Projected gradient approach to the numerical solution of the SCoTLASS

Authors:
Nickolay T. Trendafilov;Ian T. Jolliffe
Affiliations:
Faculty of Computing, Engineering and Mathematical Sciences, University of the West of England, Bristol BS16 1QY, UK;Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, Scotland, UK
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

The SCoTLASS problem-principal component analysis modified so that the components satisfy 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 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.