Affiliations: Faculty of Computer Science and Technology, Inner Mongolia University of the Nationalities, Tongliao, Inner Mongolia, China. h.wang@ulster.ac.uk | Computer Science Department, Brock University, St. Catharines, Ontario, Canada. duentsch@brocku.ca | School of Computing and Mathematics, University of Ulster, Jordanstown, Northern Ireland, UK. trindade-l@email.ulster.ac.uk
Note: [] Permanent address for correspondence: School of Computing and Mathematics, University of Ulster, Jordanstown, Northern Ireland, UK, h.wang@ulster.ac.uk. Hui Wang gratefully acknowledges support by The National Natural Science Foundation of China (61163034), Inner Mongolia Talent Development Fund (2011) and The Inner Mongolia Natural Science Foundation (2013MS0911).
Note: [] Ivo Düntsch gratefully acknowledges support by the Natural Sciences and Engineering Research Council of Canada, and by the Bulgarian National Fund of Science, contract DID02/32/2009.
Abstract: In this paper we review Lattice Machine, a learning paradigm that “learns” by generalising data in a consistent, conservative and parsimonious way, and has the advantage of being able to provide additional reliability information for any classification. More specifically, we review the related concepts such as hyper tuple and hyper relation, the three generalising criteria (equilabelledness, maximality, and supportedness) as well as the modelling and classifying algorithms. In an attempt to find a better method for classification in Lattice Machine, we consider the contextual probability which was originally proposed as a measure for approximate reasoning when there is insufficient data. It was later found to be a probability function that has the same classification ability as the data generating probability called primary probability. It was also found to be an alternative way of estimating the primary probability without much model assumption. Consequently, a contextual probability based Bayes classifier can be designed. In this paper we present a new classifier that utilises the Lattice Machine model and generalises the contextual probability based Bayes classifier. We interpret the model as a dense set of data points in the data space and then apply the contextual probability based Bayes classifier. A theorem is presented that allows efficient estimation of the contextual probability based on this interpretation. The proposed classifier is illustrated by examples.
