CN108804683A - Associate(d) matrix decomposes and the film of collaborative filtering recommends method - Google Patents
Associate(d) matrix decomposes and the film of collaborative filtering recommends method Download PDFInfo
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Abstract
Recommend method with the film of collaborative filtering in conclusion being decomposed this application discloses associate(d) matrix, includes the following steps：The original rating matrix of user is obtained, the original rating matrix of user includes score information of N number of user to the portions M film；User-eigenmatrix U is extracted using singular value decomposition based on user's original rating matrixZ；Based on user-eigenmatrix UZCalculate user's similarity matrix SIMu,v；Based on preset k values and user's similarity matrix SIMu,vCalculate the k feature neighbours set of user；K feature neighbours set and the original rating matrix of user based on user calculate the prediction scoring of every film；Prediction based on every film, which is scored, to be ranked up all films and is recommended by default rule.Disclosed method can promote recommendation accuracy of the slope one algorithms in film commending system, personalization level be improved in the case where ensureing the algorithm arithmetic speed, and reduce due to the sparse influence brought to slope one algorithms of matrix.
Description
Technical field
The invention belongs to film recommended technology fields, and in particular to associate(d) matrix decomposes and the film of collaborative filtering pushes away
Recommend method.
Background technology
Using collaborative filtering recommend being that commending system field is most ripe, a kind of general method, traditional association
It is divided into project-based collaborative filtering (Item-based Collaborative Filtering) with filter algorithm and based on use
The collaborative filtering (User-based Collaborative Filtering) at family.Slope One are a kind of Item-Based associations
The main thought of same filtering recommendation algorithms, algorithm is the scoring that specific user is predicted using the effort analysis of total user.It should
Algorithm idea is superior to traditional collaborative filtering it can be readily appreciated that can easily realize on a variety of platforms in precision and arithmetic speed
Algorithm, but its too dependent on user history scoring thus there is a problem of that cold start-up and matrix are sparse, and because it is to used in
User is all made of indiscriminate recommendation method, therefore the Shortcomings in terms of personalized expression.Therefore by user characteristics or label
Commending system is introduced, is the basis improved precision of prediction and recommend personalization.In order to solve this problem, a kind of method is pre-
Before survey to user carry out clustering, but in view of user-film matrix it is usually larger, large-scale data concentrate into
The time and space complexity that row cluster needs are too high, are not suitable for quickly being recommended using this method, and a kind of method is to use
Slope one based on label recommend, and this method compensates for personalized volume deficiency, but because user couple to a certain extent
It is a subjective process that film, which carries out scoring, and can completely does not represent user or the main spy of film to these usual labels
Sign.
Therefore, it is decomposed this application discloses associate(d) matrix and the film of collaborative filtering recommends method, can promoted
Recommendation accuracy of the slope one algorithms in film commending system improves a in the case where ensureing the algorithm arithmetic speed
Property degree, and reduce due to the sparse influence brought to slope one algorithms of matrix.
Invention content
Aiming at the above shortcomings existing in the prior art, this application discloses associate(d) matrixs to decompose and collaborative filtering
Film recommends method, can promote recommendation accuracy of the slope one algorithms in film commending system, is ensureing algorithm fortune
Personalization level is improved in the case of calculating speed, and is reduced due to the sparse influence brought to slope one algorithms of matrix.
In order to solve the above technical problems, present invention employs the following technical solutions：
Associate(d) matrix decomposes and the film of collaborative filtering recommends method, includes the following steps：
The original rating matrix of user is obtained, the original rating matrix of user includes scoring of N number of user to the portions M film
Information；
User-eigenmatrix U is extracted using singular value decomposition based on the user original rating matrixZ；
Based on the user-eigenmatrix UZCalculate user's similarity matrix SIMu,v；
Based on preset k values and user's similarity matrix SIMu,vCalculate the k feature neighbours set of user；
K feature neighbours set and the original rating matrix of the user based on user calculate the prediction scoring of every film；
Prediction based on every film, which is scored, to be ranked up all films and is recommended by default rule.
