Learning and classification of monotonic ordinal concepts

Abstract

Ordinal reasoning plays a major role in human cognition. This paper identifies an important class of classification problems of patterns taken from ordinal domains and presents efficient, incremental algorithms for learning the classification rules from examples. We show that by adopting a monotonicity assumption of the output with respect to the input, inconsistencies among examples can be easily detected and the number of possible classification rules substantially reduced. By adopting a conservative classification criterion, the required number of rules further decreases. The monotonicity and conservatism of the classification also enable the resolution of conflicts among inconsistent examples and the graceful handling of don't knows and don't cares during the learning and classification phases. Two typical examples in which the suggested classification model works well are given. The first example is taken from the financial domain and the second from machining.Le raisonnement ordinal joue un rSle important dans le traitement cognitif de I'information. Cet article traite d'une classe importante de problemes de classification des formes provenant de domaines ordinaux, et prisente des algorithmes incrkmentiels efficaces pour l'apprentissage des regles de classification a partir d'exemples. Les auteurs dimontrent qu'en adoptant une hypothese de monotoniciti de la sortie en fonction de I'entrie, les incohirences dans les exemples peuvent itre facilement detecties et le nombre de rkgles de classification possibles considirablement rCduit. En choisissant un critere de classification prudent, le nombre requis de rkgles decroit davantage. La monotoniciti et la prudence de la classification permettent egalement la solution de conflits parmi les exemples incoherents, ainsi que le traitement habile des incertitudes et des indiffirences durant les phases d'apprentissage et de classification. Deux exemples classiques dans lesquels le modele de classification propose fonctionne sont fournis. Le premier exemple est tire du domaine financier et le second de l'informatique.

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“…An attribute-score pair was considered inconsistent with another if all its attribute values were higher or equal (lower or equal) than those of the other, while its score was strictly lower (higher). More details can be found in Ben-David et al (1989;1992). Each subject classified 95 lecturers on the average.…”

“…The same training sets and holdout samples were used by the OLM (Ben-David et al, 1989;Ben-David, 1992), which is an exemplar-based LFE model (Kibler & Aha, 1987). The OLM was used since all the lecturers' attributes, as well as the final grades, were ordinal symbols.…”

Isotonic Classification Trees

“…We used the KC4, PC3, PC4 and PC5 datasets from the NASA Metrics Data Program [15], the Acceptance/Rejection, Employee Selection, Lecturers Evaluation and Social Workers Decisions from A. Ben-David [4], the Windsor Housing dataset [1], the Den Bosch Housing dataset [9], as well as several datasets from the UCI Machine Learning Repository [2]. All datasets except Den Bosch Housing are publicly available.…”

Nearest Neighbour Classification with Monotonicity Constraints

“…Table 1 gives an overview of the data sets we used. All data sets have been taken from the UCI machine learning repository [4], except for Windsor Housing 1 [2], and Employee Selection 2 [6].…”

“…The earliest work in this area known to us is the Ordinal Learning Model (OLM) of Ben-David [5,6]. They construct a so-called rule base from a set of training examples.…”