Research On Recommendation Algorithm Based On Local Low Rank Matrices Approximation

In the era of information explosion,it is difficult for users to overcome the interference from redundant data and directly find information of their interest.The recommendation system can help users find points of interest,narrow down the choices,and effectively solve the problem of information overload.Among many recommendation algorithms,the matrix decomposition-based collaborative filtering algorithm is one of the frontier areas in the research of recommendation algorithms.The matrix decomposition method assumes that the rating matrix is globally low-rank because it can be decomposed into user feature matrix and item feature matrix.The feature matrix does an inner product to approximate the rating matrix.The local low-rank matrix approximation starts from a new perspective.Starting from the phenomenon that “a few people like a small amount of goods”.That is,a rating matrix is obtained by accumulating multiple low-rank submatrices according to weight distributions.Randomly selecting anchor points and performing similarity measures,the low-rank decomposition problem of the original matrix is transformed into the low rank decomposition problem of the submatrix.And the accuracy of local low-rank matrix approximation is greatly improved compared to the other matrix decomposition algorithms.However,the local low-rank matrix approximation method is not perfect,we can still improve it.This article has a deep understanding of the local low-rank matrix approximation algorithm.In view of the existing problems,the corresponding improvement and optimization are carried out.The main work and achievements are as follows:1.We proposed a local low-rank matrix approximation method based on the optimization of anchor points.The anchor selection of the local low-rank matrix approximation is generated by random selection,which may cause problems such as insufficient anchor features,inability to cover densely populated areas,and large randomness.To solve these problems,this paper proposes an optimization algorithm for anchor point selection.The anchor point information density calculation is introduced to distribute the anchor points in the information-intensive area.At the same time,the anchor points are distributed within the feature range through the recessive factor feature clustering algorithm.It ensures that the features of the anchor itself are distinct,the anchor points are differentiated,and the distribution is more uniform.2.We proposed a local low-rank matrix approximation algorithm based on implicit feedback information.Implicit feedback information can help build a more accurate training model and improve the recommendation accuracy of the local low-rank matrix approximation algorithm.We proposed a local low-rank matrix approximation algorithm combined with user ratings preference information.By combining implicit feedback information,it analyzes the user's rating preference habits,and corrects user rating habits to give more accurate scoring predictions.At the same time,we proposed another local low-rank matrix approximation algorithm based on implicit and explicit feedback information.By adding the user's positive feedback information in the model,we get more accurate prediction results.