Inducing Uncertain Decision Tree via Cloud Model

This paper addresses the decision trees induction with uncertain data. In other words, it presents a novel method, called uncertain decision trees (UDT) to handle the uncertainty during the process of inducing decision trees. Here, uncertainty is depicted via cloud model theory, a quantitative-qualitative transforming model with uncertainty, which can well integrate the fuzziness and randomness of concepts in a unified way. In the learning stage, dataset is pre-processed by cloud transformation algorithm, which climbs data into class labels via histograms or frequency distribution, and the labels are expressed by cloud concepts. In this paper, some basic definitions are proposed, including cloud distance, cloud dissimilarity matrix, cloud index, and UDT, where cloud index is a novel splitting criterion of selecting attributes for handling uncertainty. Take data from UCI for example, this paper provided an algorithm inducing UDT, and checked its validity or appropriateness. In contrast to the classical approaches, both in the learning stage and classifying stage, the proposed method develops existing methods, and it is more consistent with the human cognition, which can support uncertainty, build UDT via cloud concepts, and classify the uncertain data. Moreover, experiments and results are compared with the current methods to illustrate the feasibility, accuracy and effectiveness of the cloud based algorithm.