Mining Ensemble Association Rules by Karnaugh Map

On-line generation association rules over data streams

Incremental mining has attracted the attention of many researchers due to its usefulness in online applications. Many algorithms have thus been proposed for incrementally mining frequent itemsets. Maintaining a frequent-itemset lattice (FIL) is difficult for databases with large numbers of frequent itemsets, especially huge databases, due to the storage of links of nodes in the lattice. However, generating association rules from a FIL has been shown to be more effective than traditional methods such as directly generating rules from frequent itemsets or frequent closed itemsets. Therefore, when the number of frequent itemsets is not huge (i.e., they can be stored in the lattice without excessive memory overhead), the lattice-based approach outperforms approaches which mine association rules from frequent itemsets/frequent closed itemsets. However, incremental algorithms for building FILs have not yet been proposed. This paper proposes an effective approach for the maintenance of a FIL based on the pre-large concept in incremental mining. The building process of a FIL is first improved using two proposed theorems regarding the paternity relation between two nodes in the lattice. An effective approach for maintaining a FIL with dynamically inserted data is then proposed based on the pre-large and the diffset concepts. The experimental results show that the proposed approach outperforms the batch approach for building a FIL in terms of execution time.

Generalized association rule mining using an efficient data structure

In knowledge mining, current trend is witnessing the emergence of a growing number of works towards defining "concise and lossless" representations. One main motivation behind is: tagging a unified framework for drastically reducing large sized sets of association rules. In this context, generic bases of association rules - whose backbone is the conjunction of the concepts of minimal generator (MG) and closed itemset (CI) - constituted so far irreducible compact nuclei of association rules. However, the inherent absence of a unique MG associated to a given CI offers an "ideal" gap towards a tougher redundancy removal even from generic bases of association rules. In this paper, we adopt the succinct system of minimal generators (SSMG), as newly redefined in [1], to be an exact representation of the MG set. Then, we incorporate the SSMG into the framework of generic bases to only maintain the succinct generic association rules. After that, we give a thorough formal study of the related inference mechanisms allowing to derive all redundant association rules starting from succinct ones. Finally, an experimental study shows that our approach makes it possible to eliminate without information loss an important number of redundant generic association rules and thus, to only present succinct and informative ones to users.

In the recent years, the growth of online marketplace explodes and has become the new norm of shopping. Access to the internet allows consumers to visit local and global online marketplace. By using online shopping, consumers can view the latest products and comparing products' prices. Online marketplace offers flexibility and eases consumers in so many ways. On the contrary, it also has some limitations. Dynamic pricing allows sellers to enhance their marketing strategy by ensuring price competitive with other sellers. The frequent occurrence of real-time price changing limits the user to get the best deal. This paper discusses the analysis of price changes using Association Rule Mining. Price-ChARM finds a frequent pattern of price changes in corresponding to different timelines. On the online marketplace, due to multiple sellers can sell the same item with different offers such as delivery speed and dynamic pricing, the comparison can be quite tricky. We collected data from two well-known portals and we represent the dataset as set of prices for different products for the purpose of frequent itemset mining. We implement the Apriori algorithm and use a total amount of 3,960 records. We generate association rules from the frequent itemsets found in the records and visualize the confidence of 0.9 rules. The association rules represent the pattern of price changes in the portals. This study eases consumer shopping experiences by understanding the trend of price changes to provide a better decision in making a purchase. Â

In this paper, we extend the traditional association rule problem by allowing a weight to be associated with each item in a transaction to reflect the interest/intensity of each item within the transaction. In turn, this provides us with an opportunity to associate a weight parameter with each item in a resulting association rule; we call them weighted association rules (WAR). One example of such a rule might be 80% of people buying more than three bottles of soda will also be likely to buy more than four packages of snack food, while a conventional association rule might just be 60% of people buying soda will be also be likely to buy snack food. Thus WARs cannot only improve the confidence of the rules, but also provide a mechanism to do more effective target marketing by identifying or segmenting customers based on their potential degree of loyalty or volume of purchases. Our approach mines WARs by first ignoring the weight and finding the frequent itemsets (via a traditional frequent itemset discovery algorithm), followed by introducing the weight during the rule generation. Specifically, the rule generation is achieved by partitioning the weight domain space of each frequent itemset into fine grids, and then identifying the popular regions within the domain space to derive WARs. This approach does not only support the batch mode mining, i.e., finding WARs for the dataset, but also supports the interactive mode, i.e., finding and refining WARs for a given (set) of frequent itemset(s).

