ShiftNMFk: Nonnegative Matrix Factorization using k-means clustering and accounting for signal temporal shifts

NMFk is a novel unsupervised machine learning methodology which allows for automatic identification of the optimal number of features (signals) present in the data when NMF (Nonnegative Matrix Factorization) analyses are performed. Classical NMF approaches do not allow for automatic estimation of the number of features. NMFk estimates the number of features k through k-means clustering coupled with regularization constraints.

NMFk can be applied to perform:

Feature extraction (FE)
Blind source separation (BSS)
Detection of disruptions / anomalies
Image recognition
Separation of (physics) processes
Discovery of unknown dependencies and phenomena
Development reduced-order/surrogate models
Identification of dependencies between model inputs and outputs
Guiding development of physics models representing the ML analyzed data
Data classification
Blind predictions
Optimization of data acquisition (optimal experimental design)
Labeling of datasets for supervised ML analyses

NMFk provides high-performance computing capabilities to solve problems with Shared and Distributed Arrays in parallel. The parallelization allows for utilization of multi-core / multi-processor environments. GPU and TPU accelerations are also available through existing Julia packages.

NMFk methodology and applications are discussed in the the papers and presentations listed below.

Installation

After starting Julia, execute:

import Pkg; Pkg.add("ShiftNMFk")

to access the latest released version. To utilize the latest updates (commits) use:

import Pkg; Pkg.add(Pkg.PackageSpec(name="ShiftNMFk", rev="master"))

Docker

docker run --interactive --tty montyvesselinov/tensors

The docker image provides access to all TensorDecomposition packages.

Applications:

NMFk has been applied in a wide range of real-world applications. The analyzed datasets include model outputs, laboratory experimental data, and field tests:

Climate modeling
Material characterization using X rays
Reactive mixing
Molecular dynamics
Contaminant transport
Induced seismicity
Phase separation of co-polymers
Oil / Gas extraction from unconventional reservoirs

Videos:

Progress of nonnegative matrix factorization process:

Videos are also available at YouTube

Notebooks:

A series of Jupyter notebooks demonstrating NMFk have been developed:

Other Examples:

Patent:

Alexandrov, B.S., Vesselinov, V.V., Alexandrov, L.B., Stanev, V., Iliev, F.L., Source identification by non-negative matrix factorization combined with semi-supervised clustering, US20180060758A1

Publications:

Vesselinov, V.V., Mudunuru, M., Karra, S., O'Malley, D., Alexandrov, B.S., Unsupervised Machine Learning Based on Non-Negative Tensor Factorization for Analyzing Reactive-Mixing, 10.1016/j.jcp.2019.05.039, Journal of Computational Physics, 2019. PDF
Vesselinov, V.V., Alexandrov, B.S., O'Malley, D., Nonnegative Tensor Factorization for Contaminant Source Identification, Journal of Contaminant Hydrology, 10.1016/j.jconhyd.2018.11.010, 2018. PDF
O'Malley, D., Vesselinov, V.V., Alexandrov, B.S., Alexandrov, L.B., Nonnegative/binary matrix factorization with a D-Wave quantum annealer, PlosOne, 10.1371/journal.pone.0206653, 2018. PDF
Stanev, V., Vesselinov, V.V., Kusne, A.G., Antoszewski, G., Takeuchi,I., Alexandrov, B.A., Unsupervised Phase Mapping of X-ray Diffraction Data by Nonnegative Matrix Factorization Integrated with Custom Clustering, Nature Computational Materials, 10.1038/s41524-018-0099-2, 2018. PDF
Iliev, F.L., Stanev, V.G., Vesselinov, V.V., Alexandrov, B.S., Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals PLoS ONE, 10.1371/journal.pone.0193974. 2018. PDF
Stanev, V.G., Iliev, F.L., Hansen, S.K., Vesselinov, V.V., Alexandrov, B.S., Identification of the release sources in advection-diffusion system by machine learning combined with Green function inverse method, Applied Mathematical Modelling, 10.1016/j.apm.2018.03.006, 2018. PDF
Vesselinov, V.V., O'Malley, D., Alexandrov, B.S., Contaminant source identification using semi-supervised machine learning, Journal of Contaminant Hydrology, 10.1016/j.jconhyd.2017.11.002, 2017. PDF
Alexandrov, B., Vesselinov, V.V., Blind source separation for groundwater level analysis based on non-negative matrix factorization, Water Resources Research, 10.1002/2013WR015037, 2014. PDF

Research papers are also available at Google Scholar, ResearchGate and Academia.edu

Presentations:

Vesselinov, V.V., Physics-Informed Machine Learning Methods for Data Analytics and Model Diagnostics, M3 NASA DRIVE Workshop, Los Alamos, 2019. PDF
Vesselinov, V.V., Unsupervised Machine Learning Methods for Feature Extraction, New Mexico Big Data & Analytics Summit, Albuquerque, 2019. PDF
Vesselinov, V.V., Novel Unsupervised Machine Learning Methods for Data Analytics and Model Diagnostics, Machine Learning in Solid Earth Geoscience, Santa Fe, 2019. PDF
Vesselinov, V.V., Novel Machine Learning Methods for Extraction of Features Characterizing Datasets and Models, AGU Fall meeting, Washington D.C., 2018. PDF
Vesselinov, V.V., Novel Machine Learning Methods for Extraction of Features Characterizing Complex Datasets and Models, Recent Advances in Machine Learning and Computational Methods for Geoscience, Institute for Mathematics and its Applications, University of Minnesota, 10.13140/RG.2.2.16024.03848, 2018. PDF
Vesselinov, V.V., Mudunuru. M., Karra, S., O'Malley, D., Alexandrov, Unsupervised Machine Learning Based on Non-negative Tensor Factorization for Analysis of Filed Data and Simulation Outputs, Computational Methods in Water Resources (CMWR), Saint-Malo, France, 10.13140/RG.2.2.27777.92005, 2018. PDF
O'Malley, D., Vesselinov, V.V., Alexandrov, B.S., Alexandrov, L.B., Nonnegative/binary matrix factorization with a D-Wave quantum annealer PDF
Vesselinov, V.V., Alexandrov, B.A, Model-free Source Identification, AGU Fall Meeting, San Francisco, CA, 2014. PDF

Presentations are also available at slideshare.net, ResearchGate and Academia.edu

Extra information

For more information, visit monty.gitlab.io, [tensordecompositions.github.io],(https://tensordecompositions.github.io), and tensors.lanl.gov

Installation behind a firewall

Julia uses git for package management. Add in the .gitconfig file in your home directory:

[url "https://"]
        insteadOf = git://

or execute:

git config --global url."https://".insteadOf git://

Julia uses git and curl to install packages. Set proxies:

export ftp_proxy=http://proxyout.<your_site>:8080
export rsync_proxy=http://proxyout.<your_site>:8080
export http_proxy=http://proxyout.<your_site>:8080
export https_proxy=http://proxyout.<your_site>:8080
export no_proxy=.<your_site>

For example, if you are doing this at LANL, you will need to execute the following lines in your bash command-line environment:

export ftp_proxy=http://proxyout.lanl.gov:8080
export rsync_proxy=http://proxyout.lanl.gov:8080
export http_proxy=http://proxyout.lanl.gov:8080
export https_proxy=http://proxyout.lanl.gov:8080
export no_proxy=.lanl.gov

SmartTensors / ShiftNMFk.jl