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APPLICATION OF NEURAL NETWORKS IN REGRESSION PROBLEMS WITH QUALITATIVE DATA ON AN EXAMPLE OF GEMSTONES VALUATION

Janusz Morajda

Abstract

The paper considers a problem of gemstones valuation, based on real data. The main goal includes constructing a model that determines the evaluated price of a given stone on the basis of its description, expressed as a set of input variables values. A classic approach, utilising a multiple linear regression tool, is compared with nonlinear multilayer perceptrons. As the dataset contains a number of qualitative variables (e.g. gemstone colour purity, the clarity of the structure and a symbol of the certifying authority), the important part of solving the problem is selecting and implementing a proper method of encoding qualitative variables in a numeric form that is accepted by statistical and neural tools. The adoption of method for numerical representation of qualitative information is primarily determined by the scale of measurement for a given variable. In the research presented here, some classic encoding methods have been considered: for nominal variables – “one out of N”, “equilateral coding”, and representation based on a single numerical variable; for variables expressed on an ordinal scale, additionally selected variants of so called thermometric methods can be implemented. A number of experiments, with the use of Statistica software packet, have been made, and their results have been presented and discussed. Conclusions show generally higher effectiveness of neural networks over the multiple linear regression in the considered issue, but also significant indications concerning qualitative data preprocessing (encoding them in a numeric form) for valuation models have been introduced.

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DOI resolver: doi.org/10.5593/sgemsocial2018/1.5/S05.010

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