Abstract: Most score prediction studies are based on the assumption that the missing values are random． However， the missing data of the score matrix of the actual on-line recommendation system is non-random． Incorrect assumptions about the missing data can lead to biased parameter estimation and prediction． In order to improve the accuracy of non-random missing score matrix filling，the internal principle of user and item score matrix was analyzed in this paper． It presents a method to transform the score matrix of user and object into the equivalent bilateral block diagonal matrix by row or column transformation． Then the matrix decomposition method was applied to different blocks to decompose and predict the score，making local data update and decomposition become a reality． The experimental results on the public test dataset show that the proposed method can improve the score filling effect，solve the problem of non-random score missing effectively，and improve the prediction accuracy of the recommendation system． The improved block matrix also has a better speedup ratio in the distributed processing experiment，which shows that the proposed method has better scalability．

Key words: matrix decomposition, recommendation system, singular value decomposition, score prediction