15000115
Direct interesting rule generation
An association rule generation algorithm usually generates too many rules including a lot of uninteresting ones. Many interestingness criteria are proposed to prune those uninteresting rules. However, they work in post-pruning process and hence do not improve the rule generation efficiency. We discuss properties of informative rule set and conclude that the informative rule set includes all interesting rules measured by many commonly used interestingness criteria, and that rules excluded by the informative rule set are forwardly prunable, i.e. they can be removed in the rule generation process instead of post pruning. Based on these properties, we propose a direct interesting rule generation algorithm, DIG, to directly generate interesting rules defined by any of 12 interestingness criteria. We further show experimentally that DIG is faster and uses less memory than Apriori.
6713735
Construct robust rule sets for classification
We study the problem of computing classification rule sets from relational databases so that accurate predictions can be made on test data with missing attribute values. Traditional classifiers perform badly when test data are not as complete as the training data because they tailor a training database too much. We introduce the concept of one rule set being more robust than another, that is, able to make more accurate predictions on test data with missing attribute values. We show that the optimal class association rule set is as robust as the complete class association rule set. We then introduce the k-optimal rule set, which provides predictions exactly the same as the optimal class association rule set on test data with up to k missing attribute values. This leads to a hierarchy of k-optimal rule sets in which decreasing size corresponds to decreasing robustness, and they all more robust than a traditional classification rule set. We introduce two methods to find k-optimal rule sets, i.e. an optimal association rule mining approach and a heuristic approximate approach. We show experimentally that a k-optimal rule set generated by the optimal association rule mining approach performs better than that by the heuristic approximate approach and both rule sets perform significantly better than a typical classification rule set (C4.5Rules) on incomplete test data.
12799351
Mining risk patterns in medical data
In this paper, we discuss a problem of finding risk patterns in medical data. We define risk patterns by a statistical metric, relative risk, which has been widely used in epidemiological research. We characterise the problem of mining risk patterns as an optimal rule discovery problem. We study an anti-monotone property for mining optimal risk pattern sets and present an algorithm to make use of the property in risk pattern discovery. The method has been applied to a real world data set to find patterns associated with an allergic event for ACE inhibitors. The algorithm has generated some useful results for medical researchers.
6271246
Mining Optimal Class Association Rule Set
We define an optimal class association rule set to be the minimum rule set with the same prediction power of the complete class association rule set. Using this rule set instead of the complete class association rule set we can avoid redundant computation that would otherwise be required for mining predictive association rules and hence improve the efficiency of the mining process significantly. We present an efficient algorithm for mining the optimal class association rule set using an upward closure property of pruning weak rules before they are actually generated. We have implemented the algorithm and our experimental results show that our algorithm generates the optimal class association rule set, whose size is smaller than 1/17 of the complete class association rule set on average, in significantly less time than generating the complete class association rule set. Our proposed criterion has been shown very effective for pruning weak rules in dense databases.
16942821
Mining the optimal class association rule set
We define an optimal class association rule set to be the minimum rule set with the same predictive power of the complete class association rule set. Using this rule set instead of the complete class association rule set we can avoid redundant computation that would otherwise be required for mining predictive association rules and hence improve the efficiency of the mining process significantly. We present an efficient algorithm for mining the optimal class association rule set using an upward closure property of pruning weak rules before they are actually generated. We have implemented the algorithm and our experimental results show that our algorithm generates the optimal class association rule set, whose size is smaller than 1/17 of the complete class association rule set on average, in significantly less rime than generating the complete class association rule set. Our proposed criterion has been shown very effective for pruning weak rules in dense databases.
15049854
On optimal rule discovery
In machine learning and data mining, heuristic and association rules are two dominant schemes for rule discovery. Heuristic rule discovery usually produces a small set of accurate rules, but fails to find many globally optimal rules. Association rule discovery generates all rules satisfying some constraints, but yields too many rules and is infeasible when the minimum support is small. Here, we present a unified framework for the discovery of a family of optimal rule sets and characterize the relationships with other rule-discovery schemes such as nonredundant association rule discovery. We theoretically and empirically show that optimal rule discovery is significantly more efficient than association rule discovery independent of data structure and implementation. Optimal rule discovery is an efficient alternative to association rule discovery, especially when the minimum support is low.
10151357
Introducing a Rule Importance Measure
Association rule algorithms often generate an excessive number of rules, many of which are not significant. It is difficult to determine which rules are more useful, interesting and important. We introduce a rough set based Rule Importance Measure to select the most important rules. We use ROSETTA software to generate multiple reducts. Apriori association rule algorithm is then applied to generate rule sets for each data set based on each reduct. Some rules are generated more frequently than the others among the total rule sets. We consider such rules as more important. We define rule importance as the frequency of an association rule generated across all the rule sets. Rule importance is different from either rule interestingness measures or rule quality measures because of their application tasks, the processes where the measures are applied and the contents they measure. The experimental results from an artificial data set, UCI machine learning datasets and an actual geriatric care medical data set show that our method reduces the computational cost for rule generation and provides an effective measure of how important is a rule.
37515044
ECSP: An Efficient Cluster Based P2P Architecture
15549324
A Rough Set Based Model to Rank the Importance of Association Rules
Association rule algorithms often generate an excessive number of rules, many of which are not significant. It is difficult to determine which rules are more useful, interesting and important. We introduce a rough set based process by which a rule importance measure is calculated for association rules to select the most appropriate rules. We use ROSETTA software to generate multiple reducts. Apriori association rule algorithm is then applied to generate rule sets for each data set based on each reduct. Some rules are generated more frequently than the others among the total rule sets. We consider such rules as more important. We define rule importance as the frequency of an association rule among the rule sets. Rule importance is different from rule interestingness in that it does not consider the predefined knowledge on what kind of information is considered to be interesting. The experimental results show our method reduces the number of rules generated and at the same time provides a measure of how important is a rule.
36212113
Independent triangles covering given vertices of a graph
Let G be a simple graph of order n, k a positive integer with n≥3k and X a set of any k vertices of G. We show that if the minimum degree G)≥(n + k)=2, then G contains k independent triangles covering all vertices of X ; and if the minimum degree (G)≥(n+2k)=2, then G contains k independent triangles such that each triangle contains exactly one vertex of X . The bounds on the minimum degree of G in above results are sharp. Some conjectures about independent triangles covering some given vertices are proposed.
2257002
Power-performance considerations of parallel computing on chip multiprocessors
This paper looks at the power-performance implications of running parallel applications on chip multiprocessors (CMPs). First, we develop an analytical model that, for the first time, puts together parallel efficiency, granularity of parallelism, and voltage/frequency scaling, to establish a formal connection with the power consumption and performance of a parallel code running on a CMP. We then conduct detailed simulations of parallel applications running on a detailed power-performance CMP model to confirm the analytical results and provide further insights. Both analytical and experimental models show that parallel computing can bring significant power savings and still meet a given performance target by choosing granularity and voltage/frequency levels judiciously. The particular choice, however, is dependent on the application's parallel efficiency curve and the process technology utilized, which our model captures. Likewise, analytical model and experiments show the effect of a limited power budget on the application's scalability curve. In particular, we show that a limited power budget can cause a rapid performance degradation beyond a number of cores, even in the case of applications with excellent scalability properties. On the other hand, our experiments show that, when a limited power budget is in place, power-thrifty memory-bound applications may actually enjoy better scalability than more compute-intensive codes, even if the latter would exhibit higher scalability in a power-unconstrained scenario.