Abstract

Nonnegative Matrix Factorization (NMF) is an unsupervised learning method for extracting latent features in high-dimensional nonnegative data. This report presents NMF strategies based on the solution of the systems of ordinary differen- tial equations associated with both static and time dependent data. Here the NMF minimization problem is treated in two ways: we start off by deriving dynami- cal systems using the gradient descent approach and finish off with quasi-Newton optimization. The steepest descent approach by itself is divided into two cases: con- strained and unconstrained minimization. Given a time-varying objective function or a nonnegative time dependent (static) data matrix Y , the approximate nonneg- ative factors of Y can be obtained by taking the limit points of the trajectories of the corresponding ODEs. In the case when the data to deal with is time dependent, it is a good practice to devise an NMF strategy that captures the time dependency. In either of the above cases the natural thing to do is solve the continuous-time dy- namical systems derived from iterative optimization schemes and construct NMF algorithms based on the solution curves.

Autore Pugliese

• Del Buono Nicoletta

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Anno di pubblicazione

2014

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