  Hyperdimensional computing (HDC), also known as vector symbolic architectures
(VSA), is a computing framework used within artificial intelligence and
cognitive computing that operates with distributed vector representations of
large fixed dimensionality. A critical step for designing the HDC/VSA solutions
is to obtain such representations from the input data. Here, we focus on
sequences and propose their transformation to distributed representations that
both preserve the similarity of identical sequence elements at nearby positions
and are equivariant to the sequence shift. These properties are enabled by
forming representations of sequence positions using recursive binding and
superposition operations. The proposed transformation was experimentally
investigated with symbolic strings used for modeling human perception of word
similarity. The obtained results are on a par with more sophisticated
approaches from the literature. The proposed transformation was designed for
the HDC/VSA model known as Fourier Holographic Reduced Representations.
However, it can be adapted to some other HDC/VSA models.
