Orthogonality and Orthography: Introducing Measured Distance into Semantic Space

This paper explores a new technique for encoding structured information into a semantic model, for the construction of vector representations of words and sentences. As an illustrative application, we use this technique to compose robust representations of words based on sequences of letters, that are tolerant to changes such as transposition, insertion and deletion of characters. Since these vectors are generated from the written form or orthography of a word, we call them ‘orthographic vectors’. The representation of discrete letters in a continuous vector space is an interesting example of a Generalized Quantum model, and the process of generating semantic vectors for letters in a word is mathematically similar to the derivation of orbital angular momentum in quantum mechanics. The importance (and sometimes, the violation) of orthogonality is discussed in both mathematical settings.This work is grounded in psychological literature on word representation and recognition, and is also motivated by potential technological applications such as genre-appropriate spelling correction. The mathematical method, examples and experiments, and the implementation and availability of the technique in the Semantic Vectors package are also discussed.