A Modified Principal Component Technique Based on the LASSO

A Modified Principal Component Technique Based on the LASSO

2003 | Ian T. Jolliffe, Nickolay T. Trendafilov, and Mudassir Uddin
The article introduces a modified principal component technique based on the LASSO (Least Absolute Shrinkage and Selection Operator) to improve the interpretability of principal components. The LASSO method, originally proposed by Tibshirani for multiple regression, introduces a bound on the sum of the absolute values of the coefficients, allowing some coefficients to be exactly zero. This approach is adapted to principal component analysis (PCA) to create a new technique called SCoTLASS (Simplified Component Technique based on the LASSO). The authors explore the properties of SCoTLASS both theoretically and through simulation studies, demonstrating its effectiveness in simplifying the interpretation of principal components. They compare SCoTLASS with traditional PCA, rotated PCA (RPCA), and other methods, showing that SCoTLASS can produce simpler and more interpretable components while retaining a significant portion of the variance. The article also discusses the implementation of SCoTLASS, the choice of the tuning parameter \( t \), and potential extensions and limitations of the method.The article introduces a modified principal component technique based on the LASSO (Least Absolute Shrinkage and Selection Operator) to improve the interpretability of principal components. The LASSO method, originally proposed by Tibshirani for multiple regression, introduces a bound on the sum of the absolute values of the coefficients, allowing some coefficients to be exactly zero. This approach is adapted to principal component analysis (PCA) to create a new technique called SCoTLASS (Simplified Component Technique based on the LASSO). The authors explore the properties of SCoTLASS both theoretically and through simulation studies, demonstrating its effectiveness in simplifying the interpretation of principal components. They compare SCoTLASS with traditional PCA, rotated PCA (RPCA), and other methods, showing that SCoTLASS can produce simpler and more interpretable components while retaining a significant portion of the variance. The article also discusses the implementation of SCoTLASS, the choice of the tuning parameter \( t \), and potential extensions and limitations of the method.
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