Multiset Neurons

TL;DR

This paper introduces multiset neurons based on real-valued similarity indices, demonstrating their robustness and effectiveness in pattern recognition tasks like image segmentation, with implications for machine learning and neuroscience.

Contribution

It presents a novel approach using real-valued Jaccard and coincidence similarity indices for neuron models, outperforming traditional methods in robustness and effectiveness.

Findings

Real-valued Jaccard and coincidence indices outperform interiority index and cross-correlation.

Coincidence-based neurons show the best overall performance across various perturbations.

Multiset neurons excel in image segmentation, offering high cost/benefit efficiency.

Abstract

The present work reports a comparative performance of artificial neurons obtained in terms of the real-valued Jaccard and coincidence similarity indices and respectively derived functionals. The interiority index and classic cross-correlation are also included for comparison purposes. After presenting the basic concepts related to real-valued multisets and the adopted similarity metrics, including the generalization of the real-valued Jaccard and coincidence indices to higher orders, we proceed to studying the response of a single neuron, not taking into account the output non-linearity (e.g.~sigmoid), respectively to the detection of gaussian two-dimensional stimulus in presence of displacement, magnification, intensity variation, noise and interference from additional patterns. It is shown that the real-valued Jaccard and coincidence approaches are substantially more robust and effective than the interiority index and the classic cross-correlation. The coincidence-based neurons are shown to have the best overall performance respectively to the considered type of data and perturbations. The potential of the multiset neurons is further illustrated with respect to the challenging problem of image segmentation, leading to impressive cost/benefit performance. The reported concepts, methods, and results, have substantial implications not only for pattern recognition and machine learning, but also regarding neurobiology and neuroscience.