Design of a Robust Least Squares Extended Algorithm for Social Network Analysis

The design of a robust least squares extended algorithm for social network analysis proposes an innovative method that integrates robust statistics and graph structure modeling, aiming to solve the problems of existing least squares algorithms being sensitive to noise and unable to effectively handle abnormal connections that are common in social networks. By constructing a robust objective function based on the Huber loss function, introducing a graph Laplace regularization term to maintain the network topology, and designing an adaptive weight adjustment mechanism to dynamically correct the influence of abnormal nodes, combined with a random coordinate descent algorithm, an efficient solution for large-scale networks is achieved. Experiments on real data sets such as Twitter and Facebook show that the algorithm has an average absolute error of only 0.32 in a 10% noise injection scenario, an abnormal connection identification accuracy of 93.6%, and an average processing time of only 7.27 minutes for a single machine to process a million-node network, which verifies its practicality and robustness in tasks such as social network relationship prediction and community discovery, and provides a new theoretical tool for complex social data analysis.