Ordinal Learning with Vector Space Based Binary Predicates and Its Application to Tahitian Pearls’ Luster Automatic Assessment

Algorithms designed to solve instance ranking problems are often a trade-off between classification and regression. We propose to solve instance ranking problems where the classes have fixed boundaries by observing that such cases can be reduced to object ranking problems. Object ranking implies determining a total order, which should imply in turn a computational cost exponential with the number of items to order. However, solving this problem in the feature space allows taking advantage of linearity, so as to ensure total order properties at no particular computational cost, in particular, without having to explicitly check for acyclicity. The proposed method is tested for classifying Tahitian pearls against their luster using photographs of commercial culture pearls ranked by experts of the profession and compared with previous support vector machine (SVM) multiclass classification. While the SVM approach had more than \( 20\% \) of error (and more than \( 13\% \) after feature selection), our method allows predicting the class of a pearl with less than \( 10\% \) of error (and less than \( 8\% \) after feature selection). Ordinal learning makes better use of implicit rank information and significantly (\( p < 10^{-4} \)) reduces classification error.