We show that classification rules used in ordinal regression are equivalent to a certain class of linear multi-class classifiers. This observation not only allows to design new learning algorithms for ordinal regression using existing methods for multi-class classification but it also allows to derive new models for ordinal regression. For example, one can convert learning of ordinal classifier...

This paper presents a structured ordinal measure method for video-based face recognition that simultaneously learns ordinal filters and structured ordinal features. The problem is posed as a non-convex integer program problem that includes two parts. The first part learns stable ordinal filters to project video data into a large-margin ordinal space. The second seeks self-correcting and discret...

dental caries is one of the most preventable yet prevalent chronic diseases worldwide. our objective was to evaluate the effect of family structure and behavioral and eyesight problems as they relate to caries severity in schoolchildren.this research was carried out on 845 primary schoolchildren aged 9 yr in kerman, iran, in 2012. ten variables, including health records, family structure inform...

Ordinal regression problem arises in situations where examples are rated in an ordinal scale. In practice, labeled ordinal data are difficult to obtain while unlabeled ordinal data are available in abundance. Designing a probabilistic semi-supervised classifier to perform ordinal regression is challenging. In this work, we propose a novel approach for semi-supervised ordinal regression using Ga...

Let λH be the term calculus of Howard’s system of constructive ordinals. I use this to name iteration gadgets (generalized ordinal notations). I isolate a family of higher order ordinal functions which give a partial semantics of λH. I indicate how λH provides an intrinsic measure of each ordinal below the Howard ordinal.1

The notion of ordinal computability is defined by generalising standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. The fundamental theorem on ordinal computability states that a set x of ordinals is ordinal computable from ordinal parameters if and only if x is an element of the constructible universe L. In this paper we present a new proof o...

In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The delibera...

A method is proposed for classification to ordinal categories by applying the search partition analysis (SPAN) approach. It is suggested that SPAN be repeatedly applied to binary outcomes formed by collapsing adjacent categories of the ordinal scale. By a simple device, whereby successive binary partitions are constrained to be nested, a partition for classification to the ordinal states is obt...

Let us observe that there exists an ordinal number which is non empty and natural. Let a be a natural ordinal number. Note that succa is natural. The scheme Omega Ind concerns a unary predicate P , and states that: For every natural ordinal number a holds P [a] provided the following conditions are met: • P [ / 0], and • For every natural ordinal number a such that P [a] holds P [succa]. Let a,...