Based On Bayesian Network Cube Uncertainty Knowledge Representation And Reasoning Method

Multidimensional data generates considerable research activities in the fields of data mining and knowledge discovery, since it has been widely used to describe complex phenomena in real-world applications. A Bayesian network (BN) is a directed acyclic graph that has a set of random variables that makes up the nodes of the network; a set of directed edges connects the pairs of nodes; and a conditional probability table associated with each node that quantifies the effects that the parents have on the node. Inference on BN is a procedure of searching the posterior distributions of the query variables given the states of the evidence variables. When adopting BN to represent and infer probabilistic causalities among multidimensional variables (i.e. multidimensional data), the complexity of storage and inference can be very high as the state space of every multidimensional variable, which contains all the combinations of the dimensions' assignments, could become significantly large. Moreover, the inference can not be made if the given evidences are not appearing in the corresponding CPTs.There are two naive solutions to the problems stated above:we look upon the attribute variables (i.e. dimensions of multidimensional variables) as the nodes of the BN, or we classify the multidimensional variables and made the class variables as the nodes of the BN. However, the former solution will generally lead to a very complicated BN, since some irrelevant causal relations among attributes may be embodied, while relations among multidimensional variables can be lost, and there will have no attributes information in the BN corresponding to the latter case.To consider both class and attribute variables, by adopting the notation of classification, the main contributions of this thesis can be summarized as follows:●By associating each multidimensional variable with a class variable, we learn the causal relations among the class variable and the attribute variables to make up a BN, which we call local BN (LBN). On the LBN, classification can be done and the states of the class variable can then be used to represent the states of the multidimensional variable.●We learn the global network (GBN) by adding proper edges among class variables of the LBNs where casual relations exist. Since edges from one LBN to another are absolutely among class nodes, the relations among multidimensional variables are preserved, and the relations among attributes of different multidimensional variables that are less concerned are reduced.●We further propose the 2-phase learning algorithm and the 3-phase inference algorithm to support the GBN leaning and inference.