| Spectral clustering algorithm is an unsupervised clustering method based on graph theory,which can divide datasets into different categories without prior knowledge.This algorithm is widely used in various applications,such as image segmentation,text clustering,and social network analysis.However,the spectral clustering algorithm also faces several challenges and issues.For instance,one significant problem is how to mitigate the effects of sparsity and degree heterogeneity of the network on the algorithm’s performance.In order to enhance the performance of the spectral clustering algorithm on degree heterogeneous networks,both RSC and ISC algorithms have introduced a degree correction method.This involves adding a parameter to each node to balance the weight of nodes in the network.The RSC algorithm uses the average degree of all nodes in the network as the degree correction parameter,while the ISC algorithm uses the average of the maximum and minimum degrees of the network.This study conducts an in-depth exploration of these two algorithms,leveraging the principles of spectrogram theory,and then a new degree correction parameter is proposed and applied to community detection and protein complex detection.The main contributions of this study are as follows:1.Further analysis and improvement are conducted on the RSC algorithm.Initially,spectral graph theory is utilized to analyze the RSC algorithm,followed by proposing an adaptive method for selecting degree correction parameters based on the properties of Laplacian eigenvalues.Artificial network experiments explore and theoretically explain the impact of average degree,mixing parameter and the number of nodes in the largest community on the performance of the algorithm.Experimental results on real community networks show that the new degree correction parameters improve the performance of spectral clustering algorithms on degree heterogeneous networks,and theoretically explain the clustering results.2.Further analysis and improvement are conducted on the ISC algorithm.The RSC algorithm does not perform well on sparse networks.This paper improves the ISC algorithm to enhance the performance of spectral clustering on sparse networks with weak signal.Initially,spectral graph theory is utilized for a theoretical analysis of the ISC algorithm,demonstrating its effectiveness on weak signal networks and followed by proposing a degree correction parameter based on the information of neighbor nodes.The artificial network experiments explore and explain from the theoretical point of view the influence of the average degree,mixing parameter and the number of nodes in the largest community on the performance of the algorithm,and also show that the ISC algorithm has better performance on the weak signal network.Experimental results on protein-protein interaction networks indicate that the ISC algorithm with the new parameter significantly improves clustering performance,especially in terms of accuracy. |
