The discrete empirical interpolation method in class identification and data summarization

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.