The set of frequent closed itemsets uniquely determines the exact frequency of all itemsets, yet it can be orders of magnitude smaller than the set of all frequent itemsets. In this paper we present CHARM, an efficient algorithm for mining all frequent closed itemsets. It enumerates closed sets using a dual itemset-tidset search tree, using an efficient hybrid search that skips many levels. It also uses a technique called diffsets to reduce the memory footprint of intermediate computations. Finally it uses a fast hash-based approach to remove any “non-closed” sets found during computation. An extensive experimental evaluation on a number of real and synthetic databases shows that CHARM significantly outperforms previous methods. It is also linearly scalable in the number of transactions.

Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be prohibitively large. To overcome this problem, recently several proposals have been made to construct a concise representation of the frequent itemsets, instead of mining all frequent itemsets. The main goal of this paper is to identify redundancies in the set of all frequent itemsets and to exploit these redundancies in order to reduce the result of a mining operation. We present deduction rules to derive tight bounds on the support of candidate itemsets. We show how the deduction rules allow for constructing a minimal representation for all frequent itemsets. We also present connections between our proposal and recent proposals for concise representations and we give the results of experiments on real-life datasets that show the effectiveness of the deduction rules. In fact, the experiments even show that in many cases, first mining the concise representation, and then creating the frequent itemsets from this representation outperforms existing frequent set mining algorithms.

We introduce the notion of iceberg concept lattices...

The set of frequent closed itemsets uniquely determines the exact frequency of all itemsets, yet it can be orders of magnitude smaller than the set of all frequent itemsets. In this paper, we present CHARM, an efficient algorithm for mining all frequent closed itemsets. It enumerates closed sets using a dual itemset-tidset search tree, using an efficient hybrid search that skips many levels. It also uses a technique called diffsets to reduce the memory footprint of intermediate computations. Finally, it uses a fast hashbased approach to remove any "nonclosed" sets found during computation. We also present CHARM-L, an algorithm that outputs the closed itemset lattice, which is very useful for rule generation and visualization. An extensive experimental evaluation on a number of real and synthetic databases shows that CHARM is a state-of-the-art algorithm that outperforms previous methods. Further, CHARM-L explicitly generates the frequent closed itemset lattice.

Due to the potentially immense amount of frequent sets that can be generated from transactional databases, recent studies have demonstrated the need for concise representations of all frequent sets.

Mining frequent itemsets is one of the main problems in data mining. Much effort went into developing efficient and scalable algorithms for this problem. When the support threshold is set too low, however, or the data is highly correlated, the number of frequent itemsets can become too large, independently of the algorithm used. Therefore, it is often more interesting to mine a reduced collection of interesting itemsets, i.e., a condensed representation. Recently, in this context, the non-derivable itemsets were proposed as an important class of itemsets. An itemset is called derivable when its support is completely determined by the support of its subsets. As such, derivable itemsets represent redundant information and can be pruned from the collection of frequent itemsets. It was shown both theoretically and experimentally that the collection of non-derivable frequent itemsets is in general much smaller than the complete set of frequent itemsets. A breadth-first, Apriori-based algorithm, called NDI, to find all non-derivable itemsets was proposed. In this paper we present a depth-first algorithm, dfNDI, that is based on Eclat for mining the non-derivable itemsets. dfNDI is evaluated on real-life datasets, and experiments show that dfNDI outperforms NDI with an order of magnitude. 1

The performance of an algorithm that mines frequent sets from transactional databases may severely depend on the specific features of the data being analyzed. Moreover, some architectural characteristics of the computational platform used -- e.g. the available main memory -- can dramatically change the runtime behaviors of the algorithm. In this paper we present DCI (Direct Count & Intersect), an e#cient data mining algorithm for discovering frequent sets from large databases, which e#ectively addresses the issues mentioned above. DCI adopts a classical level-wise approach based on candidate generation to extract frequent sets, but uses a hybrid method to determine candidate supports. The most innovative contribution of DCI relies on the multiple heuristics strategies employed, which permits DCI to adapt its behavior not only to the features of the specific computing platform, but also to the features of the dataset being mined, so that it results e#ective in mining both short and long patterns from sparse and dense datasets. The large amount of tests conducted permit us to state that DCI sensibly outperforms state-ofthe -art algorithms for both synthetic and real-world datasets. Finally we also discuss the parallelization strategies adopted in the design of ParDCI, a distributed and multi-threaded implementation of DCI. ParDCI

data analysis

Abstract. We are designing new data mining techniques on boolean contexts to identify a priori interesting concepts, i.e., closed sets of objects (or transactions) and associated closed sets of attributes (or items). We propose a new algorithm D-Miner for mining concepts under constraints. We provide an experimental comparison with previous algorithms and an application to an original microarray dataset for which D-Miner is the only one that can mine all the concepts.

Abstract. Solving inductive queries which have to return complete collections of patterns satisfying a given predicate has been studied extensively the last few years. The specific problem of frequent set mining from potentially huge boolean matrices has given rise to tens of efficient solvers. Frequent sets are indeed useful for many data mining tasks, including the popular association rule mining task but also feature construction, association-based classification, clustering, etc. The research in this area has been boosted by the fascinating concept of condensed representations w.r.t. frequency queries. Such representations can be used to support the discovery of every frequent set and its support without looking back at the data. Interestingly, the size of condensed representations can be several orders of magnitude smaller than the size of frequent set collections. Most of the proposals concern exact representations while it is also possible to consider approximated ones, i.e., to trade computational complexity with a bounded approximation on the computed support values. This paper surveys the core concepts used in the recent works on condensed representation for frequent sets. 1