An optimization approach to achieve unsupervised segmentation and binding in a dynamical network

We present a novel network of oscillatory units, whose behavior is described by the amplitude and phase of oscillations. We derive the network dynamics from an objective function that rewards both the faithfulness and the sparseness of representation. The resulting network architecture is simple, and the dynamics are straightforward to interpret. This network functions in an unsupervised manner, and is able to form unique representations for a set of inputs. Once the set of inputs is learnt, the network can deconvolve mixtures of inputs. A significant capability of the network is that it segments its inputs into components that most contribute to the classification of a given input object. Network units exhibit synchronization through phase locking after an initial settling period. The behavior of deconvolution is determined by the amplitude of units in an output layer, while segmentation is simultaneously determined through phase similarity between the input and output layer units. Thus, the network exhibits the binding of specific input units and the output units that represent a classification of these input units by means of phase similarity.