nonnegative matrix factorization

Neural correlates of sparse coding and dimensionality reduction

Brains face the fundamental challenge of extracting relevant information from high-dimensional external stimuli in order to form the neural basis that can guide an organism's behavior and its interaction with the world. One potential approach to addressing this challenge is to reduce the number of variables required to represent a particular input space (i.e., dimensionality reduction). We review compelling evidence that a range of neuronal responses can be understood as an emergent property of nonnegative sparse coding (NSC)—a form of efficient population coding due to dimensionality reduction and sparsity constraints.

3D visual response properties of MSTd emerge from an efficient, sparse population code

Using a dimensionality reduction technique known as non-negative matrix factorization, we found that a variety of medial superior temporal (MSTd) neural response properties could be derived from MT-like input features. The responses that emerge from this technique, such as 3D translation and rotation selectivity, spiral tuning, and heading selectivity, can account for a number of empirical results. These findings (1) provide a further step toward a scientific understanding of the often nonintuitive response properties of MSTd neurons; (2) suggest that response properties, such as complex motion tuning and heading selectivity, might simply be a byproduct of MSTd neurons performing dimensionality reduction on their inputs; and (3) imply that motion perception in the cortex is consistent with ideas from the efficient-coding and free-energy principles.