Least Squares and Related

David Ramírez, Ignacio Santamaría and Louis Scharf
Additional contact information
David Ramírez: Universidad Carlos III de Madrid
Ignacio Santamaría: Universidad de Cantabria
Louis Scharf: Colorado State University

Chapter 2 in Coherence, 2022, pp 33-77 from Springer

Abstract: 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.

Keywords: Least squares; Total least squares; Regularized least squares; Procrustes problems; Multidimensional scaling; Johnson-Lindenstrauss lemma (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-13331-2_2

Ordering information: This item can be ordered from
http://www.springer.com/9783031133312

DOI: 10.1007/978-3-031-13331-2_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().