Frequent itemset(頻繁項目集)的探勘在資料探勘的領域中已經是很典型的問題了，關於這方面已經有非常的多的研究，而因為frequent closed itemset(頻繁閉項目集)有著資料較少但卻完全沒有丟失任何frequent itemset所有的資訊的特性，frequent closed itemset的探勘成為近來較為重要的課題。在以往的研究中，若我們以運算資料來做區分的話，主要可以分為horizontal format(水平格式)與vertical format(垂直格式)兩大類，horizontal format與vertical format的資料我們可以很容易的轉換，對應兩種不同資料格式的方法有著不同的特點，但無論是哪一種格式，目前諸多的方法都需要做「closed」的檢查，針對答案是否為閉集合做額外的檢查是一種負擔，我們綜合了水平格式與垂直格式的作法設計了一個新方法，這個方法的特點之一，就是不需要再檢查答案是否為閉集合，而且針對某些情況下的資料集，我們的方法能有非常好的效能表現。

Frequent itemset mining is a typical question in the data mining domain. There are many researches about this problem already. We can use frequent closed itemset to find all frequent itemset, and the number of frequent closed itemset is much smaller than frequent itemset. Because of these strong points, frequent closed itemset mining becomes an important topic recently. In former researches, we can separate the approaches by data format into two ways: horizontal format and vertical format. And they can be transformed to each other easily. However, no matter what kind of format we use, we have to check if the answer is "closed". And that is overhead. Our new approach uses both horizontal format and vertical format data at the same time. One characteristics of this approach is that we do not need to check “closed” again. Moreover, in certain special dataset our approach has extremely good performance.

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