Department of Applied Mathematics

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Browsing Department of Applied Mathematics by Subject "Applied mathematics"

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    A conceptual framework for the development of intelligent, learning style- and computer-based educational software for topics from operations research
    (Stellenbosch : Stellenbosch University, 1999-11) Du Plessis, S. A. (Sameul Altenstadt); De Kock, H. C.; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences.
    ENGLISH ABSTRACT: The purpose of this study was to construct a conceptual framework for the development of intelligent, learning style- and computer-based educational software and to apply it to linear programming (LP). A secondary goal was to extend the framework to also include other topics from Operations Research. The system that resulted from this study was named GEORGE, in honor of the inventor of the simplex method George Dantzig. GEORGE utilizes fuzzy interpretations of learning style inventories and models of teaching and learning to determine a student's learning and teaching style preferences. An individualized tutoring strategy is then computed and used to present the course material to the student. A whole range of modes of presentation can be included in such a strategy, from drill-and-practice exercises, demonstrations and step-by-step tutorials to flow- and step charts and point-and-query interfaces. GEORGE keeps a practical and effective student model and controls the tutoring with a domain- and motivational based planner. The models of teaching and learning, mentioned above, are based on the results of fuzzy interpretations of Kolb's learning style inventory (experimental learning), a Myers Briggs Type Indicator Test (personality), La Haye's temperament test, a visualizer-verbalizer questionnaire, a study preference guide (sequential/global preferences), the model of teaching and learning of Felder and Silverman (for engineering education), Neethling's Brain Profile Test, a model of teaching and learning that is based on left and right brain preferences, and Sternberg's model of thinking styles. GEORGE consists of six modules, namely a problem solving or domain expert module, a generic questioning module, a presentation module, an "artificial psychologist" module, a student model module and a tutorial module. The generic questioning module is used to generate tutoring and testing material for GEORGE and the "artificial psychologist" module is used primarily to supply students with individualized psychological help, from study techniques and emotional matters to motivation and goal setting. The remaining four modules correspond more or less with the four modules of a traditional intelligent tutoring system. A number of artificial intelligence techniques i.e. natural language understanding, fuzzy expert and fuzzy decision making systems, induction and neural networks, are used in the implementation of different components of GEORGE. Applications of De Bono's thinking skills also play an important role in a number of components (teaching students how to think), the presentation of various personal development or self improvement techniques are very prominent (in the "artificial psychologist" module), and the accommodation of differences among users (especially learning style preferences) receives high priority. The implementation of the various components of GEORGE resulted in a number of useable computer-based learning modules. These demonstration programs illustrate the various concepts within the suggested general framework. The system was developed in Turbo Pascal and integrated within the "Windows"-environment with the help of the authoring system, EasyTutor. GEORGE will eventually be extended to become not only a computer-based tutor of LP topics, but also a Resourceful Environment for the Clever Tutoring of other Operations Research techniques (RECTOR). Guidelines regarding the transformation of GEORGE into RECTOR are provided. RECTOR, and parts thereof, should be used in a very similar way as in GEORGE, to supply computer support of lectures, to provide computer-assisted learning, to conduct computer-based learning, to create a computer environment for calculations and as a source of self-paced and open access material.
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    Minimum density hyperplanes
    (Journal of Machine Learning Research, 2016) Pavlidis, Nicos G.; Hofmeyr, David P.; Tasoulis, Sotiris K.
    Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark data sets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification.