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.

title: Introducing a Rule Importance Measure
abstract: 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.

title: Rule Evaluations, Attributes, and Rough Sets: Extension and a Case Study
abstract: Manually evaluating important and interesting rules generated from data is generally infeasible due to the large number of rules extracted. Different approaches such as rule interestingness measures and rule quality measures have been proposed and explored previously to extract interesting and high quality association rules and classification rules. Rough sets theory was originally presented as an approach to approximate concepts under uncertainty. In this paper, we explore rough sets based rule evaluation approaches in knowledge discovery. We demonstrate rule evaluation approaches through a real-world geriatric care data set from Dalhousie Medical School. Rough set based rule evaluation approaches can be used in a straightforward way to rank the importance of the rules. One interesting system developed along these lies in HYRIS (HYbrid Rough sets Intelligent System). We introduce HYRIS through a case study on survival analysis using the geriatric care data set.

title: Discovering and ranking important rules
abstract: Decision rules generated from reducts can fully describe a data set. We introduce a new method of evaluating rules by taking advantage of rough sets theory. We consider rules generated from the original data set as attributes in the new constructed decision table. Reducts generated from this new decision table contain essential attributes, which are the rules. Only important rules are contained in the reducts. Experiments on an artificial data set and a medical data set show that the "reduct rules" are more important, and this new method provides an automatic and effective way of ranking rules.

title: Evaluation strategies for automatic linguistic indexing of pictures
abstract: With the rapid technological advances in machine learning and data mining, it is now possible to train computers with hundreds of semantic concepts for the purpose of annotating images automatically using keywords and textual descriptions. We have developed a system, the automatic linguistic indexing of pictures (ALIP) system, using a 2-D multiresolution hidden Markov model. The evaluation of such approaches opens up challenges and interesting research questions. The goals of linguistic indexing are often different from those of other fields including image retrieval, image classification, and computer vision. In many application domains, computer programs that can provide semantically relevant keyword annotations are desired, even if the predicted annotations are different from those of the gold standard. In this paper, we discuss evaluation strategies for automatic linguistic indexing of pictures. We provide both objective and subjective evaluation methods. Finally, we report experimental results using our ALIP system.

title: Mining the smallest association rule set for predictions
abstract: Mining transaction databases for association rules usually generates a large number of rules, most of which are unnecessary when used for subsequent prediction. In this paper we define a rule set for a given transaction database that is much smaller than the association rule set but makes the same predictions as the association rule set by the confidence priority. We call this subset the informative rule set. The informative rule set is not constrained to particular target items; and it is smaller than the non-redundant association rule set. We present an algorithm to directly generate the informative rule set, i.e., without generating all frequent itemsets first, and that accesses the database less often than other unconstrained direct methods. We show experimentally that the informative rule set is much smaller than both the association rule set and the non-redundant association rule set, and that it can be generated more efficiently.

title: Some properties of Ramsey numbers
abstract: In this paper, some properties of Ramsey numbers are studied, and the following results are presented. 
1. 
(1) For any positive integers k1, k2, …, km l1, l2, …, lm (m > 1), we have 
r ∏i=1m ki + 1, ∏i=1m li + 1 ≥ ∏i=1m [ r (ki + 1,li + 1) − 1] + 1 
. 
 
2. 
(2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have 
r ∑i=1m ki + 1, ∑j=1n lj + 1 ≥ ∑i=1m∑j=1n r (ki + 1,lj + 1) − mn + 1 
. Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties.

title: Mining Optimal Class Association Rule Set
abstract: 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.

title: An internet routing forensics framework for discovering rules of abnormal BGP events
abstract: Abnormal BGP events such as attacks, misconfigurations, electricity failures, can cause anomalous or pathological routing behavior at either global level or prefix level, and thus must be detected in their early stages. Instead of using ad hoc methods to analyze BGP data, in this paper we introduce an Internet Routing Forensics framework to systematically process BGP routing data, discover rules of abnormal BGP events, and apply these rules to detect the occurrences of these events. In particular, we leverage data mining techniques to train the framework to learn rules of abnormal BGP events, and our results from two case studies show that these rules are effective. In one case study, rules of worm events discovered from the BGP data during the outbreaks of the CodeRed and Nimda worms were able to successfully detect worm impact on BGP when an independent worm, the Slammer, subsequently occurred. Similarly, in another case study, rules of electricity blackout events obtained using BGP data from the 2003 East Coast blackout were able to detect the BGP impact from the Florida blackout caused by Hurricane Frances in 2004.