Analysis of two-mode network data using nonnegative matrix factorization

Abstract Nonnegative matrix factorization has been offered as a fast and effective method for analyzing nonnegative two-mode proximity data. The goal is to structurally represent a nonnegative proximity matrix as the product of two lower-dimensional nonnegative matrices. Goodness of fit is typically measured as the sum of the squared deviations between the observed matrix elements and the estimated elements yielded by the product of the matrix factors. The preservation of nonnegativity of the factors has been touted as a major practical advantage over comparable decomposition methods (e.g., principal component analysis, singular-value decomposition, spectral analysis) because of its propensity for a more coherent additive interpretation. We provide descriptions of the nonnegative matrix factorization model and a rescaled gradient descent algorithm for estimating the factors. A small numerical example is provided along with application to three network matrices from the empirical literature.

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