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

The purpose of this paper is to extend an analysis presented in earlier work which investigated the dynamical behavior of a network of oscillatory units described by the amplitude of and phase of oscillations, and to present an objective function that can be successfully applied to multi‐layer networks.

In this paper, an objective function is presented that can be successfully applied to multi‐layer networks. The behavior of the objective function is explained through its ability to achieve a sparse representation of the inputs in complex‐valued space.

It is found that if the activity of each network unit is represented by a phasor in the complex plane, then sparsity is achieved when there is maximal phase separation in the complex plane. Increasing the spread of feedback connections is shown to improve segmentation performance significantly but does not affect separation performance. This enables a quantitative approach to characterizing and understanding cortical function.

The formulation of the multi‐layer objective function and the interpretation of its behavior through sparsity in complex space are novel contributions of this paper.