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Three-way principal balance analysis: algorithm and interpretation

Author

Listed:
  • Violetta Simonacci

    (University of Naples - Federico II)

  • Michele Gallo

    (University of Naples - L’Orientale)

Abstract

Compositional Data Analysis can be useful for unveiling relative variability patterns among variables describing the parts of a phenomenon. Compositions are often represented as orthonormal balances associated with a sequential binary partition (SBP). Principal balances analysis (PBA) is a tool used to find a meaningful SBP by subsequently maximizing explained variability. The exact estimation of PBA is prohibitive for large datasets; therefore, algorithms providing an acceptable approximation are used instead. For compositional data of third-order, such exploratory search must account for third-mode variability. To this end, this work introduces a three-way adaptation of PBA in which estimation is carried out by Tucker3. A study on the composition of academic recruitment fields by Italian macro-region and gender/role is carried out to illustrate the merits of this procedure.

Suggested Citation

  • Violetta Simonacci & Michele Gallo, 2024. "Three-way principal balance analysis: algorithm and interpretation," Annals of Operations Research, Springer, vol. 342(3), pages 1429-1443, November.
    • Handle: RePEc:spr:annopr:v:342:y:2024:i:3:d:10.1007_s10479-022-04782-5
    DOI: 10.1007/s10479-022-04782-5
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