7/29/2019 digest_Multilayer Nonnegative Matrix Factorization Using Projected Gradient Approaches, paper

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Multilayer Nonnegative Matrix Factorization Using Projected Gradient Approaches,

paper

Jie Fu

https://sites.google.com/site/bigaidream/

Keywords: NMF, Hierarchical

Introduction

[Open Issues] The performance of many existing NMF algorithms may be quite poor, especially,

when the unknown nonnegative components are badly scaled (ill-conditioned data),

insufficiently sparse, and a number of observations is equal or only slightly greater than a

number of latent components.

[Solution] the authors developed a simple hierarchical and multistage{deep learning?} procedure

in which they perform a sequential decomposition of nonnegative matrices as follows:

1. Perform the basic decomposition X=A1S1 using any available NMF algorithm.2. The results obtained from the first stage are used to perform the similar decomposition

S1=A2S2 using the same or different update rules, and so on.

The model has the form: X=A1A2ALSL, with the basis matrix defined as A=A1A2AL.

Physically, this means that we build up a system that has many layers or cascade connection of L

mixing subsystems.

The key point is that the learning (update) process to find parameters of sub-matrices A l and Sl is

performed sequentially, i.e., layer by layer and in each layer we use multi-start initialization.

The toolbox can be found here:http://www.bsp.brain.riken.jp/index.php

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