Recently, ordinal regression, which predicts categories of ordinal scale, has received considerable attention. In this paper, we propose a new approach to solve ordinal regression problems within the learning vector quantization framework. It extends the previous approach termed ordinal generalized matrix learning vector quantization with a more suitable and natural cost function, leading to mo...

In this paper, we present a model for comparing groups on scale score outcomes. The has number of features that make it desirable analysis scores. is based ordinal regression, hence able to capture the shape data even when are highly discrete, or display marked ceiling floor effects. Additionally, incorporates hierarchical modelling create accurate summaries differences in scores across groups....

In this paper, we address the Multi-Instance-Learning (MIL) problem when bag labels are naturally represented as ordinal variables (Multi–Instance–Ordinal Regression). Moreover, we consider the case where bags are temporal sequences of ordinal instances. To model this, we propose the novel Multi-Instance Dynamic Ordinal Random Fields (MI-DORF). In this model, we treat instance-labels inside the...

We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor-Bendixson ranks (of trees). We prove the following results: 1) The ordinal height of any automatic wellfounded partial order is bounded by ω; 2) The ordinal heights of automatic well-founded r...

§0. The ordinal numbers were Georg Cantor’s deepest contribution to mathematics. After the natural numbers 0, 1, . . . , n, . . . comes the first infinite ordinal number ù, followed by ù + 1, ù + 2, . . . , ù + ù, . . . and so forth. ù is the first limit ordinal as it is neither 0 nor a successor ordinal. We follow the von Neumann convention, according to which each ordinal number α is identifi...

Recent research has demonstrated the negative impact of makeup on automated face recognition. In this work, we introduce a patch-based ensemble learning method, which uses multiple subspaces generated by sampling patches from before-makeup and after-makeup face images, to address this problem. In the proposed scheme, each face image is tessellated into patches and each patch is represented by a...

The objective of this paper is to introduce an ordinal representation system which has been employed in the determination of the proof{theoretic strength of 1 2 comprehension and related systems.

We show that in the presence of large cardinals proper forcings do not change the theory of L(R) with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.