1. A computer-implemented method to apply a query to a set of documents, comprising: by a computer: reconstructing a document term matrix XεR N×M where N is a number of documents and M is a number of words, by minimizing reconstruction errors with min ∥X−UA∥, where A is a fixed projection matrix and U is a column orthogonal matrix; determining a loss function and parameter gradients to generate U; fixing U while determining the loss function and sparse regularization constraints on the projection matrix A; generating parameter coefficients and generating a sparse projection matrix A; and generating a Sparse Latent Semantic Analysis (Sparse SLA) model and applying the model to a set of documents and displaying documents matching a query.
2. The computer-implemented method of claim 1 , wherein the document-term matrix comprises XεR N×M , where N is the number of documents and M is the number of words, and where a column orthogonal matrices UεR N×D (U T U=I) and VεR M×D (V T V=I) represent document and word embeddings into a latent space, and where I comprises a unity matrix.