Closed-Itemset Incremental-Mining Problem

Knowledge mining from single graph plays an important role in decision support systems on single graphs such as social networks, bioinformatics, etc. In recent years, the problem of Frequent Subgraph Mining (FSM) from a single graph have been developed and attracted several studies. However, the problem of mining association rules or links from frequent subgraphs has not had many contributions. In this article, we state the problem of direct mining association rules from frequent subgraphs. Existing approaches on this topic perform the task in two phases. First, they traverse the search space to directly discover parent-child relationships from the discovered frequent subgraphs, then association rules are generated. We propose a one-phase algorithm, named So-GPARs, to generate rules as soon as frequent supergraphs are constructed from already existing frequent subgraphs. Our experiments on three single graph datasets show that the one-phase algorithm is more efficient than the two-phase algorithm in terms runtime of the rules generating phase.

In this paper, we study the issues of mining and maintaining association rules in a large database of customer transactions. The problem of mining association rules can be mapped into the problems of finding large itemsets which are sets of items bought together in a sufficient number of transactions. We revise a graph-based algorithm to further speed up the process of itemset generation. In addition, we extend our revised algorithm to maintain discovered association rules when incremental or decremental updates are made to the databases. Experimental results show the efficiency of our algorithms. The revised algorithm significantly improves over the original one on mining association rules. The algorithms for maintaining association rules are more efficient than re-running the mining algorithms for the whole updated database and outperform previously proposed algorithms that need multiple passes over the database.

Discovering calendar-based temporal association rules

In this paper we study two orthogonal extensions of the classical data mining problem of mining association rules, and show how they naturally interact. The first is the extension from a propositional representation to datalog, and the second is the condensed representation of frequent itemsets by means of Formal Concept Analysis (FCA). We combine the notion of frequent datalog queries with iceberg concept lattices (also called closed itemsets) of FCA and introduce two kinds of iceberg query lattices as condensed representations of frequent datalog queries. We demonstrate that iceberg query lattices provide a natural way to visualize relational association rules in a non-redundant way.

DEFINITION Let I be a set of binary-valued attributes, called items. A set X ⊆ I is called an itemset. A transaction database D is a multiset of itemsets, where each itemset, called a transaction, has a unique identifier, called a tid. The support of an itemset X in a dataset D, denoted sup(X), is the fraction of transactions in D where X appears as a subset. X is said to be a frequent itemset in D if sup(X) ≥ minsup, where minsup is a user defined minimum support threshold. An (frequent) itemset is called closed if it has no (frequent) superset having the same support. An association rule is an expression A ⇒ B, where A and B are itemsets, and A ∩ B = ∅. The support of the rule is the joint probability of a transaction containing both A and B, given as sup(A ⇒ B) = P (A ∧ B) = sup(A ∪ B). The confidence of a rule is the conditional probability that a transaction contains B, given that it contains A, given as: conf(A ⇒ B) = P (B|A) = P (A∧B) P (A) = sup(A∪B) sup(A) . A rule is frequent if the itemset A∪B is frequent. A rule is confident if conf ≥ minconf , where minconf is a user-specified minimum threshold. The aim of non-redundant association rule mining is to generate a rule basis, a small, non-redundant set of rules, from which all other association rules can be derived.

A provided data from a transactional database, has supported technical development which can automatically find product association or items saved in the database. This finding association rules between saved product in database known as mining association rules. There are so many theories and algorithm developed for conducting mining association rules. One of algorithm developed is Apriori algorithm. This method, has a main goal to find the maximum frequent itemset. Next, this frequent itemset will be generated into associative rules which are not shown before in the database, become valuable information for considering materials in the decision process. Apriori algorithm is a interpretation technique of mining association rules, will be implemented into a web based software. On the software test which use in some different data, it’s concluded that time for mining association rules depends on the presence of every item in every transaction, total of transaction, minimum support and minimum confidence. For smaller value of minimum support and minimum confidence that entered, program will generate more association rules, vice versa.

