Multilayer Multiset Neuronal Networks -- MMNNs

TL;DR

This paper introduces multilayer multiset neuronal networks based on coincidence similarity, demonstrating their effectiveness in pattern recognition and image segmentation, especially with the use of counter-prototype points and gradient-based training.

Contribution

It presents the novel architecture of multilayer multiset neurons with coincidence similarity and explores the use of counter-prototypes for improved segmentation performance.

Findings

Effective segmentation of complex regions achieved with single prototype and counter-prototype points.

Balanced accuracy landscapes are smooth with multiple attraction basins.

Gradient-based optimization successfully trains various network architectures.

Abstract

The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization, and robustness to data perturbations and outliers. These features allow multiset neurons, which are based on the coincidence similarity operation, to perform effective pattern recognition applications, including the challenging task of image segmentation. A few prototype points have been used in previous related approaches to represent each pattern to be identified, each of them being associated with respective multiset neurons. The segmentation of the regions can then proceed by taking into account the outputs of these neurons. The present work describes multilayer multiset neuronal networks incorporating two or more layers of coincidence similarity neurons. In addition, as a means to improve performance, this work also explores the utilization of counter-prototype points, which are assigned to the image regions to be avoided. This approach is shown to allow effective segmentation of complex regions despite considering only one prototype and one counter-prototype point. As reported here, the balanced accuracy landscapes to be optimized in order to identify the weight of the neurons in subsequent layers have been found to be relatively smooth, while typically involving more than one attraction basin. The use of a simple gradient-based optimization methodology has been demonstrated to effectively train the considered neural networks with several architectures, at least for the given data type, configuration of parameters, and network architecture.