Efficient Closure Checking Mechanism for Cube Miner Algorithm

Abstract
This paper, we propose an efficient closure checking mechanism for three dimensional closed pattern mining from 3D datasets. We propose Cube Miner+ which extends the cube miner algorithm and incorporates the proposed closure checking scheme. We also aim at optimizing the existing algorithm by incorporating additional optimization techniques to reduce computation time.
Keyword:Data mining, closed patterns, mining methods, Algorithms.
I.Introduction
Mining frequent patterns or item sets is a fundamental and essential problem in many data mining applications. Frequent item sets play an essential role in many data mining tasks that tries to find interesting patterns from databases, such as association rules, correlations, sequences, episodes, classifiers, clusters and many more. The task of discovering all frequent item sets is quite challenging. The search space is exponential in the number of items occurring in the database. The support threshold limits the output to a hopefully reasonable subspace. Also, such databases could be massive, containing millions of transactions, making support counting a tough problem. The mining of the complete set of frequent item sets will lead to a number of huge and redundant item sets. Fortunately, this problem can be reduced to the mining of frequent closed item sets, which results in a much smaller number of item sets. A frequent closed item set is either a maximal frequent item set, or a frequent item set whose support is higher than the supports of all its proper supersets.
Frequent pattern mining is a fundamental step to several essential data mining tasks. It is an unsupervised mining technique that identifies all subsets of items or attributes frequently occurring in many database records or transactions. The concept of frequent closed pattern mining is proposed to overcome the problems of redundant patterns and rules and to enumerate feasible patterns from very long frequent patterns. Frequent closed pattern mining is found to be efficient in many application domains like market-basket analysis, www usage mining, gene expression data analysis, etc. In a typical gene expression data analysis, items denote gene expression properties in biological situations. Here, the frequent sets denote the sets of genes that are frequently co-regulated and thus can be suspected to participate to a common function within the cells. Frequent Closed Pattern Mining can reveal patterns about how the expression of one gene may be associated with the expression of a set of genes under a set of environments.
Given such information, we can easily infer that the genes involved participate in some kind of gene networks. Moreover, such association rules can be used to relate the expression of genes to their cellular environments and time periods simultaneously. Such associations can help to detect cancer genes in different cancer developing stages, especially when cancer is caused by a set of genes acting together in-stead of a single gene. It is however possible to use the properties of Galois connection to compute the closed sets on the smaller dimension and derive the closed sets on the other dimension. column set. Several algorithms [2] [5] [6] are proposed to mine frequent closed patterns from 2D space. In 3D frequent closed pattern mining (FCP), patterns are generated from 3D datasets comprising of height set, row set and column set.
The 2D frequent set mining problem concerns the computation of sets of attributes that are true together in enough transactions, i.e., given a frequency threshold. The patterns are generated from a 2D dataset which comprises of row set and column set. Several algorithms [2] [5] [6] are proposed to mine frequent closed patterns from 2D space coming up with the 3D datasets. The Frequent closed cube (FCC), which generalizes the notion of 2D frequent closed pattern to 3D context with two approaches called Representative Slice Mining algorithm (RSM) that exploits 2D FCP mining algorithms to mine FCCs and Cube Miner that directly mines from 2D Dataset