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Multi-Dimensional Scaling of Sparse Block Diagonal Similarity Matrix

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Data Science

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Abstract

Similarity matrix represents the relationship of n objects and gives us a useful information about these objects. Several models for analyzing this data assume that each object of n objects is embedded as a point or a vector in t dimensional “common space” of n objects in general. However, these models are not appropriate for analyzing a sparse block diagonal similarity matrix as each block diagonal matrix indicates us that each member of the set of objects in a block is represented as a point or a vector in not “common space,” but, “sub-space.” And a model is proposed to analyze this type of a sparse block diagonal similarity matrix. And application to a real data set will be shown.

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Authors and Affiliations

  1. School of Management and Information Sciences, Tama University, 4-1-1 Hijirigaoka, Tama-shi, Tokyo, 206-0022, Japan

    Tadashi Imaizumi

Authors
  1. Tadashi Imaizumi
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Correspondence to Tadashi Imaizumi .

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Editors and Affiliations

  1. Department of Political Sciences, University of Naples Federico II, Napoli, Italy

    Francesco Palumbo

  2. Department of Statistical Sciences Paolo Fortunati, Alma Mater Studiorum, University of Bologna, Bologna, Italy

    Angela Montanari

  3. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maurizio Vichi

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Imaizumi, T. (2017). Multi-Dimensional Scaling of Sparse Block Diagonal Similarity Matrix. In: Palumbo, F., Montanari, A., Vichi, M. (eds) Data Science . Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-55723-6_20

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