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Local Intrinsic Dimensionality Based Features for Clustering

  • Paola Campadelli
  • Elena Casiraghi
  • Claudio Ceruti
  • Gabriele Lombardi
  • Alessandro Rozza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8156)

Abstract

One of the fundamental tasks of unsupervised learning is dataset clustering, to partition the input dataset into clusters composed by somehow “similar” objects that “differ” from the objects belonging to other classes. To this end, in this paper we assume that the different clusters are drawn from different, possibly intersecting, geometrical structures represented by manifolds embedded into a possibly higher dimensional space. Under these assumptions, and considering that each manifold is typified by a geometrical structure characterized by its intrinsic dimensionality, which (possibly) differs from the intrinsic dimensionalities of other manifolds, we code the input data by means of local intrinsic dimensionality estimates and features related to them, and we subsequently apply simple and basic clustering algorithms, since our interest is specifically aimed at assessing the discriminative power of the proposed features. Indeed, their encouraging discriminative quality is shown by a feature relevance test, by the clustering results achieved on both synthetic and real datasets, and by their comparison to those obtained by related and classical state-of-the-art clustering approaches.

Keywords

Local features Intrinsic dimensionality Dataset clustering Multi-manifold structures 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Paola Campadelli
    • 1
  • Elena Casiraghi
    • 1
  • Claudio Ceruti
    • 2
  • Gabriele Lombardi
    • 1
  • Alessandro Rozza
    • 3
  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  3. 3.Dipartimento di Scienze ApplicateUniversità degli Studi di Napoli Parthenope Centro Direzionale di NapoliNapoliItaly

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