Recently math formula search engines have become a useful tool for novice users learning a new topic. While systems exist already with the ability to do formula retrieval, they rely on prefix matching and typed query entries. This can be an obstacle for novice users who are not proficient with languages used to express formulas such as LaTeX, or do not remember the left end of a formula, or wish to match formulas at multiple locations (e.g., using `$\int \quad\quad dx$' as a query). We generalize a one dimensional spatial encoding for word spotting in handwritten document images, the Pyramidal Histogram of Characters or PHOC, to obtain the two-dimensional XY-PHOC providing robust spatial embeddings with modest storage requirements, and without requiring costly operations used to generate graphs. The spatial representation captures the relative position of symbols without needing to store explicit edges between symbols. Our spatial representation is able to match queries that are disjoint subgraphs within indexed formulas. Existing graph and tree-based formula retrieval models are not designed to handle disjoint graphs, and relationships may be added to a query that do not exist in the final formula, making it less similar for matching.

XY-PHOC embeddings provide a simple spatial embedding providing competitive results in formula similarity search and autocompletion, and supports queries comprised of symbols in two dimensions, without the need to form a connected graph for search.

Library of Congress Subject Headings

Mathematics--Formulae--Data processing; Information retrieval; Optical pattern recognition; Writing--Data processing; Search engines--Programming

Publication Date


Document Type


Student Type


Degree Name

Computer Science (MS)

Department, Program, or Center

Computer Science (GCCIS)


Richard Zanibbi

Advisor/Committee Member

Zack Butler

Advisor/Committee Member

Edith Hemaspaandra


RIT – Main Campus

Plan Codes