The Research On Robust Recommendation Algorithm Based On Matrix Factorization

When shilling attacks exist, the existing collaborative recommendation algorithmsbased on matrix factorization have the following limitations： The item bias and item’sfeature matrix are vulnerable to shilling attacks; the estimation of the parameters issensitive to outliers; the robustness of the recommendation algorithms is relatively poorwhen facing shilling attacks; the robustness is improved at a cost of accuracy. To solve theabove problems, on the basis of existing researches, in this paper we make some depthstudy of robust recommendation from the following four aspects: user (item) bias, thefeature extraction of rating matrix, the strategy of choosing neighbors, the robust estimate.Firstly, we propose a robust collaborative recommendation algorithm based on leastmedian squares estimator. We introduce the least median squares estimator and reweightedleast squares estimator in robust statistics. Then we construct the weight function by leastmedian squares estimator and apply the method of weight calculation to reweighted leastsquares estimator, which can filter out the largest residuals and reduce the increment oftarget item’s feature vector caused by shilling attacks.Secondly, we propose a robust collaborative recommendation algorithm based onkernel function and Welsch reweighted M-estimator. We first combine the median withuser and item biases calculation, which can limit the influence of shilling attacks on userand item biases because median is insensitive to outliers. Then we introduce the kernelfunction and apply it to similarity computation, which can obtain the information ofsimilar users by nonlinear inner product operation. Finally, we combine the user and itembiases based on median and the similarity based on kernel function with matrixfactorization model, and introduce the Welsch reweighted M-estimator to realize therobust estimate of user feature matrix and item feature matrix.Thirdly, we propose a robust collaborative recommendation algorithm based onnonlinearity and Cauchy reweighted M-estimator. We first introduce the kernel principalcomponent analysis which is a method of nonlinear feature extraction of rating matrix, thismethod extends the feature extraction of rating matrix from linear to nonlinear and reduces the increment of target item’s feature vector caused by shilling attacks. Then we present amethod of robust estimation based on Cauchy reweighted M-estimator, in order to realizethe robust estimate of user feature matrix and item feature matrix.Finally, we develop the robust collaborative recommendation algorithms and conductexperiments on the MoviLens dataset to demonstrate its effectiveness.