Frame Selection Based On Mixtures Of Trees In Discrete Data

The model of mixtures of Chow-Liu trees (MixTree) as a probabilistic model for the discrete multidimensional structure decomposing method often has a slow convergence speed, which causes unstable tree structure. In this chapter we present a sub-structure selection method using MixTree to search for subsets of variables with stable local tree dependent structures that can be used to help design a sparse structure in a data warehouse, which can save resources and improve search efficiency. Inspired by the theory in number theory that each integer has a unique prime factorization, we introduce an accelerated searching scheme that, by labeling variables with prime or square numbers, identifies stable sub-structures voted by several MixTree models recursively by products of the labels of newly linked variables. Simulations reveal that this selection method performs well in mining the frame of variables from data, and the tree dependency of variables ensures our results with good interpretability.