Ordinal regression

About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.

Extreme ranking analysis in robust ordinal regression

Abstract: We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a preference model that is compatible with preference information provided by the DM. We refer to both, the well-known UTAGMS method, which builds the set of general additive value functions compatible with DM's preferences, and newly introduced in this paper PROMETHEEGKS, which constructs the set of compatible outranking models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible preference models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.

Multi-output Laplacian dynamic ordinal regression for facial expression recognition and intensity estimation

Abstract: Automated facial expression recognition has received increased attention over the past two decades. Existing works in the field usually do not encode either the temporal evolution or the intensity of the observed facial displays. They also fail to jointly model multidimensional (multi-class) continuous facial behaviour data; binary classifiers — one for each target basic-emotion class — are used instead. In this paper, intrinsic topology of multidimensional continuous facial affect data is first modeled by an ordinal manifold. This topology is then incorporated into the Hidden Conditional Ordinal Random Field (H-CORF) framework for dynamic ordinal regression by constraining H-CORF parameters to lie on the ordinal manifold. The resulting model attains simultaneous dynamic recognition and intensity estimation of facial expressions of multiple emotions. To the best of our knowledge, the proposed method is the first one to achieve this on both deliberate as well as spontaneous facial affect data.

Sequential Ordinal Modeling with Applications to Survival Data

Abstract: Summary. This paper considers the class of sequential ordinal models in relation to other models for ordinal response data. Markov chain Monte Carlo (MCMC) algorithms, based on the approach of Albert and Chib (1993, Journal of the American Statistical Association88, 669–679), are developed for the fitting of these models. The ideas and methods are illustrated in detail with a real data example on the length of hospital stay for patients undergoing heart surgery. A notable aspect of this analysis is the comparison, based on marginal likelihoods and training sample priors, of several nonnested models, such as the sequential model, the cumulative ordinal model, and Weibull and log-logistic models.

Measuring the performance of ordinal classification

Abstract: Ordinal classification is a form of multiclass classification for which there is an inherent order between the classes, but not a meaningful numeric difference between them. The performance of such classifiers is usually assessed by measures appropriate for nominal classes or for regression. Unfortunately, these do not account for the true dimension of the error. The goal of this work is to show that existing measures for evaluating ordinal classification models suffer from a number of important shortcomings. For this reason, we propose an alternative measure defined directly in the confusion matrix. An error coefficient appropriate for ordinal data should capture how much the result diverges from the ideal prediction and how "inconsistent" the classifier is in regard to the relative order of the classes. The proposed coefficient results from the observation that the performance yielded by the Misclassification Error Rate coefficient is the benefit of the path along the diagonal of the confusion matrix. We carry out an experimental study which confirms the usefulness of the novel metric.