An Algorithm for Finding Projections with Extreme Kurtosis

  • Cinzia Franceschini
  • Nicola Loperfido
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 227)


Projection pursuit is a multivariate statistical technique aimed at finding interesting low-dimensional data projections. A projection pursuit index is a function which associates a data projection to a real value measuring its interestingness: the higher the index, the more interesting the projection. Consequently, projection pursuit looks for the data projection which maximizes the projection pursuit index. The absolute value of the fourth standardized cumulant is a prominent projection pursuit index. In the general case, a projection achieving either minimal or maximal kurtosis poses computational difficulties. We address them by an algorithm which converges to the global optimum, whose computational advantages are illustrated with air pollution data.


Fourth moment Kurtosis Projection pursuit Tensor 



The authors would like to thank an anonymous referee for her/his comments which greatly helped in improving the present paper.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Economia (DEC)Università degli Studi “G. d’Annunzio” di Chieti-PescaraPescaraItaly
  2. 2.Dipartimento di Economia, Società e Politica (DESP)Università degli Studi di Urbino “Carlo Bo”UrbinoItaly

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