推荐系统:关联规则(2)
Apriori Algorithm 是关联规则领域里最具影响力的基础算法。它是由 Rakesh Agrawal 在 1994 年提出的,详细的介绍在这里《Fast Algorithms for Mining Association Rules》。十几年过去了,不少学者围绕着 Apriori 进行了诸多改良。但与 1994 年相比,目前基于互联网的应用,数据量大了几十倍甚至是几百倍,因此,基于 Apriori 的算法逐渐暴露出其运算成本过高的问题。但不管怎样,对于大师及其做出的贡献,我们也只有高山仰止的份儿。
Apriori 是一种广度优先算法,通过多次扫描数据库来获取支持度大于最小支持度的频繁项集。它的理论基础是频繁项集的两个单调性原则:频繁项集的任一子集一定是频繁 的;非频繁项集的任一超集一定是非频繁的。晦涩的理论我这里就不多写了,有兴趣的可以去看论文。我把里面的例子给翻译一下,图文并茂,简明易懂。
某数据库 DB 里有 4 条事务记录,取最小支持度(min support)为 0.5,则计算频繁项集的过程如下:
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扫描DB |
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取满足 最小支持度 项集 |
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扫描DB |
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取满足 最小支持度 项集 |
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扫描DB |
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取满足 最小支持度 项集 |
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如上可以看出,在海量数据的情况下,Apriori 算法的运算过程有 2 个问题:
- 需要多次扫描数据库,时间成本很高;
- 运算过程中需要产生大量的候选集,空间成本也非常高。
针对 Apriori 算法所做的改进也基本上是围绕着解决这两个问题进行的,如在扫描DB前首先进行以便事务合并和压缩,数据分区或抽样等。
Weka 里有 Apriori 算法的 Java 实现,非常值得一看。
貌似 wikipedia 已经解封了,呵呵!
预报:关联规则(3),关于 FP-Growth 算法。
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