Projected gradient approach to the numerical solution of the SCoTLASS

Trendafilov, Nickolay T. and Jolliffe, Ian T. (2006). Projected gradient approach to the numerical solution of the SCoTLASS. Computational Statistics and Data Analysis, 50(1) pp. 242–253.

DOI: https://doi.org/10.1016/j.csda.2004.07.017

Abstract

The SCoTLASS problem—principal component analysis modified so that the components satisfy 11 the Least Absolute Shrinkage and Selection Operator (LASSO) constraint—is reformulated as a dynamical system on the unit sphere. The LASSO inequality constraint is tackled by exterior penalty
13 function.A globally convergent algorithm is developed based on the projected gradient approach. The
algorithm is illustrated numerically and discussed on a well-known data set.

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About

• Item ORO ID
• 3925
• Item Type
• Journal Item
• ISSN
• 0167-9473
• Extra Information
• 2nd Special issue on Matrix Computations and Statistics
• Keywords
• Principal component analysis; Simple structure components; LASSO constraint; Penalty function;Constrained optimization; Gradient dynamical system on manifolds; Steepest ascent vector flows; Optimality conditions
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Nickolay Trendafilov