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Dimension-Adaptive Bounds on Compressive FLD Classification

  • Ata Kabán
  • Robert J. Durrant
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8139)

Abstract

Efficient dimensionality reduction by random projections (RP) gains popularity, hence the learning guarantees achievable in RP spaces are of great interest. In finite dimensional setting, it has been shown for the compressive Fisher Linear Discriminant (FLD) classifier that for good generalisation the required target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data points. However these bounds depend on the dimensionality d of the original data space. In this paper we give further guarantees that remove d from the bounds under certain conditions of regularity on the data density structure. In particular, if the data density does not fill the ambient space then the error of compressive FLD is independent of the ambient dimension and depends only on a notion of ‘intrinsic dimension’.

Keywords

Random Projections Compressed Learning Intrinsic Dimension 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ata Kabán
    • 1
  • Robert J. Durrant
    • 1
  1. 1.School of Computer ScienceThe University of BirminghamBirminghamUK

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