Abstract
The recommendation algorithm based on Singular Value Decomposition (SVD)++ is a widely used algorithm for its good prediction performance. However, with the rapid increase of data in smart societies, the poor computational performance of the SVD++ recommendation algorithm becomes a prominent disadvantage, for it takes a longer time to optimize the objective function during constructing the prediction model. The learning rate function is a significant factor in the prediction model based on the SVD++ recommendation algorithm. It can directly affect the convergence speed of the prediction model and the performance of the model. The traditional model uses an exponential function, natural exponential function or piecewise constant as its learning rate function. In this paper, a novel adaptive learning rate (ALR) function is proposed, which combines the exponential with linear functions, and the function is applied to the SVD++ recommendation algorithm. The highlights of the paper are as follows. First, with a larger initial value, the proposed function descends quicker and tends to the end with a less step. Second, the theoretical properties of the proposed learning rate function are verified through theoretical analysis, including the theoretical proof of its convergence and the iteration speed comparison. Compared to the existing learning rate functions, the proposed ALR function works better on the convergence speed through mathematical derivation. Finally, the novel ALR function is applied to the SVD++ recommendation algorithm as recommendation model ALRSVD++. Some existing learning rate methods are used as benchmarks for illustrating the computation and prediction performances of proposed ALR function and its ALRSVD++ model. Experimental results demonstrated that the SVD++ recommendation algorithm based on the proposed ALR function improved computational efficiency of the training model ALRSVD++ significantly. Especially, to the larger size training dataset, the iterations and training time based on the proposed ALR function and ALRSVD++ model reduced in a great deal, without greatly sacrificing the recommendation performance.
Highlights
Recommender systems can provide personalized recommendations to users based on their interests in a few minutes
Obtain the error of predicted ratings and the actual value according to Eq(7); (3) Learning the variables bu, bi, puf, qif, and yjf by gradient descent method; using the proposed adaptive learning rate (ALR) function to minimize the objective function of Eq(5); (4) Calculate a new prediction rui according to the variable values obtained in step (3); (5) If the error eui is less than the threshold emin, set the optimal variables by the updated variables, continue to Step (6); otherwise jump to Step (2); (6) Model training complete, get the prediction model by setting every variable to Eq(2) using the optimal values in Step (5)
The CLRSVD++ algorithm did not stop iterating over ten thousand of iterations in model training, in Fig.2 only showed the 300 iterations. This meant that the convergence speed based on the proposed ALRSVD++ was the highest compared to all benchmark methods
Summary
Recommender systems can provide personalized recommendations to users based on their interests in a few minutes. The methods used to improve the prediction accuracy mainly include the following: (1) joining other information on the basis of the original SVD algorithm, such as confidence parameters, the implicit information and time information [19], so as to comprehensively improve the performance of the recommendation model; (2) joining other information on the basis of the improved algorithm, such as the bias information of the user and the item [20]; (3) using the characteristics of other types of matrices to finish the rate prediction [21]. Obtain the error of predicted ratings and the actual value according to Eq(7); (3) Learning the variables bu, bi, puf , qif , and yjf by gradient descent method; using the proposed ALR function to minimize the objective function of Eq(5); (4) Calculate a new prediction rui according to the variable values obtained in step (3);. Get the number of iterations m, training time t; (7) Compute the predicted ratings of the users for items on the test data according to the prediction model Eq(2); (8) Evaluate the performance of the prediction model by RMSE, iterations m, training time t
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