@article{Chen2014, 
author = {Jie Chen and Shu Zhao and Yanping Zhang},
title = {Hierarchical Covering Algorithm},
year = {2014},
journal = {Tsinghua Science and Technology},
volume = {19},
number = {1},
pages = {76-81},
keywords = {deep architecture, hierarchy, fuzzy equivalence relation, covering tree, MNIST dataset},
url = {https://www.sciopen.com/article/10.1109/TST.2014.6733210},
doi = {10.1109/TST.2014.6733210},
abstract = {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.}
}