There has been increasing interest in the problem of building accurate data mining models over aggregate data, while protecting privacy at the level of individual records. One approach for this problem is to randomize the values in individual records, and only disclose the randomized values. The model is then built over the randomized data, after first compensating for the randomization (at the aggregate level). This approach is potentially vulnerable to privacy breaches: based on the distribution of the data, one may be able to learn with high confidence that some of the randomized records satisfy a specified property, even though privacy is preserved on average.In this paper, we present a new formulation of privacy breaches, together with a methodology, "amplification", for limiting them. Unlike earlier approaches, amplification makes it is possible to guarantee limits on privacy breaches without any knowledge of the distribution of the original data. We instantiate this methodology for the problem of mining association rules, and modify the algorithm from [9] to limit privacy breaches without knowledge of the data distribution. Next, we address the problem that the amount of randomization required to avoid privacy breaches (when mining association rules) results in very long transactions. By using pseudorandom generators and carefully choosing seeds such that the desired items from the original transaction are present in the randomized transaction, we can send just the seed instead of the transaction, resulting in a dramatic drop in communication and storage cost. Finally, we define new information measures that take privacy breaches into account when quantifying the amount of privacy preserved by randomization.

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.

Association rule discovery algorithms generate all rules satisfying minimum support and confidence thresholds. These techniques yield too many rules and are infeasible when the minimum support is low. Recently, Li [1] proposed the Optimal Rule Discovery (ORD) algorithm that discovers a family of rule sets that maximizes a range of interestingness metrics, other than the commonly used confidence metric. In addition, the discovered optimal class association rule set is the minimum subset of rules with the same predictive power as the complete class association rule set. Moreover, ORD is significantly more efficient than association rule discovery independent of the data structure and the implementation. Due to the existence of huge amounts of data, it is important to investigate efficient methods for distributed/parallel mining of rules. In this paper, we propose EDP-ORD an efficient distributed/parallel extension of the ORD algorithm. We theoretically disclose a relationship between locally large and globally large rules and use it in reducing the number of generated rules and the exchanged messages at each site/partition. Moreover, we empirically compare EDP-ORD with a naive distributed/parallel ORD version on five benchmark datasets. The experimental results shows that the reduction in number of generated rules at each site can reach 44% while the reduction in total size of exchanged messages can reach 58%.

MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules

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.

Efficiently mining frequent itemsets and association rules on the encrypted outsourced data remains a great challenge for the time-consuming ciphertext computations. Nowadays, it has been not well addressed for privacy-preserving frequent itemsets and association rule mining schemes with mining efficiency, dataset, and query confidentiality simultaneously. In this paper, we investigate the study of privacy issues on frequent itemset mining and association rule mining on outsourced data in a two-cloud model, where the data are encrypted and outsourced by multiple owners holding different public keys. We develop several secure computation protocols based on additively homomorphic cryptosystem and additive secret sharing, which enable the clouds could securely mine the frequent itemsets and association rules. Furthermore, we also design two kinds of frequent itemset and association rule query service models, i.e., service customers query the cloud-mined results, and service customers query with their own decided threshold. The proposed scheme not only supports the mining process on the data encrypted by multiple public keys without compromising the security of the datasets, query data and query results, but also offline users. In addition, the experimental results show that our query scheme is much more efficient than the state-of-the-art work.

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.

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).

In order to trace the changes of association rules over an online data stream efficiently, this paper proposes two different methods of generating all association rules directly over the changing set of currently frequent itemsets. While all of the currently frequent itemsets are monitored by the estDec method, all the association rules of every frequent itemset in the prefix tree of the estDec method are generated. For this purpose, a traversal stack is introduced to efficiently enumerate all association rules. These online methods can avoid the drawbacks of the conventional two-step approach. In an on-line environment, a user may be interested in finding those association rules whose antecedents or consequents are fixed to be a specific itemset. Since generating all the association rules may take too long to produce them timely, two additional methods, namely Assoc-X and Assoc-Y, are introduced. Finally, the proposed methods are compared by a series of experiments to identify their various characteristics.