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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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An Extended DEIM Algorithm for Subset Selection and Class Identification.

Emily P Hendryx1, Béatrice M Rivière2, Craig G Rusin3

  • 1Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, OK 73034-5207, USA.

Machine Learning
|June 21, 2021
PubMed
Summary
This summary is machine-generated.

A new extension of the discrete empirical interpolation method (DEIM), called E-DEIM, can identify more data classes than standard DEIM. This method is effective for subset and pattern identification tasks in machine learning.

Keywords:
class identificationdiscrete empirical interpolation methodlow rank datasubset selection

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Area of Science:

  • Machine Learning
  • Data Science
  • Numerical Analysis

Background:

  • The discrete empirical interpolation method (DEIM) is a technique for selecting representative data subsets, primarily used in reducing dimensionality for physical models.
  • DEIM's application in subset and pattern identification within the machine learning community is not widely recognized.
  • A key limitation of DEIM is that the number of selected indices cannot exceed the data matrix's rank, hindering the identification of all classes when classes outnumber the rank.

Purpose of the Study:

  • To address the limitations of the standard DEIM algorithm in identifying all data classes when the number of classes exceeds the data matrix rank.
  • To introduce a novel extension of DEIM, termed E-DEIM, designed to overcome the rank limitation.
  • To explore the theoretical underpinnings of using DEIM extensions for CUR matrix factorization for data approximation.

Main Methods:

  • Development and application of the extended discrete empirical interpolation method (E-DEIM).
  • Theoretical analysis of DEIM extensions for CUR matrix factorization.
  • Empirical evaluation of E-DEIM variations on two distinct datasets, comparing performance against standard DEIM and other established methods.

Main Results:

  • The E-DEIM extension successfully identified additional data classes beyond those selectable by the standard DEIM algorithm.
  • Results indicate that E-DEIM can effectively handle datasets where the number of classes surpasses the data matrix rank.
  • The deterministic E-DEIM approach, incorporating coherence, demonstrated comparable or superior performance to other evaluated methods in class identification tasks.

Conclusions:

  • The proposed E-DEIM offers a viable solution to the class identification limitations of the standard DEIM algorithm.
  • E-DEIM enhances subset and pattern identification capabilities, particularly in scenarios with a high number of data classes.
  • The E-DEIM method, including its theoretical basis for CUR factorization, should be considered for future class-identification tasks in machine learning.