  Neural network models of early sensory processing typically reduce the
dimensionality of streaming input data. Such networks learn the principal
subspace, in the sense of principal component analysis (PCA), by adjusting
synaptic weights according to activity-dependent learning rules. When derived
from a principled cost function these rules are nonlocal and hence biologically
implausible. At the same time, biologically plausible local rules have been
postulated rather than derived from a principled cost function. Here, to bridge
this gap, we derive a biologically plausible network for subspace learning on
streaming data by minimizing a principled cost function. In a departure from
previous work, where cost was quantified by the representation, or
reconstruction, error, we adopt a multidimensional scaling (MDS) cost function
for streaming data. The resulting algorithm relies only on biologically
plausible Hebbian and anti-Hebbian local learning rules. In a stochastic
setting, synaptic weights converge to a stationary state which projects the
input data onto the principal subspace. If the data are generated by a
nonstationary distribution, the network can track the principal subspace. Thus,
our result makes a step towards an algorithmic theory of neural computation.
