Image Browsing: Semantic Analysis of NN k Networks

Given a collection of images and a set of image features, we can build what we have previously termed NNk networks by representing images as vertices of the network and by establishing arcs between any two images if and only if one is most similar to the other for some weighted combination of features. An earlier analysis of its structural properties revealed that the networks exhibit small-world properties, that is a small distance between any two vertices and a high degree of local structure. This paper extends our analysis. In order to provide a theoretical explanation of its remarkable properties, we investigate explicitly how images belonging to the same semantic class are distributed across the network. Images of the same class correspond to subgraphs of the network. We propose and motivate three topological properties which we expect these subgraphs to possess and which can be thought of as measures of their compactness. Measurements of these properties on two collections indicate that these subgraphs tend indeed to be highly compact.