1. Although two-class and nominal data classification problems have been thoroughly analysed in the literature, the ordinal sibling has not received nearly as much attention yet.
紧接着：
Nonetheless, many real life problems require the classification of items into naturally ordered classes，The scenarios involved range from information retrieval (Herbrich et al., 1999a) and collaborative filtering (Shashua and Levin, 2002) to econometric modeling (Mathieson, 1995) and medical sciences (Cardoso et al., 2005). It is worth pointing out that distinct tasks of relational learning, where an example is no longer associated with a class or rank, which include preference learning and reranking (Shen and Joshi, 2005), are topics of research on their own.
Conventional methods for nominal classes or for regression problems could be employed to solve ordinal data problems. However, the use of techniques designed specifically for ordered classes yields simpler and with better performance classifiers. Although the ordinal formulation seems conceptually simpler than the nominal one, difficulties to incorporate in the algorithms this piece of additional information—the order—may explain the widespread use of conventional methods to tackle the ordinal data problem.
This work addresses this void by introducing in Section 2 the data replication method, a nonparametric procedure for the classification of ordinal data. The underlying paradigm is the extension of the original data set with additional variables, reducing the classification task to the well known twoclass problem. Starting with the simpler linear case, already established in Cardoso et al. (2005), the section develops the nonlinear case; from there the method is extended to incorporate the procedure
of Frank and Hall (2001). Finally, the generic version of the data replication method is presented, allowing partial constraints on variables。
Section 4 describes the experimental methodology and the algorithms under comparison; results are reported and discussed in the succeeding sections. Finally, conclusions are drawn and future work is outlined in Section 8
Although the foregoing analysis enables one to classify unseen examples in the original data set, classification can be done directly in the extended data set, using the binary classifier, without explicitly resorting to the original data set.
2. Although both LDA and KDA have been applied to classification problems, they have not been applied to the ordinal regression problem because ordinal information can not be used.
Nonetheless 尽管如此/但是，