In this thesis we study nonnegative rank of matrices and nonnegative matrix factorization. We first present the basic properties of nonnegative rank, methods for bounding it and approximate nonnegative matrix factorization based on multiplicative updates. We show that the error of the considered iterative algorithm does not increase with each iteration. In the practical part of the thesis, we apply the method to text mining of book descriptions from the Goodreads platform. Using nonnegative matrix factorization, we extract the main topics from two datasets and interpret them on the most important words. We compare the results with principal component analysis. The comparison shows that nonnegative matrix factorization provides clearer and more interpretable topics, which makes it a suitable method for discovering thematic structures in textual data.
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