Retrieving documents with mathematical content

Many documents with mathematical content are published on the Web, but conventional search engines that rely on keyword search only cannot fully exploit their mathematical information. In particular, keyword search is insufficient when expressions in a document are not annotated with natural keywords or the user cannot describe her query with keywords. Retrieving documents by querying their mathematical content directly is very appealing in various domains such as education, digital libraries, engineering, patent documents, medical sciences, etc. Capturing the relevance of mathematical expressions also greatly enhances document classification in such domains. Unlike text retrieval, where keywords carry enough semantics to distinguish text documents and rank them, math symbols do not contain much semantic information on their own. In fact, mathematical expressions typically consist of few alphabetical symbols organized in rather complex structures. Hence, the structure of an expression, which describes the way such symbols are combined, should also be considered. Unfortunately, there is no standard testbed with which to evaluate the effectiveness of a mathematics retrieval algorithm. In this paper we study the fundamental and challenging problems in mathematics retrieval, that is how to capture the relevance of mathematical expressions, how to query them, and how to evaluate the results. We describe various search paradigms and propose retrieval systems accordingly. We discuss the benefits and drawbacks of each approach, and further compare them through an extensive empirical study.