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The degree of integration was evaluated by Mantel-t tests providing a coefficient of matrix correlation R (below the diagonal) and the probability that correlation between random matrices is less than observed (above the diagonal).

During testing started by make testAll, random matrices are generated in the dimensions specified by those arrays.

Therefore, we analyze the case where random matrices are considered.

In [16], Baraniuk et al. have been proved that many random matrices are good measurement matrices.

Random matrices are matrices whose entries are random numbers, subject to suitable probability distributions, such as matrix normal distribution.

Equivalent random matrices were generated by randomly shuffling entire columns within each matrix (R1 random matrices) (Figure S2), the numbers within individual columns (R2 random matrices) (Figure S3), and a combination of these two shuffling strategies (R3 random matrices) (Figure S4).

For the sake of validation, 1000 random matrices were generated and compared with the STRIKE matrix.

However, the correlation between columns of real g matrices is larger than for synthetic (purely random) matrices.

The random projection matrix is of size (d=200,m=32×32).

where is an observable random matrix,,, and are known matrices, respectively., are unknown matrices.

The statistical significance of correlations between distance matrices was obtained from 5,000 random permutations of matrix elements.