Significance Delta Reasoning with p-Adic Neural Networks: Application to Shot Change Detection in Video

A new possibility to extract significant changes is given by the so-called p-adic number system. p-Adic metric as opposed to a conventional Euclidean metric is based on hierarchical encoding of information. p-Adic and more generally ultrametric spaces have been already used for modeling the functioning of cognitive systems for their property of inducing hierarchy in decision-making process. In this paper, we benefit from this property in modeling delta reasoning. Indeed p-adics give a possibility to extract significant information, in particular significant delta-changes and furthermore, to preserve this hierarchical structure in the process of performing various operations on the data. Hence, we can create p-adic neural networks operating on hierarchical strings of information. In this paper, an algorithm of random learning of p-adic neural networks is applied to the problem of detection of changes in streams of video information such as shot boundaries.