L1 Splines with Locally Computed Coefficients

Abstract

An algorithm for calculating univariate L1 spline fits that involves multiple minimizations of the spline functional on each iteration was created. The computational results for this algorithm indicate overall good performance of the procedure but the procedure is computationally more expensive than desired. We formulated a new potential algorithm in which there will be only one minimization of the spline functional on each iteration. We also continued development of a new L1 "Multiple Component Detection and Analysis" (L1 MCDA) algorithm, which is a fundamental and complete reformulation of Principal Component Analysis in a framework exclusively based on the L1 norm. Direct connection with heavy-tailed statistics is a guiding principle. We completed design of and computational results for the 2D case. The extension of L1 MCDA to 3D is currently under way.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2013
Accession Number
ADA585562

Entities

People

  • John E. Lavery
  • Shu-cherng Fang

Organizations

  • North Carolina State University

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  • Human Systems

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