Hierarchical covering algorithm

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.