Zhangyan Xu

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.

Efficient attribute reduction based on discernibility matrix

To reduce the time complexity of attribute reduction algorithm based on discernibility matrix, a simplified decision table is first introduced, and an algorithm with time complexity O(|C||U|) is designed for calculating the simplified decision table. And then, a new measure of the significance of an attribute is defined for reducing the search space of simplified decision table. A recursive algorithm is proposed for computing the attribute significance that its time complexity is of O(|U/C|) . Finally, an efficient attribute reduction algorithm is developed based on the attribute significance. This algorithm is equal to existing algorithms in performance and its time complexity is O(|C||U|) + O(|C|2|U/C|).

INDEX-MAXMINER: A NEW MAXIMAL FREQUENT ITEMSET MINING ALGORITHM

Because of the inherent computational complexity, mining the complete frequent item-set in dense datasets remains to be a challenging task. Mining Maximal Frequent Item-set (MFI) is an alternative ...

Meta itemset: a new concise representation of frequent itemset

The sheer size of all frequent itemsets is one challenging problem in data mining research. Based on both closed itemset and maximal itemset, meta itemset which is a new concise representation of frequent itemset is proposed. It is proved that both closed itemset and maximal itemset are special cases of meta itemset. The set of all closed itemsets and the set of all maximal itemsets form the upper bound and the lower bound of the set of all meta itemsets. Then, property and pruning strategies of meta itemset are discussed. Finally, an efficient algorithm for mining meta itemset is proposed. Experimental results show that the proposed algorithm is effective and efficient.

New Attribute Reduction Based on Rough Set

With more than twenty years development, rough set theory has been successfully applied in the fields of expert systems, machine learning, and knowledge discovery in databases. Attribute reduction is an important research issue in rough set theory. At present, there are many different attribute reduction definitions, for example, attribute reduction based on Pawlak, based on information entropy and based on Skowrons discernibility matrix, etc. In this paper, a new measurement with parameter is provided based on rough set. Then monotony of the new measurement with parameter is proved. So definition of attribute reduction based on the new measurement with parameter is got. At the same time, it is proved that attribute reduction based on Skowrons discernibility matrix and on information entropy are the special cases of the new proposed attribute reduction. Therefore the new attribute reduction in rough set is very meaningful.

Attribute Reduction Algorithm Based on the Simplified Discernibility Matrix of Granularity

This paper gives the definition of discernibility matrix of granularity in decision table and the corresponding attribute reduction and the definition of discernibility matrix of granularity in the simplified decision table and the corresponding attribute reduction. Therefore, verifying the equivalence of the definition of attribute reduction in the simplified decision table and the definition of attribute reduction based on relative granularity of decision table. On the basis of the above theories, a new algorithm is designed based on knowledge granulation for attribute reduction in simplified decision table, and the corresponding complexity of time is reduced to O(|C|2|U′ pos ||U|). Finally, an example is given to illustrate the validity of the new algorithm.

A quick attribute reduction algorithm based on knowledge granularity

The research of knowledge granularity has been a hotspot at home and abroad. In incomplete information systems of the rough set, we give a formula, which calculates the attribute frequency directly without acquiring the discernibility matrix. Then applying it to the field of knowledge granularity, we give a quick calculation of the attribute reduction algorithm, which of the time complexity is O(|C|2 |U |) in the worst case. The example result shows that the algorithm is correct and efficient.

The Extended Alpha-triple I Algorithm Based on the Generalized Implication Operator

In this paper, the classical implication operator is generalized, and then the definition of generalized implication operator on [0, 1] is proposed. Based on generalized implication operator, the extended alpha-triple I principle is presented by generalizing the alpha-triple I algorithm. By analyzing the essence of alpha-triple Fuzzy Modus Ponens (FMP) and alpha-triple Fuzzy Modus Tollens (FMT) principles, and based on the generalized implication operator, the generalized calculating formula of extended alpha-triple I algorithm is proposed. At the same time, the reversibility on the proposed alpha-triple I algorithm is discussed. It is proved that Compositional Rule of Inference (CRI) is a special case of extended alpha-triple I algorithm. Finally, two implication operations are proposed to validate the proposed generalized equation.