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Title: Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform

Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task.more » All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.« less
Authors:
ORCiD logo [1] ; ORCiD logo [2] ; ORCiD logo [2] ; ORCiD logo [2] ; ORCiD logo [2] ; ORCiD logo [2] ; ORCiD logo [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). The Institute for Functional Imaging of Materials and Computer Science and Mathematics Division
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). The Institute for Functional Imaging of Materials and Center for Nanophase Materials Sciences
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Published Article
Journal Name:
Advanced Structural and Chemical Imaging
Additional Journal Information:
Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2198-0926
Publisher:
Springer
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 47 OTHER INSTRUMENTATION; Unmixing; Image segmentation; Scanning probe microscopy; Matrix factorization; Big data; High performance
OSTI Identifier:
1435364
Alternate Identifier(s):
OSTI ID: 1474632

Kannan, Ramakrishnan, Ievlev, Anton, Laanait, Nouamane, Ziatdinov, Maxim A., Vasudevan, Rama K., Jesse, Stephen, and Kalinin, Sergei V.. Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform. United States: N. p., Web. doi:10.1186/s40679-018-0055-8.
Kannan, Ramakrishnan, Ievlev, Anton, Laanait, Nouamane, Ziatdinov, Maxim A., Vasudevan, Rama K., Jesse, Stephen, & Kalinin, Sergei V.. Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform. United States. doi:10.1186/s40679-018-0055-8.
Kannan, Ramakrishnan, Ievlev, Anton, Laanait, Nouamane, Ziatdinov, Maxim A., Vasudevan, Rama K., Jesse, Stephen, and Kalinin, Sergei V.. 2018. "Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform". United States. doi:10.1186/s40679-018-0055-8.
@article{osti_1435364,
title = {Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform},
author = {Kannan, Ramakrishnan and Ievlev, Anton and Laanait, Nouamane and Ziatdinov, Maxim A. and Vasudevan, Rama K. and Jesse, Stephen and Kalinin, Sergei V.},
abstractNote = {Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task. All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.},
doi = {10.1186/s40679-018-0055-8},
journal = {Advanced Structural and Chemical Imaging},
number = 1,
volume = 4,
place = {United States},
year = {2018},
month = {4}
}

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