Partial classification in the belief function framework

Abstract

Partial, or set-valued classification assigns instances to sets of classes, making it possible to reduce the probability of misclassification while still providing useful information. This paper reviews approaches to partial classification based on the Dempster-Shafer theory of belief functions. To define the utility of set-valued predictions, we propose to extend the utility matrix using an Ordered Weighted Average operator, allowing us to model the decision maker's attitude towards imprecision using a single parameter. Various decision criteria are analyzed comprehensively. In particular, two main strategies are distinguished: partial classification based on complete preorders among partial assignments, and partial preorders among complete assignments. Experiments with UCI and simulated Gaussian data sets show the superiority of partial classification in terms of average utility, as compared to single-class assignment and classification with rejection.

Evidential fully convolutional network for semantic segmentation

“…Thanks to the generality and expressiveness of the belief-function formalism, an evidential classifier provides more informative outputs than those of conventional classifiers (e.g., a neural network with a softmax output layer). The flexibility of evidential classifiers can be exploited for uncertain data classification [40] and set-valued classification [8,26]. Therefore, it may be advantageous to combine an FCN-based model with an evidential classifier for semantic segmentation.…”

“…The act with the highest pignistic expected utility can then be selected. Other decision criteria in the belief function framework are reviewed in [11] and [26].…”

“…For semantic segmentation problems with imprecise prediction, we adopt the approach described in [26] for set-valued classification under uncertainty, which allows the assignment of a pixel to any non-empty subset A of Ω. The set of acts thus potentially becomes F = {f A : A ⊆ Ω, A = ∅}, where f A denotes the assignment to a subset A.…”

“…For decision-making with F, the utility matrix U has to be extended to a matrix U of size (2 M − 1) × M, where each element u A,j denotes the utility of assigning a pixel to set A of classes when the true label is ω j . Following [26], this extension is performed as follows.…”

“…in which case the OWA operator becomes the average. In this study, following [26], we determine the weight vector g of the OWA operator by adapting O'Hagan's method [29].…”