Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

Measurement scales and scale independence in the Analytic Hierarchy Process

Abstract: One approach to evaluate the relative performance of decision alternatives with respect to multiple criteria is provided by the analytic hierarchy process. The method is based on pairwise comparisons between attributes, and several numerical measurement scales for the ratio statements have been proposed. The choice of measurement scale is re-examined, and new arguments supporting the measurement scale of geometric progression are derived. Separately from the measurement scale considerations, the effects of the scale parameter in geometric measurement scale are also studied. By using a regression model for pairwise comparisons data, it is shown that the statistical inference does not depend on the value of the scale parameter in the case of a single pairwise comparison matrix. It is also shown when the scale independence of statistical inference can be achieved in a decision hierarchy. This requires the use of the geometric-mean aggregation rule instead of the traditional arithmetic-mean aggregation. The results of the case study demonstrate that the measurement scale and the aggregation rule have potentially large impacts on decision support. Copyright © 2000 John Wiley & Sons, Ltd.

Random forests for metric learning with implicit pairwise position dependence

Abstract: Metric learning makes it plausible to learn semantically meaningful distances for complex distributions of data using label or pairwise constraint information. However, to date, most metric learning methods are based on a single Mahalanobis metric, which cannot handle heterogeneous data well. Those that learn multiple metrics throughout the feature space have demonstrated superior accuracy, but at a severe cost to computational efficiency. Here, we adopt a new angle on the metric learning problem and learn a single metric that is able to implicitly adapt its distance function throughout the feature space. This metric adaptation is accomplished by using a random forest-based classifier to underpin the distance function and incorporate both absolute pairwise position and standard relative position into the representation. We have implemented and tested our method against state of the art global and multi-metric methods on a variety of data sets. Overall, the proposed method outperforms both types of method in terms of accuracy (consistently ranked first) and is an order of magnitude faster than state of the art multi-metric methods (16x faster in the worst case).

Parameter Set Selection via Clustering of Parameters into Pairwise Indistinguishable Groups of Parameters

Abstract: Selecting a set of parameters to be estimated from experimental data is an important problem with many different types of applications. However, the computational effort grows drastically with the ...