Sparse Principal Component Analysis via Fractional Function Regularity

Table 1

Loadings and variance of numerical results of PCA, SPCA, and FP-SPCA methods in Case 1, where the SPCA and FP-SPCA methods have the same performance in obtaining the sparse loadings while FP-SPCA performs better than SPCA in adjusted variance. (%) denotes the adjusted variance.

	PCA			SPCA		FP-SPCA
	PC1	PC2	PC3	PC1	PC2	PC1	PC2
	0.3708	0.1993	−0.2698	0.5	0	0.5	0
	0.3708	0.1993	−0.2698	0.5	0	0.5	0
	0.3708	0.1993	−0.2698	0.5	0	0.5	0
	0.3708	0.1993	−0.2698	0.5	0	0.5	0
	0.2625	−0.4228	0.0483	0	−0.5	0	−0.5
	0.2625	−0.4228	0.0483	0	−0.5	0	−0.5
	0.2625	−0.4228	0.0483	0	−0.5	0	−0.5
	0.2625	−0.4228	0.0483	0	−0.5	0	−0.5
	0.2954	0.2510	0.5914	0	0	0	0
	0.2954	0.2510	0.5914	0	0	0	0
(%)	58.99	33.10	7.91	32.49	29.86	40.00	36.76