Degree-Corrected Distribution-Free Model for Community Detection in Weighted Networks

Grunnleggende konsepter

A degree-corrected distribution-free model is proposed to detect communities in weighted networks, which extends previous distribution-free models by considering node degree heterogeneity. An efficient spectral clustering algorithm is designed to fit the model, with theoretical guarantees on consistent estimation.

Sammendrag

The content presents a Degree-Corrected Distribution-Free Model (DCDFM) for community detection in weighted networks. The key highlights are:

DCDFM extends previous distribution-free models by allowing nodes within the same community to have different expected degrees, making it more suitable for real-world weighted networks.
An algorithm called nDFA is designed based on spectral clustering to fit the DCDFM model. Theoretical analysis shows nDFA enjoys consistent estimation under the proposed model.
A general modularity is proposed as an extension of Newman's modularity to measure the performance of community detection methods on weighted networks, including those with negative edge weights.
Experiments on simulated and real-world networks demonstrate the advantages of the degree-corrected model and the effectiveness of the general modularity.

Statistikk

The content does not contain any explicit numerical data or statistics. The focus is on the theoretical model and algorithm development.

Sitater

None.

Viktige innsikter hentet fra

Degree-corrected distribution-free model for community detection in weighted networks

by Huan Qing klokken arxiv.org 04-08-2024

https://arxiv.org/pdf/2111.10553.pdf

Dypere Spørsmål

What are some potential applications of the DCDFM model beyond community detection in weighted networks

The DCDFM model has potential applications beyond community detection in weighted networks. One application could be in anomaly detection, where the model can be used to identify unusual patterns or outliers in weighted networks. By considering node heterogeneity and allowing for negative edge weights, the model can capture complex relationships and deviations from the norm. Another application could be in recommendation systems, where the model can be used to analyze user-item interactions in weighted networks and provide personalized recommendations based on the latent structural information captured by the model.

How can the proposed nDFA algorithm be further improved in terms of computational efficiency for large-scale networks

To improve the computational efficiency of the nDFA algorithm for large-scale networks, several strategies can be implemented. One approach could be to parallelize the algorithm to leverage the computational power of multiple processors or GPUs. This would help speed up the processing of large datasets by distributing the workload across multiple cores. Additionally, optimizing the algorithm's implementation by reducing redundant calculations and memory usage can also enhance its efficiency. Implementing data preprocessing techniques to reduce the dimensionality of the input data can further improve the algorithm's performance on large-scale networks.

Are there other ways to extend the classical modularity measure to better capture the community structure in weighted networks with negative edge weights

Extending the classical modularity measure to better capture the community structure in weighted networks with negative edge weights can be achieved by incorporating the magnitude and direction of the edge weights into the modularity calculation. One approach could be to modify the modularity formula to account for the sign of the edge weights, giving more weight to positive or negative interactions based on the community structure. Additionally, developing a modularity measure that considers the balance between positive and negative interactions within communities can provide a more nuanced understanding of the network's community structure. This enhanced modularity measure can better capture the complex relationships in weighted networks with negative edge weights.