  Low-dimensional word vectors have long been used in a wide range of
applications in natural language processing. In this paper we shed light on
estimating query vectors in ad-hoc retrieval where a limited information is
available in the original query. Pseudo-relevance feedback (PRF) is a
well-known technique for updating query language models and expanding the
queries with a number of relevant terms. We formulate the query updating in
low-dimensional spaces first with rotating the query vector and then with
scaling. These consequential steps are embedded in a query-specific projection
matrix capturing both angle and scaling. In this paper we propose a new but not
the most effective technique necessarily for PRF in language modeling, based on
the query projection algorithm. We learn an embedded coefficient matrix for
each query, whose aim is to improve the vector representation of the query by
transforming it to a more reliable space, and then update the query language
model. The proposed embedded coefficient divergence minimization model (ECDMM)
takes top-ranked documents retrieved by the query and obtains a couple of
positive and negative sample sets; these samples are used for learning the
coefficient matrix which will be used for projecting the query vector and
updating the query language model using a softmax function. Experimental
results on several TREC and CLEF data sets in several languages demonstrate
effectiveness of ECDMM. The experimental results reveal that the new
formulation for the query works as well as state-of-the-art PRF techniques and
outperforms state-of-the-art PRF techniques in a TREC collection in terms of
MAP,P@5, and P@10 significantly.
