Efficient segmentation in multi-layer oscillatory networks

Abstract

In earlier work, we derived the dynamical behavior of a network of oscillatory units described by the amplitude and phase of oscillations. The dynamics were derived from an objective function that rewards both the faithfulness and the sparseness of representation. After unsupervised learning, the network is capable of separating mixtures of inputs, and also segmenting the inputs into components that most contribute to the classification of a given input object.In the current paper, we extend our analysis to multi-layer networks, and demonstrate that the dynamical equations derived earlier can be successfully applied to multi-layer networks. The topological connectivity between the different layers are derived from biological observations in primate visual cortex, and consist of receptive fields that are topographically mapped between layers. We explore the role of feedback connections, and show that increasing the diffusivity of feedback connections significantly improves segmentation performance, but does not affect separation performance.

An objective function utilizing complex sparsity for efficient segmentation in multi‐layer oscillatory networks

“…Our current method is able to achieve a segmentation accuracy of 94 percent, as shown in Figure 17. This is better than the segmentation accuracy of 90 percent presented in Rao et al (2008a). This result can be also compared with Figures 8 and 9 of Rao et al (2008b), where it was not possible to achieve a segmentation accuracy higher than 80 percent.…”

“…From Figure 16, we observe that when the diameter of lateral connectivity is 5, the separation accuracy is 85 percent, which is the best network performance. In contrast, the earlier approach presented in Rao et al (2008a) was able to achieve a separation of accuracy of 75 percent. Our current method is able to achieve a segmentation accuracy of 94 percent, as shown in Figure 17.…”

“…This shows that the multi‐layer network presented in this paper is able to provide superior segmentation performance as compared with a two‐layer network. The approach of this paper is also superior to our previously presented formulation for multi‐layer networks (Rao et al , 2008a).…”

“…This is the first explicit presentation of an objective function for a multi‐layer system of oscillatory units. Our previous work (Rao et al , 2008a) did not present such an objective function, and instead used an intuitive extension of the formulation in Rao et al (2008b). The work in Rao et al (2008a) used a sin term to account for the influence of the z layer on the amplitudes of the y layer, rather than a cos term as used in the current formulation.…”

“…Our previous work (Rao et al , 2008a) did not present such an objective function, and instead used an intuitive extension of the formulation in Rao et al (2008b). The work in Rao et al (2008a) used a sin term to account for the influence of the z layer on the amplitudes of the y layer, rather than a cos term as used in the current formulation. Though the system behavior in both cases is satisfactory, the justification for the use of the sin term is harder to establish.…”