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Procrustes Solution

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Geospatial Algebraic Computations

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Abstract

This chapter presents the minimization approach known as “Procrustes” which falls within the multidimensional scaling techniques discussed in Sect. 9.2.2. Procrustes analysis is the technique of matching one configuration into another in-order to produce a measure of match. In adjustment terms, the partial Procrustes problem is formulated as the least squares problem of transforming a given matrix \(\mathbf{A}\) into another matrix \(\mathbf{B}\) by an orthogonal transformation matrix \(\mathbf{T}\) such that the sum of squares of the residual matrix \(\mathbf{E} = \mathbf{A} -{\boldsymbol BT}\) is minimum.

It seems very strange that up to now Procrustes analysis has not been widely applied in geodetic literature. With this technique linearization problems of non linear equations system and iterative procedures of computation could be avoided, in general, with significant time saving and less analytical difficulties

F. Crosilla

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Notes

  1. 1.

    http://www.mythweb.com/encyc/gallery/procrustes_c.html ©Mythweb.com

  2. 2.

    July-September 1996; 8:(1).

  3. 3.

    ©Chapman and Hall Press.

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Authors and Affiliations

  1. Curtin University, Perth, West Australia, Australia

    Joseph L. Awange

  2. Budapest University of Technology and Economics, Budapest, Hungary

    Béla Paláncz

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  1. Joseph L. Awange
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  2. Béla Paláncz
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Awange, J.L., Paláncz, B. (2016). Procrustes Solution. In: Geospatial Algebraic Computations. Springer, Cham. https://doi.org/10.1007/978-3-319-25465-4_9

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