It is preferably based on the user original rating matrix and user-eigenmatrix U is extracted using singular value decompositionZTool
Body method includes：
The original rating matrix of user is subjected to the matrix decomposition based on SVD, thenIn formula,
SVD indicates singular value decomposition, RumFor the original rating matrix of the user, UZFor user-eigenmatrix, user and potential spy are indicated
Matrix-vector description between sign, SZFor diagonal matrix, indicate that the singular value matrix after dimensionality reduction indicates the singular value square after dimensionality reduction
Battle array (z*z), z are dimensionality reduction dimension, VZFor film-eigenmatrix, indicate that film is described with latent matrix-vector between the features.
Preferably, described to be based on the user-eigenmatrix UZCalculate user's similarity matrix SIMu,vSpecific method packet
It includes：
Extract user-eigenmatrix UZ, it is based on formula
Calculate user's similarity of potential feature；
Wherein UjkUser's set of potential feature j and k is indicated while possessing, j and k indicate that any two is different potential
Feature,Indicate that the user of potential feature j is averaged preference degree,Indicate that the user of potential feature k is averaged preference degree, ru,jAnd expression
User u is to the preference degree of potential feature j, ru,kIndicate preference degrees of the user u to potential feature k；U is any one in N number of user
User；User-eigenmatrix UZIn element numerical value represent preference degree of the user to potential feature；
User's similarity matrix SIM is constituted by the set for the user's similarity being calculatedu,v。
It is preferably based on preset k values and user's similarity matrix SIMu,vCalculate the k feature neighbours set of user
Specific method include：
Potential characteristic similarity threshold tau is setf, τfIndicate that the similarity threshold of potential feature f, f are any one potential spy
Sign；
Based on SIMu,vAnd potential characteristic similarity threshold taufThe k feature neighbours for calculating user gather { Neibhgoru}。
The k feature neighbours set and the original rating matrix of the user for being preferably based on user calculate the pre- of every film
Test and appraisal point specific method include：
Based on formulaCalculate the deviation between arbitrary two films；
In formula, devm,nIndicate the deviation of film m and film n, film m and film n indicate in the portions M film arbitrary two not
Identical film, Sm,n(x) it indicates simultaneously to gather the user of film m and film n scorings, and Sm,n(x)∈{Neibhgoru,
Card () indicates Sm,n(x) number for the element for including in, umIndicate scorings of the user u for film m, unIndicate user u for
The scoring of film n；
Based on formulaCalculate the prediction scoring of every film；
In formula, wherein Nummn=Sm,n(x), PumIt scores for the prediction of film m, runIndicate scorings of the user u to film n,
IuIndicate the set of the film other than film m.
Recommend method with the film of collaborative filtering in conclusion being decomposed this application discloses associate(d) matrix, including such as
Lower step：The original rating matrix of user is obtained, the original rating matrix of user includes that N number of user believes the scoring of the portions M film
Breath；User-eigenmatrix U is extracted using singular value decomposition based on user's original rating matrixZ；Based on user-eigenmatrix UZMeter
Calculate user's similarity matrix SIMu,v；Based on preset k values and user's similarity matrix SIMu,vCalculate the k feature neighbours collection of user
It closes；K feature neighbours set and the original rating matrix of user based on user calculate the prediction scoring of every film；Based on every electricity
All films are ranked up and are recommended by default rule by the prediction scoring of shadow.Disclosed method can promote slope
Recommendation accuracy of the one algorithms in film commending system improves personalized journey in the case where ensureing the algorithm arithmetic speed
Degree, and reduce due to the sparse influence brought to slope one algorithms of matrix.
Description of the drawings
Fig. 1 is that associate(d) matrix disclosed by the invention decomposes the flow chart for recommending method with the film of collaborative filtering.
Specific implementation mode
The present invention is described in further detail below in conjunction with the accompanying drawings.
Recommend method with the film of collaborative filtering as shown in Figure 1, being decomposed this application discloses associate(d) matrix, including such as
Lower step：
S101, the original rating matrix of user is obtained, the original rating matrix of user includes N number of user to the portions M film
Score information；
S102, user-eigenmatrix U is extracted using singular value decomposition based on the original rating matrix of the userZ；
S103, it is based on the user-eigenmatrix UZCalculate user's similarity matrix SIMu,v；
S104, preset k values and user's similarity matrix SIM are based onu,vCalculate the k feature neighbours set of user；
S105, the k feature neighbours set based on user and the original rating matrix of the user calculate the prediction of every film
Scoring；
S106, the prediction based on every film score and all films are ranked up and are recommended by default rule.
