Multiset neurons

Abstract

The present work addresses the adoption of multiset similarity, more specifically the real-valued Jaccard and coincidence indices, as an element underlying artificial neurons. The overlap/interiority index, cosine similarity, and Euclidean distance are also considered. Special attention is given to the features adopted to characterize the patterns provided as input to neurons. After presenting the basic concepts related to real-valued multisets and the coincidence similarity index, including the generalization of the real-valued Jaccard and coincidence indices to higher orders, as well as a description of their special properties, we introduce multiset neurons with and without a non-linearity stage. Important issues related to the selectivity and sensitivity of the implemented comparisons, as well as the effect of localized perturbations of individual features are then addressed. We proceed to study the response of single linear multiset neurons 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 tend to be more robust and effective than the interiority index and the cross-correlation. The coincidence-based neurons are shown to have enhanced overall performance respectively to the considered type of data and perturbations. The potential of multiset neurons is further illustrated with respect to the challenging problem of color and gray-level image segmentation. The reported concepts, methods, and results have several implications not only for pattern recognition and machine learning, but also regarding several other related areas including signal processing, image analysis, and neuroscience.