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Learning features invariant to arbitrary transformations in the data is arequirement for any recognition system, biological or artificial. It is nowwidely accepted that simple cells in the primary visual cortex respond tofeatures while the complex cells respond to features invariant to differenttransformations. We present a novel two-layered feedforward neural model thatlearns features in the first layer by spatial spherical clustering andinvariance to transformations in the second layer by temporal sphericalclustering. Learning occurs in an online and unsupervised manner following theHebbian rule. When exposed to natural videos acquired by a camera mounted on acat's head, the first and second layer neurons in our model develop simple andcomplex cell-like receptive field properties. The model can predict by learninglateral connections among the first layer neurons. A topographic map to theirspatial features emerges by exponentially decaying the flow of activation withdistance from one neuron to another in the first layer that fire in closetemporal proximity, thereby minimizing the pooling length in an online mannersimultaneously with feature learning.

Learning Features and their Transformations by Spatial and Temporal Spherical Clustering