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Fig. 5 The relationship between the functional and anatomical space and theoretical predictions. (A) Three sampling methods (A1) and RCCA (see text). When RCCA≈0 (A2), the anatomical sampling (ASap) resembles the random sampling (RSap), and while when RCCA≈1 (A4), ASap is similar to the functional sampling (FSap). (B) Distribution of neurons in the functional space inferred by MDS. Each neuron is color-coded by its projection along the first canonical direction v⃗ anat in the anatomical space (see text). Data based on fish 6, same for (C-E). (C) Similar to (B) but plotting neurons in the anatomical space with color based on their projection along v⃗ func in the functional space (see text). (D) Dimensionality (DPR ) across sampling methods: average DPR under RSap (circles), average and individual brain region DPR under ASap (squares and dots), and DPR under FSap for the most correlated neuron cluster (triangles; Methods). Dashed and solid lines are theoretical predictions for DPR under RSap and FSap, respectively (Methods). (E) The CI of correlation matrices under three sampling methods in six animals (colors). **p < 0.01; ***p < 0.001; one-sided paired t tests: RSap versus ASap, p = 0.0010; RSap versus FSap, p = 0.0004; ASap versus FSap, p = 0.0014.