Discovering the hierarchical structures of differ- ent classes of object behaviors can satisfy the requirements of various degrees of abstraction in association analysis, be- havior modeling, data preprocessing, patte...Discovering the hierarchical structures of differ- ent classes of object behaviors can satisfy the requirements of various degrees of abstraction in association analysis, be- havior modeling, data preprocessing, pattern recognition and decision making, etc. In this paper, we call this process as associative categorization, which is different from classical clustering, associative classification and associative cluster- ing. Focusing on representing the associations of behaviors and the corresponding uncertainties, we propose the method for constructing a Markov network （MN） from the results of frequent pattern mining, called item-associative Markov net- work （IAMN）, where nodes and edges represent the frequent patterns and their associations respectively. We further dis- cuss the properties of a probabilistic graphical model to guar- antee the IAMN＇s correctness theoretically. Then, we adopt the concept of chordal to reflect the closeness of nodes in the IAMN. Adopting the algorithm for constructing join trees from an MN, we give the algorithm for IAMN-based associa- tive categorization by hierarchical bottom-up aggregations of nodes. Experimental results show the effectiveness, efficiency and correctness of our methods.展开更多
Let V be a vertex operator superalgebra and m, n ∈ 1/2 ?+. We construct an A n (V)-A m (V)-bimodule A n,m (V) which characterizes the action of V from the level m subspace to level n subspace of an admissible V-modul...Let V be a vertex operator superalgebra and m, n ∈ 1/2 ?+. We construct an A n (V)-A m (V)-bimodule A n,m (V) which characterizes the action of V from the level m subspace to level n subspace of an admissible V-module. We also construct the Verma type admissible V-module from an A m (V)-module by using bimodules展开更多
文摘Discovering the hierarchical structures of differ- ent classes of object behaviors can satisfy the requirements of various degrees of abstraction in association analysis, be- havior modeling, data preprocessing, pattern recognition and decision making, etc. In this paper, we call this process as associative categorization, which is different from classical clustering, associative classification and associative cluster- ing. Focusing on representing the associations of behaviors and the corresponding uncertainties, we propose the method for constructing a Markov network （MN） from the results of frequent pattern mining, called item-associative Markov net- work （IAMN）, where nodes and edges represent the frequent patterns and their associations respectively. We further dis- cuss the properties of a probabilistic graphical model to guar- antee the IAMN＇s correctness theoretically. Then, we adopt the concept of chordal to reflect the closeness of nodes in the IAMN. Adopting the algorithm for constructing join trees from an MN, we give the algorithm for IAMN-based associa- tive categorization by hierarchical bottom-up aggregations of nodes. Experimental results show the effectiveness, efficiency and correctness of our methods.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571119, 10671027)
文摘Let V be a vertex operator superalgebra and m, n ∈ 1/2 ?+. We construct an A n (V)-A m (V)-bimodule A n,m (V) which characterizes the action of V from the level m subspace to level n subspace of an admissible V-module. We also construct the Verma type admissible V-module from an A m (V)-module by using bimodules
