Building Hierarchies of Probabilistic Decision Tables

Abstract

This workshop introduces the basic idea of rough set theory and the procedure of building the hierarchies of probabilistic decision tables in the frame work of the Variable Precision Rough Set model (VPRS model). Rough set theory was introduced by Pawlak with respect to the study of intelligent systems characterized by insufficient and incomplete information. The VPRS model proposed by Ziarko was an extended rough set model. Over the past twenty years, rough set theory has been an active area of research. The decision tables, their derivations and the corresponding algorithms have played an essential role in these researches. Decision tables can be classified into various categories, such as deterministic decision tables, non-deterministic decision tables, and probabilistic decision tables. A probabilistic decision table is extracted from data based on the VPRS model, in which one observation can have more than one decision. Thus, a probabilistic decision table usually has a boundary region that, however, usually can be treated as a new domain and used to build a new decision table. If applying this method recursively, a hierarchy of linear structure of the decision tables can be constructed, which can be as a classifier to classify unknown objects. After the hierarchy is built, its performance can be improved by two techniques: pruning each table and incremental learning. Pruning the tables can simplify the structure of the hierarchy and remove redundant information, if available, so as to improve its efficiency. The purpose of incremental learning is to reflect the presentation of newly added training objects while retaining knowledge acquired from old data. A common approach to classify unknown objects by holistic-matching methods is classification that is often suffered by the variations of unknown objects. When applying the hierarchy as the classifier, in order to overcome such limitations, a method called probabilistic distance-based method was utilized to match unknown objects to the corresponding category. This workshop has four sections. It first introduces the basic concepts of rough set theories, especially the VPRS model and the hierarchy of probabilistic decision tables. Then, the procedure of building the hierarchy and pruning each decision table are covered. After that, it describes how to classify unknown objects, applying the hierarchy as a classifier. Finally, how to perform incremental learning is included.