Non-Negative Matrix Factorization, Convexity and Isometry

  title={Non-Negative Matrix Factorization, Convexity and Isometry},
  author={Nikolaos Vasiloglou and Alexander G. Gray and David V. Anderson},
In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive Factorization. We subsequently explore four novel… CONTINUE READING
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