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.

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: 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: 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: A new degree condition for graphs to have [a, b]-factor
abstract: Let t ( ⩾ 3 ) , a and b be integers with 0 ⩽ a b . A graph is called K 1 , t -free if it contains no K 1 , t as an induced subgraph. We prove that every K 1 , t -free G has an [ a , b ] -factor if its minimum degree is at least ( t - 1 ) ( a + 1 ) + b b b + a ( t - 1 ) 2 ( t - 1 ) - t - 1 b b + a ( t - 1 ) 2 ( t - 1 ) 2 - 1 . This degree condition is sharp.

title: On optimal rule discovery
abstract: 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.

title: An embedded still image coder with rate-distortion optimization
abstract: It is well known that the fixed rate coder achieves optimality when all coefficients are coded with the same rate-distortion (R-D) slope. In this paper, we show that the performance of the embedded coder can be optimized in a rate-distortion sense by coding the coefficients with decreasing R-D slope. We denote such a coding strategy as rate-distortion optimized embedding (RDE). RDE allocates the available coding bits first to the coefficient with the steepest R-D slope, i.e., the largest distortion decrease per coding bit. The resultant coding bitstream can be truncated at any point and still maintain an optimal R-D performance. To avoid the overhead of coding order transmission, we use the expected R-D slope, which can be calculated from the coded bits and is available in both the encoder and the decoder. With the probability estimation table of the QM-coder, the calculation of the R-D slope can be just a lookup table operation. Experimental results show that the rate-distortion optimization significantly improves the coding efficiency in a wide bit rate range.

title: Cycles Containing Given Subsets in 1-Tough Graphs