Rough Discretization of Gene Expression Data

We adapt the rough set-based approach to deal with the gene expression data, where the problem is a huge amount of genes (attributes) a?A versus small amount of experiments (objects) u?U. We perform the gene reduction using standard rough set methodology based on approximate decision reducts applied against specially prepared data. We use rough discretization - Every pair of objects (x,y)xU yields a new object, which takes values "\ge a(x)" if and only if a(y)\ge a(x); and "\le a(x)" otherwise; over original genes-attributes aA. In this way: 1) We work with desired, larger number of objects improving credibility of the obtained reducts; 2) We produce more decision rules, which vote during classification of new observations; 3) We avoid an issue of discretization of real-valued attributes, difficult and leading to unpredictable results in case of any data sets having much more attributes than objects. We illustrate our method by analysis of the gene expression data related to breast cancer.