Kernel methods for Multi-labelled classification and Categorical regression problems

This report presents a SVM like learning system to handle multi-label problems. Such problems arise naturally in bio-informatics. Consider for instance the MIPS Yeast genome database in [12], it is formed by around 3,300 genes associated to their functional classes. One gene can have many classes, and different genes do not belong to the same number of functional categories. Such a problem can not be solved directly with classical approaches and it is generally decomposed into many two-class problems. The binary decomposition has been done partially by different researchers [12] on the Yeast dataset but it does not provide a satisfactory answer. We explore in this report a new direct approach. It is based on a large margin ranking system that shares a lot of common properties with Support Vector Machines. We tested it on a toy problem and on real datasets with positive results. We also present a new method to do feature selection with multi-labelled datasets. Our method is based on the multiplicative update rule defined in [17].