Definition of hierarchcal attributed random graph and its application to computer vision and machine learning

Abstract

An attributed graph was defined to represent both sturctural and semantic information contained in structural objects. When uncertainty exists in descrption of a structural object either due to noise or minor deformation, a probabilistic description of the object ensemble is necessary. For this purpose, we define an attributed random graph, which can be considered as a generalization of conventional ones, to include multiple attributes as well as numeric attribute instead of a single nominal attribute in random vertices and edges. Then, we derived the equations for an entropy of a random graph to reflect the variability of the random graph. For the representation of a complex object, the object is decomposed into several parts, and it is described by these decomposed parts and their relations. In general, the parts can be the primitive elements that can not be decomposed further, or still can be decomposed into their subparts. Therefore, the hierarchical description method is very natural and the hierarchical description is represented by a hierarchical graph whose vertices represent either primitive elements or graphs. This graphs also have vertices which contain primitive elements or graphs. When some uncertainty exists in the hierarchical description of a complex object either due to noise of minor deformation, a probabilistic desdription of the object ensemble is also necessary. For this purpose, we formally define the hierarchical attributed random graph and derive the equations for the entropy calculation of the hierarchical random graph. We adopt this concepts to three parts to computer vision and machine learning such as incremental clustering of attributed graphs, optimal isomorphism between two random graphs and optimal isomorphism between two hierarchical attributed graphs. First, we introduce an incremental clustering system to group the patterns represented by attributed graphs as an application example. The purpose of this system is to take a succ...