deep architecture, hierarchy, fuzzy equivalence relation, covering tree, MNIST dataset
The concept of deep learning has been applied to many domains, but the definition of a suitable problem depth has not been sufficiently explored. In this study, we propose a new Hierarchical Covering Algorithm (HCA) method to determine the levels of a hierarchical structure based on the Covering Algorithm (CA). The CA constructs neural networks based on samples’ own characteristics, and can effectively handle multi-category classification and large-scale data. Further, we abstract characters based on the CA to automatically embody the feature of a deep structure. We apply CA to construct hidden nodes at the lower level, and define a fuzzy equivalence relation R¯ on upper spaces to form a hierarchical architecture based on fuzzy quotient space theory. The covering tree naturally becomes from R¯. HCA experiments performed on MNIST dataset show that the covering tree embodies the deep architecture of the problem, and the effects of a deep structure are shown to be better than having a single level.
Tsinghua University Press
Jie Chen, Shu Zhao, Yanping Zhang. Hierarchical Covering Algorithm. Tsinghua Science and Technology 2014, 19(1): 76-81.