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.

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 run --interactive --tty montyvesselinov/tensors

The docker image provides access to all TensorDecomposition packages.

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

• Progress of nonnegative matrix factorization process:

Videos are also available at YouTube

A series of Jupyter notebooks demonstrating NMFk have been developed:

• Blind Source Separation (i.e. Feature Extraction)
• Blind Prediction
• Unmixing concentration data

• Machine Learning
• Blind Source Separation (i.e. Feature Extraction)
• Source Identification

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

• 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

• 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

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

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

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

or execute:

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

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

export ftp_proxy=https://proxyout.<your_site>:8080
export rsync_proxy=https://proxyout.<your_site>:8080
export http_proxy=https://proxyout.<your_site>:8080
export https_proxy=https://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=https://proxyout.lanl.gov:8080
export rsync_proxy=https://proxyout.lanl.gov:8080
export http_proxy=https://proxyout.lanl.gov:8080
export https_proxy=https://proxyout.lanl.gov:8080
export no_proxy=.lanl.gov