Online contrastive PCA with Hebbian / anti-Hebbian plasticity

Living organisms receive an immense amount of information per unit time, but much of it is of little relevance for behavior. A simple approach to process this high-dimensional input is to focus on a lower-dimensional subspace and ignore the directions that are less informative. Principal component analysis (PCA) achieves this by discarding the directions with low variance. Such an approach is, however, inefficient in cases where the irrelevant directions are very noisy, thus having greater variance than the relevant ones. If we have access to representative samples of variability in irrelevant directions ("negative samples"), we can achieve better efficiency by using a contrastive variant of PCA, as in Abid et al. (2017). Contrastive PCA (cPCA) finds the subspace of highest relevant variance, associated with positive samples, while minimizing the variance associated with irrelevant information, as inferred from negative samples.

Here we build an online, biologically plausible variant of cPCA, which we call cPCA*, and show that it has a number of realistic features. In particular, cPCA* can be implemented as a circuit comprised of two-compartment neurons. The feedforward connectivity undergoes Hebbian or anti-Hebbian plasticity depending on whether it is processing a positive or a negative sample. We posit that positive and negative samples arrive via the same pathway and propose that the indication of which samples are positive or negative can be done either explicitly (e.g., using neuromodulatory signals) or implicitly (e.g., based on temporal ordering). Altering the sign of the plasticity in relation to the order in which signals arrive suggests a possible relation to Spike Timing Dependent Plasticity (STDP).