We explore a new problem of mining general temporal association rules in publication databases. In essence, a publication database is a set of transactions where each transaction T is a set of items of which each item contains an individual exhibition period. The current model of association rule mining is not able to handle the publication database due to the following fundamental problems, i.e., 1) lack of consideration of the exhibition period of each individual item and 2) lack of an equitable support counting basis for each item. To remedy this, we propose an innovative algorithm progressive-partition-miner (abbreviated as PPM) to discover general temporal association rules in a publication database. The basic idea of PPM is to first partition the publication database in light of exhibition periods of items and then progressively accumulate the occurrence count of each candidate 2-itemset based on the intrinsic partitioning characteristics. Algorithm PPM is also designed to employ a filtering threshold in each partition to early prune out those cumulatively infrequent 2-itemsets. The feature that the number of candidate 2-itemsets generated by PPM is very close to the number of frequent 2-itemsets allows us to employ the scan reduction technique to effectively reduce the number of database scans. Explicitly, the execution time of PPM is, in orders of magnitude, smaller than those required by other competitive schemes that are directly extended from existing methods. The correctness of PPM is proven and some of its theoretical properties are derived. Sensitivity analysis of various parameters is conducted to provide many insights into Algorithm PPM.

Multi-dimensional semantic clustering of large databases for association rule mining

The association rule mining can be divided into two steps. The first step is to find out all frequent itemsets, whose occurrences are greater than or equal to the user-specified threshold. The second step is to generate reliable association rules based on all frequent itemsets found in the first step. Identifying all frequent itemsets in a large database dominates the overall performance in the association rule mining. In this paper, we propose an efficient hash-based method, HMFS, for discovering the maximal frequent itemsets. The HMFS method combines the advantages of both the DHP (Direct Hashing and Pruning) and the Pincer-Search algorithms. The combination leads to two advantages. First, the HMFS method, in general, can reduce the number of database scans. Second, the HMFS can filter the infrequent candidate itemsets and can use the filtered itemsets to find the maximal frequent itemsets. These two advantages can reduce the overall computing time of finding the maximal frequent itemsets. In addition, the HMFS method also provides an efficient mechanism to construct the maximal frequent candidate itemsets to reduce the search space. We have implemented the HMFS method along with the DHP and the Pincer-Search algorithms on a Pentium III 800 MHz PC. The experimental results show that the HMFS method has better performance than the DHP and the Pincer-Search algorithms for most of test cases. In particular, our method has significant improvement over the DHP and the Pincer-Search algorithms when the size of a database is large and the length of the longest itemset is relatively long.

Frequent itemset mining and association rule mining are fundamental problems in data mining. Despite of the intensive and continuous researches on frequent itemset mining, one essential and not completely solved drawback still remains. The drawback is pattern explosion: a huge number of frequent itemsets, or patterns, will be often derived. The association rule mining takes over the same drawback since each association rule consists of two frequent itemsets. One promising solution for alleviating this essential drawback practically as a post-processing is to rank the patterns and rules from various aspects and to identify which one to be examined first. In this paper, we propose to utilize the technology of representation learning to rank frequent itemsets and association rules. More specifically, we develop several evaluation measures for frequent itemsets and association rules by using the vector representations of items, transactions and frequent patterns which are obtained by existing representation learning techniques. By employing vector representations of three kinds of objects, various rankings reflecting different aspects can expect to be obtained.

Mining generalized association rules among items in the presence of taxonomy and with nonuniform minimum support has been recognized as an important model in the data mining community. In real applications, however, the work of discovering interesting association rules is an iterative process; the analysts have to continuously adjust the constraint of minimum support to discover real informative rules. How to reduce the response time for each remining process thus becomes a crucial issue. In this paper, we examine the problem of maintaining the discovered multi-supported generalized association rules when the multiple minimum support constraint is refined and propose a novel algorithm called RGA_MSR to accomplish the work. By keeping and utilizing the set of frequent itemsets and negative border, and adopting vertical intersection counting strategy, the proposed RGA_MSR algorithm can significantly reduce the computation time spent on rediscovery of frequent itemsets and has very good performance.

