Hierarchical growing cell structures: TreeGCS

We propose a hierarchical clustering algorithm (TreeGCS) based upon the Growing Cell Structure (GCS) neural network of Fritzke. Our algorithm refines and builds upon the GCS base, overcoming an inconsistency in the original GCS algorithm, where the network topology is susceptible to the ordering of the input vectors. Our algorithm is unsupervised, flexible, and dynamic and we have imposed no additional parameters on the underlying GCS algorithm. Our ultimate aim is a hierarchical clustering neural network that is both consistent and stable and identifies the innate hierarchical structure present in vector-based data. We demonstrate improved stability of the GCS foundation and evaluate our algorithm against the hierarchy generated by an ascendant hierarchical clustering dendogram. Our approach emulates the hierarchical clustering of the dendogram. It demonstrates the importance of the parameter settings for GCS and how they affect the stability of the clustering

An introduction to spectral distances in networks (extended version)

Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an overview of the spectral distances, highlighting their behavior in some basic cases of static and dynamic synthetic and real networks

Network based scoring models to improve credit risk management in peer to peer lending platforms

Financial intermediation has changed extensively over the course of the last two decades. One of the most significant change has been the emergence of FinTech. In the context of credit services, fintech peer to peer lenders have introduced many opportunities, among which improved speed, better customer experience, and reduced costs. However, peer-to-peer lending platforms lead to higher risks, among which higher credit risk: not owned by the lenders, and systemic risks: due to the high interconnectedness among borrowers generated by the platform. This calls for new and more accurate credit risk models to protect consumers and preserve financial stability. In this paper we propose to enhance credit risk accuracy of peer-to-peer platforms by leveraging topological information embedded into similarity networks, derived from borrowers' financial information. Topological coefficients describing borrowers' importance and community structures are employed as additional explanatory variables, leading to an improved predictive performance of credit scoring models

Ranking and clustering of nodes in networks with smart teleportation

Random teleportation is a necessary evil for ranking and clustering directed networks based on random walks. Teleportation enables ergodic solutions, but the solutions must necessarily depend on the exact implementation and parametrization of the teleportation. For example, in the commonly used PageRank algorithm, the teleportation rate must trade off a heavily biased solution with a uniform solution. Here we show that teleportation to links rather than nodes enables a much smoother trade-off and effectively more robust results. We also show that, by not recording the teleportation steps of the random walker, we can further reduce the effect of teleportation with dramatic effects on clustering.Comment: 10 pages, 7 figure

Topological enslavement in evolutionary games on correlated multiplex networks

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner's dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions