This paper presents a new algorithm, A-Close, for discovering frequent closed itemsets in large databases. The algorithm is based on the closed itemset lattice, which is a sub-order of the itemset lattice and often much smaller. By focusing on the closed itemset lattice, the algorithm reduces the search space and improves efficiency. The paper shows that the set of frequent closed itemsets is sufficient to determine a reduced set of association rules, thus addressing the problem of limiting the number of rules produced without information loss. The algorithm uses a closure mechanism based on the Galois connection to find frequent closed itemsets. Experiments comparing A-Close to the Apriori algorithm show that A-Close is very efficient for dense and/or correlated data, such as statistical or text data. The algorithm is implemented in C++ and tested on synthetic and census data. The results show that A-Close outperforms Apriori in terms of execution time and number of database passes, especially for correlated data. The paper also discusses the scalability of the algorithm and its application in data mining, including unsupervised classification. The algorithm is efficient and effective for mining association rules in large databases.This paper presents a new algorithm, A-Close, for discovering frequent closed itemsets in large databases. The algorithm is based on the closed itemset lattice, which is a sub-order of the itemset lattice and often much smaller. By focusing on the closed itemset lattice, the algorithm reduces the search space and improves efficiency. The paper shows that the set of frequent closed itemsets is sufficient to determine a reduced set of association rules, thus addressing the problem of limiting the number of rules produced without information loss. The algorithm uses a closure mechanism based on the Galois connection to find frequent closed itemsets. Experiments comparing A-Close to the Apriori algorithm show that A-Close is very efficient for dense and/or correlated data, such as statistical or text data. The algorithm is implemented in C++ and tested on synthetic and census data. The results show that A-Close outperforms Apriori in terms of execution time and number of database passes, especially for correlated data. The paper also discusses the scalability of the algorithm and its application in data mining, including unsupervised classification. The algorithm is efficient and effective for mining association rules in large databases.