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Agreement Analysis of Quality Measures for Dimensionality Reduction

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Topological Methods in Data Analysis and Visualization IV (TopoInVis 2015)

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Abstract

High-dimensional data sets commonly occur in various application domains. They are often analysed using dimensionality reduction methods, such as principal component analysis or multidimensional scaling. To determine the reliability of a particular embedding of a data set, users need to analyse its quality. For this purpose, the literature knows numerous quality measures. Most of these measures concentrate on a single aspect, such as the preservation of relative distances, while others aim to balance multiple aspects, such as intrusions and extrusions in k-neighbourhoods. Faced with multiple quality measures with different ranges and different value distributions, it is challenging to decide which aspects of a data set are preserved best by an embedding. We propose an algorithm based on persistent homology that permits the comparative analysis of different quality measures on a given embedding, regardless of their ranges. Our method ranks quality measures and provides local feedback about which aspects of a data set are preserved by an embedding in certain areas. We demonstrate the use of our technique by analysing quality measures on different embeddings of synthetic and real-world data sets.

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Author information

Authors and Affiliations

  1. IWR, Heidelberg University, Heidelberg, Germany

    Bastian Rieck & Heike Leitte

Authors
  1. Bastian Rieck
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  2. Heike Leitte
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Corresponding author

Correspondence to Bastian Rieck .

Editor information

Editors and Affiliations

  1. University of Leeds, Leeds, United Kingdom

    Hamish Carr

  2. Department of Computer Science, Technical University of Kaiserslautern, Kaiserslautern, Germany

    Christoph Garth

  3. School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden

    Tino Weinkauf

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Rieck, B., Leitte, H. (2017). Agreement Analysis of Quality Measures for Dimensionality Reduction. In: Carr, H., Garth, C., Weinkauf, T. (eds) Topological Methods in Data Analysis and Visualization IV. TopoInVis 2015. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-44684-4_6

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