em>transactional database</em> consists of sequence of transaction: <img class=formulaInl alt="$T=\langle t_1,\ldots ,t_n\rangle $" src="form_1.png">. A transaction is a set of items (<img class=formulaInl alt="$t_i\in I$" src="form_2.png">). Transactions are often called <em>baskets</em>, referring to the primary application domain (i.e. market-basket analysis). A set of items is often called <em>itemset</em> by the data mining community. The <em>(absolute) support</em> or the <em>occurrence</em> of <img class=formulaInl alt="$X$" src="form_3.png"> (denoted by <img class=formulaInl alt="$supp(X)$" src="form_4.png">) is the number of transactions that are supersets of <img class=formulaInl alt="$X$" src="form_3.png"> (i.e. that <em>contain</em> <img class=formulaInl alt="$X$" src="form_3.png">). The <em>realtive support</em> is the absolute support divided by the number of transactions (i.e. <em>n</em>). An itemset is <em>frequent</em> if its support is greater or equal than its threshold value (<em>mis(X)</em>). If <img class=formulaInl alt="$X=\{i_1,\ldots, i_k\}$" src="form_5.png">, then <img class=formulaInl alt="$mis(X)=min\{mis(i_j)\}$" src="form_6.png">, where the mis values of the single items are predefined.<p>In the frequent itemset mining problem a transaction database and the mis values of the items (traditionally denoted by <em>mis(i)</em>) is given and we have to find all frequent itemsets. <p><h2>Association Rule Mining problem</h2><p>This program is also capable of mining association rules. An association rule is like an implication: <img class=formulaInl alt="$X\to Y $" src="form_7.png"> means that if itemset <em>X</em> occurs in a transaction, than itemset <em>Y</em> also occurs with high probability. This probability is given by the <em>confidence</em> of the rule. It is like an approxiamtion of <em>p(Y|X)</em>, it is the number of transactions that contain both <em>X</em> and <em>Y</em> divided by the number of transaction that contain <em>X</em>, thus <img class=formulaInl alt="$conf(X\to Y)=\frac{supp(X\cup Y)}{supp(X)}$" src="form_8.png">. The <em>relative support</em> of the association rule <img class=formulaInl alt="$X\to Y $" src="form_7.png"> is the support of itemset <img class=formulaInl alt="$X \cup Y $" src="form_9.png">. The lift of <img class=formulaInl alt="$X\to Y $" src="form_7.png"> tries to capture the independence of the antecedent and the consequent of the rule: <img class=formulaInl alt="$lift(X\to Y)=\frac{supp(X\cup Y)}{supp(X)supp(Y)}$" src="form_10.png"> An association rule is <em>valid</em> if its confidence, support and lift are greater than or equal than corresponding threshold values.<p>In the association rule mining problem a transaction database and the mis values of the items (traditionally denoted by <em>mis(i)</em>), a confidence threshold (traditionally denoted by <em>min_conf</em>), and a lift threshold is given and we have to find all valid association rules. <hr size="1"><address style="align: right;"><small>Generated on Sun Jun 20 23:41:08 2004 for APRIORI algorithm by<a href="http://www.doxygen.org/index.html"><img src="doxygen.png" alt="doxygen" align="middle" border=0 > </a>1.3.5 </small></address></body></html>⌨️ 快捷键说明
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