Several expert systems have been proposed to address the sparsity of tags associated with online content such as images and videos. However most of such systems either necessitate extracting domain-specific features, or are solely based on tag semantics, or have significant space requirements to store corpus based tag statistics. To address these shortcomings, in this work we show how ontological tag trees can be used to encode information present in a given corpus pertaining to interaction between the tags, in a space efficient manner. An ontological tag tree is defined as an undirected, weighted tree on the set of tags where each possible tag is treated as a node in the tree. We formulate the tag tree construction as an optimization problem over the space of trees on the set of tags and propose a novel local search based approach utilizing the co-occurrence statistics of the tags in the corpus. To make the proposed optimization more efficient, we initialize using the semantic relationships between the tags. The proposed approach is used to construct tag trees over tags for two large corpora of images, one from Flickr and one from a set of stock images. Extensive data-driven evaluations demonstrate that the constructed tag trees can outperform previous approaches in terms of accuracy in predicting unseen tags using a partially observed set of tags, as well as in efficiency of predicting all applicable tags for a resource.