Generating noisy monotone ordinal datasets

Abstract

Ordinal decision problems are very common inreal-life. As a result, ordinal classification models have drawn much attentionin recent years. Many ordinal problem domains assume that the output is monotonouslyrelated to the input, and some ordinal data mining models ensure this propertywhile classifying. However, no one has ever reported how accurate these modelsare in presence of varying levels of non-monotone noise. In order to do thatresearchers need an-easy-to-use tool for generating artificial ordinal datasetswhich contain both an arbitrary monotone pattern as well as user-specifiedlevels of non-monotone noise. An algorithm that generates such datasets is presentedhere in detail for the first time. Two versions of the algorithm are discussed.The first is more time consuming. It generates purely monotone datasets as thebase of the computation. Later, non-monotone noise is incrementally inserted tothe dataset. The second version is basically similar, but it is significantlyfaster.  It begins with the generation ofalmost monotone datasets before introducing the noise. Theoretical andempirical studies of the two versions are provided, showing that the second,faster, algorithm is sufficient for almost all practical applications. Some usefulinformation about the two algorithms and suggestions for further research arealso discussed.