Related papers: Flow Divergence: Comparing Maps of Flows with Rela…
We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…
The most widely used techniques for community detection in networks, including methods based on modularity, statistical inference, and information theoretic arguments, all work by optimizing objective functions that measure the quality of…
Subject of research is complex networks and network systems. The network system is defined as a complex network in which flows are moved. Classification of flows in the network is carried out on the basis of ordering and continuity. It is…
Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
Many networks display community structure which identifies groups of nodes within which connections are denser than between them. Detecting and characterizing such community structure, which is known as community detection, is one of the…
Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…
We tackle the problem of estimating flow between two images with large lighting variations. Recent learning-based flow estimation frameworks have shown remarkable performance on image pairs with small displacement and constant…
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean subset logic is usually mis-specified as the special case of…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate…
Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion…
A new method for identifying soft communities in networks is proposed. Reference nodes, either selected using a priori information about the network or according to relevant node measurements, are obtained. Distance vectors between each…
A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…
Community detection, as well as the identification of other structures like core periphery and disassortative patterns, is an important topic in network analysis. While most methods seek to find the best partition of the network according…
In this work we give a community detection algorithm in which the communities both respects the intrinsic order of a directed acyclic graph and also finds similar nodes. We take inspiration from classic similarity measures of bibliometrics,…