MAFIA: a maximal frequent itemset algorithm for transactional databases
We present a new algorithm for mining maximal frequent itemsets from a transactional database. Our algorithm is especially efficient when the itemsets in the database are very long. The search strategy of our algorithm integrates a depth-first traversal of the itemset lattice with effective pruning mechanisms. Our implementation of the search strategy combines a vertical bitmap representation of the database with an efficient relative bitmap compression schema. In a thorough experimental analysis of our algorithm on real data, we isolate the effect of the individual components of the algorithm. Our performance numbers show that our algorithm outperforms previous work by a factor of three to five.
Efficiently mining maximal frequent itemsets
We present GenMax, a backtracking search based algorithm for mining maximal frequent itemsets. GenMax uses a number of optimizations to prune the search space. It uses a novel technique called progressive focusing to perform maximality checking, and diffset propagation to perform fast frequency computation. Systematic experimental comparison with previous work indicates that different methods have varying strengths and weaknesses based on dataset characteristics. We found GenMax to be a highly efficient method to mine the exact set of maximal patterns.
GenMax: An Efficient Algorithm for Mining Maximal Frequent Itemsets
We present GenMax, a backtrack search based algorithm for mining maximal frequent itemsets. GenMax uses a number of optimizations to prune the search space. It uses a novel technique called progressive focusing to perform maximality checking, and diffset propagation to perform fast frequency computation. Systematic experimental comparison with previous work indicates that different methods have varying strengths and weaknesses based on dataset characteristics. We found GenMax to be a highly efficient method to mine the exact set of maximal patterns.
The complexity of mining maximal frequent itemsets and maximal frequent patterns
Mining maximal frequent itemsets is one of the most fundamental problems in data mining. In this paper we study the complexity-theoretic aspects of maximal frequent itemset mining, from the perspective of counting the number of solutions. We present the first formal proof that the problem of counting the number of distinct maximal frequent itemsets in a database of transactions, given an arbitrary support threshold, is #P-complete, thereby providing strong theoretical evidence that the problem of mining maximal frequent itemsets is NP-hard. This result is of particular interest since the associated decision problem of checking the existence of a maximal frequent itemset is in P.We also extend our complexity analysis to other similar data mining problems dealing with complex data structures, such as sequences, trees, and graphs, which have attracted intensive research interests in recent years. Normally, in these problems a partial order among frequent patterns can be defined in such a way as to preserve the downward closure property, with maximal frequent patterns being those without any successor with respect to this partial order. We investigate several variants of these mining problems in which the patterns of interest are subsequences, subtrees, or subgraphs, and show that the associated problems of counting the number of maximal frequent patterns are all either #P-complete or #P-hard.
SmartMiner: a depth first algorithm guided by tail information for mining maximal frequent itemsets
Maximal frequent itemsets (MR) are crucial to many tasks in data mining. Since the MaxMiner algorithm first introduced enumeration trees for mining MR in 1998, several methods have been proposed to use depth first search to improve performance. To further improve the performance of mining MR, we proposed a technique that takes advantage of the information gathered from previous steps to discover new MR. More specifically, our algorithm called SmartMiner gathers and passes tail information and uses a heuristic select function which uses the tail information to select the next node to explore. Compared with Mafia and GenMax, SmartMiner generates a smaller search tree, requires a smaller number of support counting, and does not require superset checking. Using the datasets Mushroom and Connect, our experimental study reveals that SmartMiner generates the same MFI as Mafia and GenMax, but yields an order of magnitude improvement in speed.
An improved association rules mining method
Mining maximal frequent itemsets is of paramount relevance in many of data mining applications. The ''traditional'' algorithms address this problem through scanning databases many times. The latest research has already focused on reducing the number of scanning times of databases and then decreasing the number of accessing times of I/O resources in order to improve the overall mining efficiency of maximal frequent itemsets of association rules. In this paper, we present a form of the directed itemsets graph to store the information of frequent itemsets of transaction databases, and give the trifurcate linked list storage structure of directed itemsets graph. Furthermore, we develop the mining algorithm of maximal frequent itemsets based on this structure. As a result, one realizes scanning a database only once, and improves storage efficiency of data structure and time efficiency of mining algorithm.
MAFIA: A Performance Study of Mining Maximal Frequent Itemsets
We present a performance study of the MAFIA algorithm for mining maximal frequent itemsets from a transactional database. In a thorough experimental analysis, we isolate the effects of individual components of MAFIA, including search space pruning techniques and adaptive compression. We also compare our performance with previous work by running tests on very different types of datasets. Our experiments show that MAFIA performs best when mining long itemsets and outperforms other algorithms on dense data by a factor of three to thirty.
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