Quantification and Comparison of Degree Distributions in Complex Networks

The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to compare the degree distribution of two given networks and extract the amount of similarity between the two distributions. In this paper, we propose a novel method for quantification of the degree distributions in complex networks. Based on this quantification method,a new distance function is also proposed for degree distributions, which captures the differences in the overall structure of the two given distributions. The proposed method is able to effectively compare networks even with different scales, and outperforms the state of the art methods considerably, with respect to the accuracy of the distance function

Feature Extraction from Degree Distribution for Comparison and Analysis of Complex Networks

The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree distribution is a necessary step. Moreover, many applications need a similarity function for comparison of complex networks based on their degree distributions. Such a similarity measure has many applications including classification and clustering of network instances, evaluation of network sampling methods, anomaly detection, and study of epidemic dynamics. The existing methods are unable to effectively capture the similarity of degree distributions, particularly when the corresponding networks have different sizes. Based on our observations about the structure of the degree distributions in networks over time, we propose a feature extraction and a similarity function for the degree distributions in complex networks. We propose to calculate the feature values based on the mean and standard deviation of the node degrees in order to decrease the effect of the network size on the extracted features. The proposed method is evaluated using different artificial and real network datasets, and it outperforms the state of the art methods with respect to the accuracy of the distance function and the effectiveness of the extracted features.Comment: arXiv admin note: substantial text overlap with arXiv:1307.362

Autoencoding beyond pixels using a learned similarity metric

We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic

Connectionism and psychological notions of similarity

Kitcher (1996) offers a critique of connectionism based on the belief that connectionist information processing relies inherently on metric similarity relations. Metric similarity measures are independent of the order of comparison (they are symmetrical) whereas human similarity judgments are asymmetrical. We answer this challenge by describing how connectionist systems naturally produce asymmetric similarity effects. Similarity is viewed as an implicit byproduct of information processing (in particular categorization) whereas the reporting of similarity judgments is a separate and explicit meta-cognitive process. The view of similarity as a process rather than the product of an explicit comparison is discussed in relation to the spatial, feature, and structural theories of similarity