Research On Preference Extraction Based On Nystr?m Method

Recommendation algorithms are currently widely involved in many applications,such as Taobao website which can recommend products for users according to their purchase records and browsing records.A good recommendation system can not only save users'browsing time,but also publicize the business in time.To put it simply,recommendation to users are based on the analysis of users'past records,analyzing users'potential preferences from many records,and recommending users according to users'characteristics.In recommendation system,the most important thing is to extract the user's features.In fact,the process of obtaining user's features is actually a recommendation process.Feature extraction is currently used in many fields.With the arrival of the era of big data,the scale of data is also growing.The biggest problem facing feature extraction is the size and nature of matrices.For sparse matrices,both the accuracy of the extracted features and the time complexity in the extraction process should be guaranteed.To solve the above problems,a user preference processing algorithm is designed.In view of the large scale of the matrix,the original data matrix can be sampled.In order to retain the characteristics of the pre-sampling matrix to the greatest extent,it is necessary to select the appropriate sampling method.The eigenvalues and eigenvectors can be obtained by eigenvalue decomposition of the sampled matrix.In order to ensure the accuracy of the extracted preference features,a new algorithm is designed to extract the features of the matrix.That is to say,Nystr¨om method is combined with convex nonnegative matrix factorization.The specific methods are as follows:Firstly,by using the user's score matrix,the score matrix is transformed into the user-user similarity matrix according to the distance formula.The advantage of this method is to make full use of the relationship between users,and then sample from the similarity matrix to get a sampled matrix.The adaptive sampling method is used in the sampling process.It is necessary to traverse the sampled matrix and fully exploit the characteristics of the original matrix,so as to ensure that the sampled matrix retains the characteristics of the original matrix to the maximum extent.Because of the particularity of Nystr¨om method,only column sampling of matrix is needed,which can reduce the operation time.Secondly,the approximated Nystr¨om method is used for feature decomposition.Convex non-negative matrix factorization is adopted.Different from the method of non-negative matrix factorization,the decomposition of convex nonnegative matrices is not restricted by data symbols.After decomposition,eigenvalues and eigenvectors are obtained.After Nystr¨om approximation,the size of the matrix is reduced and computational time complexity also decreases.Time complexity is reduced from O(n~3)to O(kcn),Among them,n represents the column of the original matrix.c represents the column of the sampled matrix.k is the rank of the sampled matrix.For larger matrices,especially sparse matrices,this method is crucial.Finally,feature extraction is applied to recommendation system.Nystr¨om method can reduce high-dimensional data to low-dimensional subspace.The validity of the recommendation is measured by restoring the matrix.Applying feature extraction to real life,which is very important for the research of feature extraction.