A lower-dimensional representation (e.g., approximation) of a dataset is determined. The lower-dimensional representation can be used, for example, to perform semantic document analysis. Given a matrix of input data points, where each entry of the matrix indicates a number of times a particular term in a set of terms appears in a particular document in a set of documents, a lower-dimensional compressed matrix is obtained from the matrix by sampling rows of the matrix based on a target rank parameter, a desired accuracy tolerance, leverage scores calculated for the rows, and/or distances from rows of the matrix to a span of the initial set of sampled rows. The compressed matrix is used to determine a similarity metric indicative of a degree of similarity between documents. The documents can then be classified into a same document cluster or different clusters based on whether the similarity metric satisfied a threshold value.