There is already a great number of highly efficient methods producing components with sparse loadings which significantly facilitates the interpretation of principal component analysis (PCA). However, they produce either only orthonormal loadings, or only uncorrelated components, or, most frequently, neither of them. To overcome this weakness, we introduce a new approach to define sparse PCA similar to the Dantzig selector idea already employed for regression problems. In contrast to the existing methods, the new approach makes it possible to achieve simultaneously nearly uncorrelated sparse components with nearly orthonormal loadings. The performance of the new method is illustrated on real data sets. It is demonstrated that the new method outperforms one of the most popular available methods for sparse PCA in terms of preservation of principal components properties.
CITATION STYLE
Genicot, M., Huang, W., & Trendafilov, N. T. (2015). Weakly correlated sparse components with nearly orthonormal loadings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 484–490). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_52
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