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Sequential rule mining is an important data mining task with wide applications. The current state-of-the-art algorithm (RuleGrowth) for this task relies on a pattern-growth approach to discover sequential rules. A drawback of this approach is that it repeatedly performs a costly database projection operation, which deteriorates performance for datasets containing dense or long sequences. In this paper, we address this issue by proposing an algorithm named ERMiner (Equivalence class based sequential Rule Miner) for mining sequential rules. It relies on the novel idea of searching using equivalence classes of rules having the same antecedent or consequent. Furthermore, it includes a data structure named SCM (Sparse Count Matrix) to prune the search space. An extensive experimental study with five real-life datasets shows that ERMiner is up to five times faster than RuleGrowth but consumes more memory.

Abstract. Predicting next items of sequences of symbols has many applications in a wide range of domains. Several sequence prediction models have been proposed such as DG, All-k-order markov and PPM. Recently, a model named Compact Prediction Tree (CPT) has been proposed. It relies on a tree structure and a more complex prediction algorithm to offer considerably more accurate predictions than many state-of-the-art prediction models. However, an important limitation of CPT is its high time and space complexity. In this article, we address this issue by proposing three novel strategies to reduce CPT's size and prediction time, and increase its accuracy. Experimental results on seven real life datasets show that the resulting model (CPT+) is up to 98 times more compact and 4.5 times faster than CPT, and has the best overall accuracy when compared to six state-of-the-art models from the literature: All-K-order Markov, CPT, DG, Lz78, PPM and TDAG.

Abstract. Predicting the next item of a sequence over a finite alphabet has important applications in many domains. In this paper, we present a novel prediction model named CPT (C ompact P rediction T ree) which losslessly compress the training data so that all relevant information is available for each prediction. Our approach is incremental, offers a low time complexity for its training phase and is easily adaptable for different applications and contexts. We compared the performance of CPT with state of the art techniques, namely PPM (P rediction by P artial M atching), DG (Dependency Graph) and All-K-th-Order Markov. Results show that CPT yield higher accuracy on most datasets (up to 12% more than the second best approach), has better training time than DG and PPM, and is considerably smaller than All-K-th-Order Markov.

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The Itemset Tree is an efficient data structure for performing targeted queries for itemset mining and association rule mining. It is incrementally updatable by inserting new transactions and it provides efficient querying and updating algorithms. However, an important limitation of the IT structure, concerning scalability, is that it consumes a large amount of memory. In this paper, we address this limitation by proposing an improved data structure named MEIT (Memory Efficient Itemset Tree). It offers an efficient node compression mechanism for reducing IT node size. It also performs on-the-fly node decompression for restoring compressed information when needed. An experimental study with datasets commonly used in the data mining literature representing various types of data shows that MEIT are up to 60 % smaller than IT (43% on average).

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