Table 2: Neuroimaging data: Final MISA loss values (lower is better).

MSIVA with the subspace structure $S_2$ outputs the lowest loss values in both multimodal neuroimaging datasets, thus it is considered as the optimal approach to capture the latent subspace structure in these two neuroimaging datasets. In addition, relative to the loss values in Table 1, the loss values for MSIVA are consistently lower than for the unimodal baseline, which serves as empirical evidence that MSIVA better fit these datasets.

Subspace Structure	$S_1$	$S_2$	$S_3$	$S_4$	$S_5$
UK Biobank Dataset
Unimodal Baseline	47.735	47.811	47.768	47.778	47.999
MSIVA	46.794	46.775	46.798	46.892	46.924
Patient Dataset
Unimodal Baseline	47.361	47.350	47.336	47.404	47.527
MSIVA	45.775	45.674	45.788	45.924	45.696