Online matrix factorization for Markovian data and applications to Network Dictionary Learning

11/05/2019
by   Hanbaek Lyu, et al.
39

Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of a dependent data stream remains largely unexplored. In this paper, we show that the well-known OMF algorithm for i.i.d. stream of data proposed in <cit.>, in fact converges almost surely to the set of critical points of the expected loss function, even when the data matrices form a Markov chain satisfying a mild mixing condition. Furthermore, we extend the convergence result to the case when we can only approximately solve each step of the optimization problems in the algorithm. For applications, we demonstrate dictionary learning from a sequence of images generated by a Markov Chain Monte Carlo (MCMC) sampler. Lastly, by combining online non-negative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning, which extracts `network dictionary patches' from a given network in an online manner that encodes main features of the network. We demonstrate this technique on real-world text data.

READ FULL TEXT

page 4

page 12

page 13

page 14

page 16

page 18

page 19

11/10/2020

Applications of Online Nonnegative Matrix Factorization to Image and Time-Series Data

Online nonnegative matrix factorization (ONMF) is a matrix factorization...
04/04/2019

Online Convex Dictionary Learning

Dictionary learning is a dimensionality reduction technique widely used ...
09/16/2020

Online nonnegative tensor factorization and CP-dictionary learning for Markovian data

Nonnegative Matrix Factorization (NMF) algorithms are fundamental tools ...
07/19/2021

Wave-Informed Matrix Factorization withGlobal Optimality Guarantees

With the recent success of representation learning methods, which includ...
04/16/2018

Binary Matrix Factorization via Dictionary Learning

Matrix factorization is a key tool in data analysis; its applications in...
07/30/2016

Online Nonnegative Matrix Factorization with General Divergences

We develop a unified and systematic framework for performing online nonn...

Code Repositories

ONMF_ONTF_NDL

Online Matrix/Tensor Factorization and applications to Network Dictionary Learning and images


view repo