Ordinal embedding aims at finding a low dimensional representation of objects from set constraints the form ”item j is closer to item i than k”. Typically, each object mapped onto point vector in metric space. We argue that mapping density instead provides some interesting advantages, including an inherent reflection uncertainty about itself and its relative location Indeed, this paper, we prop...

The aim of the contribution is the discussion of some types and classes of means on ordinal scales, especially kernel and shift invariant ordinal means, weighted ordinal means based on weighted divisible t–conorms (t–norms) and dissimilarity based ordinal means. Moreover, several types of ordinal arithmetic means are introduced.

There exists a family {Bα}α<ω1 of sets of countable ordinals such that (1) maxBα = α, (2) if α ∈ Bβ then Bα ⊆ Bβ , (3) if λ ≤ α and λ is a limit ordinal then Bα ∩ λ is not in the ideal generated by the Bβ , β < α, and by the bounded subsets of λ, (4) there is a partition {An}n=0 of ω1 such that for every α and every n, Bα∩An is finite.

Many classi®cation tasks can be viewed as ordinal. Use of numeric information usually provides possibilities for more powerful analysis than ordinal data. On the other hand, ordinal data allows more powerful analysis when compared to nominal data. It is therefore important not to overlook knowledge about ordinal dependencies in data sets used in data mining. This paper investigates data mining ...