Augmented Embedding of Dissimilarity Data into (Pseudo-)Euclidean Spaces (original) (raw)

Abstract

Pairwise proximities describe the properties of objects in terms of their similarities. By using different distance-based functions one may encode different characteristics of a given problem. However, to use the framework of statistical pattern recognition some vector representation should be constructed. One of the simplest ways to do that is to define an isometric embedding to some vector space. In this work, we will focus on a linear embedding into a (pseudo-)Euclidean space.

This is usually well defined for training data. Some inadequacy, however, appears when projecting new or test objects due to the resulting projection errors. In this paper we propose an augmented embedding algorithm that enlarges the dimensionality of the space such that the resulting projection error vanishes. Our preliminary results show that it may lead to a better classification accuracy, especially for data with high intrinsic dimensionality.

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References

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Author information

Authors and Affiliations

  1. Information and Communication Theory group, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands
    Artsiom Harol, Sergey Verzakov & Robert P. W. Duin
  2. School of Computer Science, University of Manchester, United Kingdom
    Elżbieta Pękalska

Authors

  1. Artsiom Harol
  2. Elżbieta Pękalska
  3. Sergey Verzakov
  4. Robert P. W. Duin

Editor information

Editors and Affiliations

  1. Hong Kong University of Science and Technology,
    Dit-Yan Yeung
  2. Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
    James T. Kwok
  3. Instituto de Telecomunicações, Instituto Superior Técnico, Lisbon, Portugal
    Ana Fred
  4. Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d’Armi, 09123, Cagliari, Italy
    Fabio Roli
  5. Faculty of Electrical Engineering, Mathematics and Computer Science, Information and Communication Theory Group, Delft University of Technology, Delft, The Netherlands
    Dick de Ridder

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© 2006 Springer-Verlag Berlin Heidelberg

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Harol, A., Pękalska, E., Verzakov, S., Duin, R.P.W. (2006). Augmented Embedding of Dissimilarity Data into (Pseudo-)Euclidean Spaces. In: Yeung, DY., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2006. Lecture Notes in Computer Science, vol 4109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11815921\_67

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