Fig. 3.

Illustration of the combination of SVD and cross-validation, corresponding to step 2 in Fig. 2. For each searchlight or ROI, j (number of runs) n (number of voxels) $\times$m (number of beta estimates) matrices are used to estimate the functional dimensionality. For all possible partitions of j runs into training, validation and test data, we first average all training runs and build all possible low-dimensional reconstructions of these averaged data using SVD. All reconstructions are then correlated with the validation run, resulting in $j-1$ correlation coefficients and respective dimensionalities. The dimensionality that results in the highest average correlation across $j-1$ runs is picked as dimensionality estimate k for this fold and a k-dimensional reconstruction of the average of the training and validation runs is correlated with a held-out test-run, resulting in a final reconstruction correlation. In total, j reconstruction correlations are returned that can be averaged and tested for significance across participants using one-sample t-tests or alike. To derive a better estimate of the underlying dimensionality, the j dimensionality estimates per participant can be submitted to the hierarchical Bayesian model (step 4 in Fig. 2).