Index-BitTableFI: An improved algorithm for mining frequent itemsets
Efficient algorithms for mining frequent itemsets are crucial for mining association rules as well as for many other data mining tasks. Methods for mining frequent itemsets have been implemented using a BitTable structure. BitTableFI is such a recently proposed efficient BitTable-based algorithm, which exploits BitTable both horizontally and vertically. Although making use of efficient bit wise operations, BitTableFI still may suffer from the high cost of candidate generation and test. To address this problem, a new algorithm Index-BitTableFI is proposed. Index-BitTableFI also uses BitTable horizontally and vertically. To make use of BitTable horizontally, index array and the corresponding computing method are proposed. By computing the subsume index, those itemsets that co-occurrence with representative item can be identified quickly by using breadth-first search at one time. Then, for the resulting itemsets generated through the index array, depth-first search strategy is used to generate all other frequent itemsets. Thus, the hybrid search is implemented, and the search space is reduced greatly. The advantages of the proposed methods are as follows. On the one hand, the redundant operations on intersection of tidsets and frequency-checking can be avoided greatly; On the other hand, it is proved that frequent itemsets, including representative item and having the same supports as representative item, can be identified directly by connecting the representative item with all the combinations of items in its subsume index. Thus, the cost for processing this kind of itemsets is lowered, and the efficiency is improved. Experimental results show that the proposed algorithm is efficient especially for dense datasets.
A new algorithm for fast mining frequent itemsets using N-lists
Mining frequent itemsets has emerged as a fundamental problem in data mining and plays an essential role in many important data mining tasks. In this paper, we propose a novel vertical data representation called N-list, which originates from an FP-tree-like coding prefix tree called PPC-tree that stores crucial information about frequent itemsets. Based on the N-list data structure, we develop an efficient mining algorithm, PrePost, for mining all frequent itemsets. Efficiency of PrePost is achieved by the following three reasons. First, N-list is compact since transactions with common prefixes share the same nodes of the PPC-tree. Second, the counting of itemsets’ supports is transformed into the intersection of N-lists and the complexity of intersecting two N-lists can be reduced to O(m + n) by an efficient strategy, where m and n are the cardinalities of the two N-lists respectively. Third, PrePost can directly find frequent itemsets without generating candidate itemsets in some cases by making use of the single path property of N-list. We have experimentally evaluated PrePost against four state-of-the-art algorithms for mining frequent itemsets on a variety of real and synthetic datasets. The experimental results show that the PrePost algorithm is the fastest in most cases. Even though the algorithm consumes more memory when the datasets are sparse, it is still the fastest one.
negFIN: An efficient algorithm for fast mining frequent itemsets
Frequent itemset mining is a basic data mining task and has numerous applications in other data mining tasks. In recent years, some data structures based on sets of nodes in a prefix tree have been presented. These data structures store essential information about frequent itemsets. In this paper, we propose another efficient data structure, NegNodeset. Similar to other such data structures, the basis of NegNodeset is sets of nodes in a prefix tree. NegNodeset employs a novel encoding model for nodes in a prefix tree based on the bitmap representation of sets. Based on the NegNodeset data structure, we propose negFIN, which is an efficient algorithm for frequent itemset mining. The efficiency of the negFIN algorithm is confirmed by the following three reasons: (1) the NegNodesets of itemsets are extracted using bitwise operators, (2) the complexity of calculating NegNodesets and counting supports is reduced to O(n), where n is the cardinality of NegNodeset, and (3) it employs a set-enumeration tree to generate frequent itemsets and uses a promotion method to prune the search space in this tree. Our extensive performance study on a variety of benchmark datasets indicates that negFIN is the fastest algorithm, compared with previous state-of-the-art algorithms. However, our algorithm runs with the same speed as dFIN on some datasets.
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