Understanding and representing the underlying structure of feature hierarchies present in complex data in intuitively understandable manner is an important issue. In this paper, we propose a data representation model that demonstrates hierarchical feature learning using NMF with sparsity constraint. We stack simple unit algorithm into several layers to take step-by-step approach in learning. By utilizing NMF as unit algorithm, our proposed network provides intuitive understanding of the learning process. It is able to demonstrate hierarchical feature development process and also discover and represent feature hierarchies in the complex data in intuitively understandable manner. We apply hierarchical multi-layer NMF to image data and document data to demonstrate feature hierarchies present in the complex data. Furthermore, we analyze the reconstruction and classification abilities of our proposed network and prove that hierarchical feature learning approach excels performance of standard shallow network. By providing underlying feature hierarchies in complex real-world data sets, our proposed network is expected to help machines develop intelligence based on the learned relationship between concepts, and at the same time, perform better with the small number of features provided for data representation.
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