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Neural network models of early sensory processing typically reduce thedimensionality of streaming input data. Such networks learn the principalsubspace, in the sense of principal component analysis (PCA), by adjustingsynaptic weights according to activity-dependent learning rules. When derivedfrom a principled cost function these rules are nonlocal and hence biologicallyimplausible. At the same time, biologically plausible local rules have beenpostulated rather than derived from a principled cost function. Here, to bridgethis gap, we derive a biologically plausible network for subspace learning onstreaming data by minimizing a principled cost function. In a departure fromprevious work, where cost was quantified by the representation, orreconstruction, error, we adopt a multidimensional scaling (MDS) cost functionfor streaming data. The resulting algorithm relies only on biologicallyplausible Hebbian and anti-Hebbian local learning rules. In a stochasticsetting, synaptic weights converge to a stationary state which projects theinput data onto the principal subspace. If the data are generated by anonstationary distribution, the network can track the principal subspace. Thus,our result makes a step towards an algorithmic theory of neural computation.

A Hebbian/Anti-Hebbian Neural Network for Linear Subspace Learning: A Derivation from Multidimensional Scaling of Streaming Data