Learning Latent Tree-structured Graphical Models Based on Fuzzy Multi-features Recursive-grouping Algorithm

Latent tree-structured graphical models explore the latent relationships among variables by introducing hidden nodes, therefore they can better model the correlations among variables. In the learning process of tree-structured graphical models, the quantity of useful features extracted from observation data of variables reflects the models capability to model the deep relationships among variables. However, the excised algorithms learn the hidden tree only by the statics which are directly computed from observation data and ignore the different features among data. For the insufficiency of these algorithms in exploring the information, a new algorithm is proposed for learning the latent tree-structured graphical model based on fuzzy multi-features recursive-grouping. First, original observation data is transformed to multi-features by fuzzy membership functions and construct multi-dimensional fuzzy feature vectors. Then, the distance between each fuzzy feature vectors is computed and synthesized to get the fuzzy multi-features distance matrix of all variables. Finally, based on the distance matrix, the latent tree graphical model is constructed by the recursive-grouping algorithm. The proposed algorithm is applied to stock return data modeling and temperature data modeling, which demonstrate the effectiveness of the algorithm.