On feature extraction using distances from reference points

Feature extraction is the key to a successfully trained classifier. Although many automatic methods exist for traditional data, other data types (e.g., sequences, graphs) usually require dedicated approaches. In this paper, we study a universal feature extraction method based on distance from reference points. First, we formalize this process and provide an instantiation based on network centrality. To reliably select the best reference points, we introduce the notion of theta-neighborhood which allows us to navigate the topography of fully connected graphs. Our experiments show that the proposed peak selection method is significantly better than a traditional top-k approach for centrality-based reference points and that the quality of the reference points is much less important than their quantity. Finally, we provide an alternative, neural network interpretation of reference points, which paves a path to optimization-based selection methods, together with a new type of neuron, called the Euclidean neuron, and the necessary modifications to backpropagation.