Combining Absolute and Relative Information with Frequency Distributions for Ordinal Classification

Abstract

A large amount of labelled data (absolute information) is usually needed for an ordinal classifier to attain a good performance. As shown in a recent paper by the present authors, the lack of a large amount of absolute information can be overcome by additionally considering some side information in the form of relative information, thus augmenting the method of nearest neighbors. In this paper, we adapt the method of nearest neighbors for dealing with a specific type of relative information: frequency distributions of pairwise comparisons (rather than a single pairwise comparison). We test the proposed method on some classical machine learning datasets and demonstrate its effectiveness.

Ordinal classification with a spectrum of information sources

“…Note that each of these couples comes with a frequency distribution represented by (𝛼 𝑗 𝑞 , 𝛽 𝑗 𝑞 ), where 𝛼 𝑗 𝑞 denotes the proportion of times that the preference order assigned is 𝐚 𝑗 𝑞 ≻ 𝐛 𝑗 𝑞 and 𝛽 𝑗 𝑞 the proportion of times that the preference order assigned is 𝐚 𝑗 𝑞 ≺ 𝐛 𝑗 𝑞 . An obvious idea, already proposed in Tang et al (2020a), would be to simply insert the value of 𝛼 𝑗 𝑞 in Eq. ( 6) and solve the corresponding optimization problem for assigning a label 𝑦 * to 𝐱 * .…”