Multiset Neurons
This work addresses robustness issues in pattern recognition and machine learning for applications like image segmentation, though it appears incremental as it builds on existing similarity metrics.
The authors tackled the problem of improving artificial neuron robustness to various perturbations by introducing neurons based on real-valued Jaccard and coincidence similarity indices, showing that these approaches are substantially more robust and effective than traditional methods like cross-correlation, with coincidence-based neurons achieving the best overall performance.
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.