基于模糊多特征递归分组算法的隐树结构图模型学习

隐树结构图模型通过引入了隐藏节点来描述变量之间的潜在关系，因而可以更好地对变量之间的相关性进行建模。树模型学习过程中，从变量观测数据所提取的有用特征数量，决定了该模型对变量间深层关系的建模能力；而现有学习算法都是对观测数据直接计算统计量来进行模型学习，未能按观测数据中的特征分类处理。针对现有算法对观测数据中信息利用不充分的不足，该文提出基于模糊多特征递归分组算法的隐树模型学习方法。首先，将变量的原始观测数据通过反映其特征的模糊隶属度函数转化成多个模糊特征，并构造多维模糊特征向量；其次，计算两两变量模糊特征向量之间的距离，并将其综合得到所有变量之间的模糊特征向量距离矩阵；最后，基于该距离矩阵，利用递归分组算法学习隐树模型。该文还将所提算法应用于股票收益数据和气温数据建模，验证了该文算法的实用性和有效性。

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.