TY - JOUR
T1 - The Sparse Principal Component Analysis Problem
T2 - Optimality Conditions and Algorithms
AU - Beck, Amir
AU - Vaisbourd, Yakov
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given dataset with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components and is applicable in a wide variety of fields including genetics and finance, just to name a few. We suggest a necessary coordinate-wise-based optimality condition and show its superiority over the stationarity-based condition that is commonly used in the literature, which is the basis for many of the algorithms designed to solve the problem. We devise algorithms that are based on the new optimality condition and provide numerical experiments that support our assertion that algorithms, which are guaranteed to converge to stronger optimality conditions, perform better than algorithms that converge to points satisfying weaker optimality conditions.
AB - Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given dataset with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components and is applicable in a wide variety of fields including genetics and finance, just to name a few. We suggest a necessary coordinate-wise-based optimality condition and show its superiority over the stationarity-based condition that is commonly used in the literature, which is the basis for many of the algorithms designed to solve the problem. We devise algorithms that are based on the new optimality condition and provide numerical experiments that support our assertion that algorithms, which are guaranteed to converge to stronger optimality conditions, perform better than algorithms that converge to points satisfying weaker optimality conditions.
KW - Numerical methods
KW - Optimality conditions
KW - Principal component analysis
KW - Sparsity constrained problems
KW - Stationarity
UR - http://www.scopus.com/inward/record.url?scp=84964403197&partnerID=8YFLogxK
U2 - 10.1007/s10957-016-0934-x
DO - 10.1007/s10957-016-0934-x
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AN - SCOPUS:84964403197
SN - 0022-3239
VL - 170
SP - 119
EP - 143
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -