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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Area of Science:

  • Numerical analysis
  • Data science
  • Machine learning

Background:

  • Discrete Empirical Interpolation Method (DEIM) is established for model order reduction.
  • DEIM shows potential for data class detection via subset selection.
  • Singular Value Decomposition (SVD) aids DEIM in identifying representative data matrix rows/columns.

Purpose of the Study:

  • To provide an overview of DEIM and related algorithms.
  • To discuss DEIM's application in statistical learning and large dataset analysis.
  • To identify future research directions for DEIM in unsupervised learning.

Main Methods:

  • Leveraging SVD for dimension reduction.
  • Utilizing interpolatory projection for subset selection.
  • Adapting DEIM for CUR matrix factorization and oversampling techniques.

Main Results:

  • DEIM effectively identifies representative data subsets.
  • DEIM-based CUR factorization preserves data interpretability.
  • DEIM-oversampling enhances index selection beyond matrix rank.

Conclusions:

  • DEIM has broad applicability, including physics-based modeling, ECG analysis, and document analysis.
  • A gap exists in literature concerning DEIM for unsupervised learning on large datasets.
  • Further exploration of DEIM in statistical learning tasks is warranted.