When it comes to association rule mining, all frequent itemsets are first found, and then the confidence level of association rules is calculated through the support degree of frequent itemsets. As all non-empty subsets in frequent itemsets are still frequent itemsets, all frequent itemsets can be acquired only by finding all maximal frequent itemsets (MFIs), whose supersets are not frequent itemsets. In this study, an algorithm, named right-hand side expanding (RHSE), which can accurately find all MFIs, was proposed. First, an Expanding Operation was designed, which, starting from any given frequent itemset, could add items using certain rules and form some supersets of given frequent itemsets. In addition, these supersets were all MFIs. Next, this operator was used to add items by taking all frequent 1-itemsets as the starting point alternately, and all MFIs were found in the end. Due to the special design of the Expanding Operation, each MFI could be found. Moreover, the path found was unique, which avoided the algorithm redundancy in temporal and spatial complexity. This algorithm, which has a high operating rate, is applicable to the big data of high-dimensional mass transactions as it is capable of avoiding the computing redundancy and finding all MFIs. In the end, a detailed experimental report on 10 open standard transaction sets was given in this study, including the big data calculation results of million-class transactions.

In order to solve these problems how to easily generate candidate frequent item sets and fast compute support of candidate item sets, an algorithm of association rules mining based on binary has been introduced. However, one presented binary mining algorithm is only suitable for mining some relative short frequent item sets since the way of generating candidate item sets is also similar to Apriori, another is only suitable for mining long frequent item sets, which generates candidate item sets by up-down search strategy. And so aiming to mining general frequent item sets, this paper proposes an algorithm of association rules double search mining based on binary, which is different from tradition association rules mining algorithm based on double search strategy. The algorithm doesn’t use combination of set theory to generate candidate item sets but binary logic operation that is also used to compute support of candidate item sets, which can use character digital to reduce the number of scanned transaction. The algorithm gets rid of shortage about some presented algorithms based on binary. The experiment based on above three algorithms indicates that the efficiency about double search strategy is fast and efficient when mining general frequent item sets which aren’t confined.

This paper shows a mathematical foundation for almost important features in the problem of discovering knowledge by association rules. The class of frequent itemsets and the association rule set are partitioned into disjoint classes by two equivalence relations based on closures. Thanks to these partitions, efficient parallel algorithms for mining frequent itemsets and association rules can be obtained. Practically, one can mine frequent itemsets as well as association rules just in the classes that users take care of. Then, we obtain structures of each rule class using corresponding order relations. For a given relation, each rule class splits into two subsets of basic and consequence. The basic one contains minimal rules and the consequence one includes in the rules that can be deducted from those minimal rules. In the rest, we consider association rule mining based on order relation min. The explicit form of minimal rules according to that relation is shown. Due to unique representations of frequent itemsets through their generators and corresponding eliminable itemsets, operators for deducting all remaining rules are also suggested. Experimental results show that mining association rules based on relation min is better than the ones based on relations of minmin and minMax in terms of reduction in mining times as well as number of basic rules.

A supermarket must have good business plan in order to meet customer desires. One way that can be done to meet customer desires is to find out the pattern of shopping purchases resulting from processing sales transaction data. Data processing produces information related to the function of the association between items of goods temporarily. Association rules functions in data mining.Association rule is one of the data mining techniques used to find patterns in combination of transaction data. Apriori algorithm can be used to find association rules. Apriori algorithm is used to find frequent itemset candidates who meet the support count. Frequent itemset that meets the support count is then processed using the temporal association rules method. The function of temporal association rules is as a time limitation in displaying the results of frequent itemsets and association rules. This study aims to produce rules from transaction data, apriori algorithm is used to form temporal association rules. The final results of this research are strong rules, they are rules that always appear in 3 years at certain time intervals with limitation on support and confidence, so that the rules can be used for business plan layout recommendations in Maharani Supermarket Demak.