The existing collaborative recommendation algorithms based on matrix factorisation (MF) have poor robustness against shilling attacks. To address this problem, in this study the authors propose a robust collaborative recommendation algorithm based on kernel function and Welsch reweighted M-estimator. They first propose a median-based method to calculate user and item biases, which can reduce the influence of shilling attacks on user and item biases because median is insensitive to outliers. Then, they present a method of similarity computation based on kernel function, which can obtain theinformation of similar users by non-linear inner product operation.
Finally, they combine the user and item biases based on median and the similarity based on kernel function with MF model, and introduce the Welsch reweighted M-estimator to realise the robust estimation of user feature matrix and item feature matrix. The experimental results on the MovieLens dataset show that the proposed algorithm outperforms the existing algorithms in terms of both recommendation accuracy and robustness, and the improvement of its robustness is not at the expense of recommendation accuracy.