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From High-dimensional to Functional Data: Stringing Via Manifold Learning

  • Harold A. Hernández-RoigEmail author
  • M. Carmen Aguilera-Morillo
  • Rosa E. Lillo
Conference paper
  • 140 Downloads
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

The study of high-dimensional data is becoming a common trend in modern research. Recently, stringing emerged as a methodology to treat high-dimensional sample vectors as realizations of smooth stochastic processes. Under the hypothesis of noisy and order-perturbed measurements, stringing introduces smooth transitions between predictors and takes advantage of Functional Data Analysis (FDA) to study the data. Once a functional representation is achieved, it is possible to visualize intrinsic patterns, or fit functional regression models.We propose manifold learning as an alternative to multidimensional scaling in the reordering step. In a simulation study we show that our proposal achieves smaller relative order errors, and that it can recover more complex relationships between predictors.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Harold A. Hernández-Roig
    • 1
    Email author
  • M. Carmen Aguilera-Morillo
    • 2
  • Rosa E. Lillo
    • 1
  1. 1.Universidad Carlos III de Madrid and uc3m-Santander Big Data InstituteMadridSpain
  2. 2.Universitat Politècnica de València and uc3m-Santander Big Data InstituteValènciaSpain

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