  In this paper, we study the problem of extracting variable-depth "logical
document hierarchy" from long documents, namely organizing the recognized
"physical document objects" into hierarchical structures. The discovery of
logical document hierarchy is the vital step to support many downstream
applications. However, long documents, containing hundreds or even thousands of
pages and variable-depth hierarchy, challenge the existing methods. To address
these challenges, we develop a framework, namely Hierarchy Extraction from Long
Document (HELD), where we "sequentially" insert each physical object at the
proper on of the current tree. Determining whether each possible position is
proper or not can be formulated as a binary classification problem. To further
improve its effectiveness and efficiency, we study the design variants in HELD,
including traversal orders of the insertion positions, heading extraction
explicitly or implicitly, tolerance to insertion errors in predecessor steps,
and so on. The empirical experiments based on thousands of long documents from
Chinese, English financial market and English scientific publication show that
the HELD model with the "root-to-leaf" traversal order and explicit heading
extraction is the best choice to achieve the tradeoff between effectiveness and
efficiency with the accuracy of 0.9726, 0.7291 and 0.9578 in Chinese financial,
English financial and arXiv datasets, respectively. Finally, we show that
logical document hierarchy can be employed to significantly improve the
performance of the downstream passage retrieval task. In summary, we conduct a
systematic study on this task in terms of methods, evaluations, and
applications.
