Interactive visual exploration of association rules with rule-focusing methodology

International audienceOn account of the enormous amounts of rules that can be produced by data mining algorithms, knowledge post-processing is a difficult stage in an association rule discovery process. In order to find relevant knowledge for decision making, the user (a decision maker specialized in the data studied) needs to rummage through the rules. To assist him/her in this task, we here propose the rule-focusing methodology, an interactive methodology for the visual post-processing of association rules. It allows the user to explore large sets of rules freely by focusing his/her attention on limited subsets. This new approach relies on rule interestingness measures, on a visual representation, and on interactive navigation among the rules. We have implemented the rule-focusing methodology in a prototype system called ARVis. It exploits the user's focus to guide the generation of the rules by means of a specific constraint-based rule-mining algorithm

Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods

Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods

Flexibility and real options analysis in power system generation expansion planning under uncertainty

Over many years, there has been a drive in the electricity industry towards better integration of environmentally friendly and renewable generation resources for power systems. Such resources show highly variable availability, impacting the design and performance of power systems. In this paper, we propose using a stochastic programming approach to optimize generation expansion planning (GEP), with explicit consideration of generator output capacity uncertainty. Flexibility implementation - via real options exercised in response to uncertainty realizations - is considered as an important design approach to the GEP problem. It more effectively captures upside opportunities, while reducing exposure to downside risks. A decision-rule based approach to real options modeling is used, combining conditional-go and finite adaptability principles. The solutions provide decision makers with easy-to-use guidelines with threshold values from which to exercise the options in operations. To demonstrate application of the proposed methodologies and decision rules, a case study situated in the Midwest United States is used. The case study demonstrates how to quantify the value of flexibility, and showcases the usefulness of the proposed approach

J-measure based hybrid pruning for complexity reduction in classification rules

Prism is a modular classification rule generation method based on the ‘separate and conquer’ approach that is alternative to the rule induction approach using decision trees also known as ‘divide and conquer’. Prism often achieves a similar level of classification accuracy compared with decision trees, but tends to produce a more compact noise tolerant set of classification rules. As with other classification rule generation methods, a principle problem arising with Prism is that of overfitting due to over-specialised rules. In addition, over-specialised rules increase the associated computational complexity. These problems can be solved by pruning methods. For the Prism method, two pruning algorithms have been introduced recently for reducing overfitting of classification rules - J-pruning and Jmax-pruning. Both algorithms are based on the J-measure, an information theoretic means for quantifying the theoretical information content of a rule. Jmax-pruning attempts to exploit the J-measure to its full potential because J-pruning does not actually achieve this and may even lead to underfitting. A series of experiments have proved that Jmax-pruning may outperform J-pruning in reducing overfitting. However, Jmax-pruning is computationally relatively expensive and may also lead to underfitting. This paper reviews the Prism method and the two existing pruning algorithms above. It also proposes a novel pruning algorithm called Jmid-pruning. The latter is based on the J-measure and it reduces overfitting to a similar level as the other two algorithms but is better in avoiding underfitting and unnecessary computational effort. The authors conduct an experimental study on the performance of the Jmid-pruning algorithm in terms of classification accuracy and computational efficiency. The algorithm is also evaluated comparatively with the J-pruning and Jmax-pruning algorithms

Automatic Induction of Classification Rules from Examples Using N-Prism

www.dis.port.ac.uk/~bramerma One of the key technologies of data mining is the automatic induction of rules from examples, particularly the induction of classification rules. Most work in this field has concentrated on the generation of such rules in the intermediate form of decision trees. An alternative approach is to generate modular classification rules directly from the examples. This paper seeks to establish a revised form of the rule generation algorithm Prism as a credible candidate for use in the automatic induction of classification rules from examples in practical domains where noise may be present and where predicting the classification for previously unseen instances is the primary focus of attention