Neural correlates of sparse coding and dimensionality reduction
Fig 4
Sparse and parts-based representations recovered by NMF resemble RFs across brain regions.
NMF (inset) can reconstruct a data matrix V (F features × S stimuli) from two reduced-rank matrices W (containing B basis functions) and H (containing the hidden coefficients of the decomposition). Any individual input stimulus (i.e., column in V, red) can be reconstructed from a linear combination (i.e., column in H, blue) of a set of basis functions (i.e., all columns in W, green). (A) A facial image can be reconstructed from a sparse activation of simulated IT neurons that preferentially respond to parts of faces (inspired by [13]). (B) An optic flow field can be reconstructed from a sparse activation of model MSTd neurons that prefer various directions of 3D self-translation and self-rotation. (C) A rat's 2D allocentric position and route-based direction of motion can be reconstructed from a sparse activation of model RSC neurons that prefer an intricate combination of LV, AV, HD, and P. For the sake of clarity, only the four most contributing hidden coefficients (out of 30) are shown. AV, angular velocity; HD, head direction; IT, inferotemporal cortex; LV, linear velocity; MSTd, dorsal subregion of the medial superior temporal area; NMF, nonnegative matrix factorization; P, 2D position; RSC, retrosplenial cortex. Adapted with permission from [46].