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The Alternating Least-Squares Algorithm for CDPCA

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Optimization in the Natural Sciences (EmC-ONS 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 499))

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Abstract

Clustering and Disjoint Principal Component Analysis (CDPCA) is a constrained principal component analysis recently proposed for clustering of objects and partitioning of variables, simultaneously, which we have implemented in R language. In this paper, we deal in detail with the alternating least-squares algorithm for CDPCA and highlight its algebraic features for constructing both interpretable principal components and clusters of objects. Two applications are given to illustrate the capabilities of this new methodology.

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Acknowledgments

The authors would like to thank the anonymous referee for all the valuable and constructive comments which have helped to improve this paper. A special thanks to Professor Maurizio Vichi for providing us a Matlab version of the ALS algorithm for performing CDPCA. This work was partially supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013.

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Authors and Affiliations

  1. University of Aveiro, Aveiro, Portugal

    Eloísa Macedo & Adelaide Freitas

Authors
  1. Eloísa Macedo
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  2. Adelaide Freitas
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Corresponding author

Correspondence to Eloísa Macedo .

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Editors and Affiliations

  1. Dept. of Mathematics, University of Aveiro, Aveiro, Portugal

    Alexander Plakhov

  2. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

  3. University of Aveiro, Aveiro, Portugal

    Adelaide Freitas

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Macedo, E., Freitas, A. (2015). The Alternating Least-Squares Algorithm for CDPCA. In: Plakhov, A., Tchemisova, T., Freitas, A. (eds) Optimization in the Natural Sciences. EmC-ONS 2014. Communications in Computer and Information Science, vol 499. Springer, Cham. https://doi.org/10.1007/978-3-319-20352-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-20352-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20351-5

  • Online ISBN: 978-3-319-20352-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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