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Taxonomies are of great value to many knowledge-rich applications. As the manual taxonomy curation costs enormous human effects, automatic taxonomy construction is in great demand. However, most existing automatic taxonomy construction methods can only build hypernymy taxonomies wherein each edge is limited to expressing the “is-a” relation. Such a restriction limits their applicability to more diverse real-world tasks where the parent-child may carry different relations. In this paper, we aim to construct a task-guided taxonomy from a domain-specific corpus, and allow users to input a “seed” taxonomy, serving as the task guidance. We propose an expansion-based taxonomy construction framework, namely HiExpan, which automatically generates key term list from the corpus and iteratively grows the seed taxonomy. Specifically, HiExpan views all children under each taxonomy node forming a coherent set and builds the taxonomy by recursively expanding all these sets. Furthermore, HiExpan incorporates a weakly-supervised relation extraction module to extract the initial children of a newly expanded node and adjusts the taxonomy tree by optimizing its global structure. Our experiments on three real datasets from different domains demonstrate the effectiveness of HiExpan for building task-guided taxonomies.