Find the 'projection matrix' to a semantic vector

"Project" each word in a word embedding matrix of \(D\) dimension along a vector of \(D\) dimensions, extracted from the same embedding space. The vector can be a single word, or a concept vector obtained from get_centroid(), get_direction(), or get_regions().

Usage

find_projection(wv, vec)

Arguments

wv

Matrix of word embedding vectors (a.k.a embedding model) with rows as words.

vec

Vector extracted from the embeddings

Value

A new word embedding matrix, each row of which is parallel to vector.

Details

All the vectors in the matrix \(A\) are projected onto the a vector, \(v\), to find the projection matrix, \(P\), defined as: $$P = \frac{A \cdot v}{v \cdot v} * v$$