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Least Squares and Related

In: Coherence

Author

Listed:
  • David Ramírez

    (Universidad Carlos III de Madrid)

  • Ignacio Santamaría

    (Universidad de Cantabria)

  • Louis Scharf

    (Colorado State University)

Abstract

This chapter begins with a review of least squares and Procrustes problems and continues with a discussion of least squares in the linear separable model, model order determination, and total least squares. A section on oblique projections addresses the problem of resolving a few modes in the presence of many. Sections on multidimensional scaling and the Johnson-Lindenstrauss lemma introduce two topics in ambient dimension reduction that are loosely related to least squares. There is an important distinction between model order reduction and ambient dimension reduction. In model order reduction, the dimension of the ambient measurement space is left unchanged, but the complexity of the model is reduced. In ambient dimension reduction, the dimension of the measurement space is reduced, under a constraint that distances or dissimilarities between high-dimensional measurements are preserved or approximated in a measurement space of lower dimension.

Suggested Citation

  • David Ramírez & Ignacio Santamaría & Louis Scharf, 2022. "Least Squares and Related," Springer Books, in: Coherence, chapter 2, pages 33-77, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-13331-2_2
    DOI: 10.1007/978-3-031-13331-2_2
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