Ordinal Data Classification Using Kernel Discriminant Analysis: A Comparison of Three Approaches

Ordinal data classification (ODC) has a wide range of applications in areas where human evaluation plays an important role, ranging from psychology and medicine to information retrieval. In ODC the output variable has a natural order; however, there is not a precise notion of the distance between classes. The recently proposed method for ordinal data, Kernel Discriminant Learning Ordinal Regression (KDLOR), is based on Linear Discriminant Analysis (LDA), a simple tool for classification. KDLOR brings LDA to the forefront in the ODC held, motivating further research. This paper compares three LDA based algorithms for ODC. The first method uses the generic framework of Frank and Hall for ODC instantiated with a kernel version of LDA. Similarly, the second method is based on the also generic Data Replication framework for ODC instantiated with the same kernel version of LDA. Both the Frank and Hall and Data Replication methods address the ODC problem by the use of a base binary classifier. Finally, the third method under comparison is KDLOR. The experiments are carried out on synthetic and real datasets. A comparison between the performances of the three systems is made based on tstatistics. The performance and running time complexity of the methods do not support any advantage of KDLOR over the other two methods.