The present invention proposes associate(d) matrix singular value decomposition and Collaborative Filtering Recommendation Algorithm (packet in view of the deficiencies of the prior art
S103 is included to S105) film recommend method, to improve prediction accuracy and realize that commending system is personalized.The present invention is main
Solve problems with：
(1) the problem of the potential feature extraction of user
The potential feature extraction of user is that the premise of personalized recommendation is carried out to user, extracts accurate, complete user
Personal potential feature can play final recommendations precision larger castering action, and to promotion user experience and
4 aspect of satisfaction has larger help；In the prior art, recommended using the slope one based on label, this method is one
It is insufficient to determine to compensate for personalized volume in degree, but because it is a subjective process that user carries out scoring to film, usually this
Can completely does not represent the main feature of user or film to a little labels, so decomposing the potential eigenmatrix generated using SVD
The potential feature vector of user can preferably be represented.
(2) user's similarity is analyzed according to user characteristics
Analysis is carried out to user's similarity to be widely used in the commending system based on collaborative filtering, effect is to phase
With hobby, feature, the behavior that shows is consistent or there are the general differentiations of the user of potential common interest progress, in the present invention
In effect be extract with similar potential feature user group, in the group use slope one algorithms, Ke Yiyou
Effect evades the influence that different characteristic user brings algorithm, recommends precision and arithmetic speed to be promoted；
(3) the excessively sparse problem of matrix
It is one of the problem of long-standing problem commending system that matrix is sparse, recommends field same in film, slope
Performance of the one algorithms on dense matrix also can be more preferable.A kind of effective solution method is exactly to be carried out to the vacancy value of matrix
Interpolation, a kind of method are the dimensions of reduction matrix.The present invention calculates suitable decomposition dimension according to the data that experiment obtains, can
With preferable solving matrix Sparse Problems.
The application improves personalization level in the case where ensureing the algorithm arithmetic speed, and reduces since matrix is sparse
The influence that slope one algorithms are brought.
Original rating matrix in the application can use the data set of increasing income that Minnesota universities of the U.S. provide
MovieLens(ml-1m)。
It is preferably based on the user original rating matrix and user-eigenmatrix U is extracted using singular value decompositionZTool
Body method includes：
The original rating matrix of user is subjected to the matrix decomposition based on SVD, thenIn formula,
SVD indicates singular value decomposition, RumFor the original rating matrix of the user, UZFor user-eigenmatrix, user and potential spy are indicated
Matrix-vector description between sign, SZFor diagonal matrix, indicate that the singular value matrix after dimensionality reduction indicates the singular value square after dimensionality reduction
Battle array (z*z), z are dimensionality reduction dimension, can be by false position, according to time used in dimensionality reduction and final recommendation accuracy in the application
Acquire the optimal solution of z values, VZFor film-eigenmatrix, indicate that film is described with latent matrix-vector between the features.
In the application, potential feature can be understood as the element species that a certain portion's film is included, and such as terrible, plot is moved
Make etc., this is based partially on python realizations, and specific implementation is as follows：
The input of above procedure section is：The original rating matrix R of userum, the matrix dimensionality z after dimensionality reduction, user u, film item
Mesh m；
Output is：User-eigenmatrix UZ, diagonal matrix SZ, film-eigenmatrix VZ；
Preferably, described to be based on the user-eigenmatrix UZCalculate user's similarity matrix SIMu,vSpecific method packet
It includes：
Extract user-eigenmatrix UZ, it is based on formula
Calculate user's similarity of potential feature；
Wherein UjkUser's set of potential feature j and k is indicated while possessing, j and k indicate that any two is different potential
Feature,Indicate that the user of potential feature j is averaged preference degree,Indicate that the user of potential feature k is averaged preference degree, ru,jAnd expression
User u is to the preference degree of potential feature j, ru,kIndicate preference degrees of the user u to potential feature k；U is any one in N number of user
User；User-eigenmatrix UZIn element numerical value represent preference degree of the user to potential feature；
User's similarity matrix SIM is constituted by the set for the user's similarity being calculatedu,v, user's similarity matrix
SIMu,vElement be user's similarity.
This is based partially on python realizations, and specific implementation is as follows：
The input of above procedure section is：User-eigenmatrix UZ, modified cosine similarity formula
Output is：User's similarity matrix SIMu,v
It is preferably based on preset k values and user's similarity matrix SIMu,vCalculate the k feature neighbours set of user
Specific method include：
Potential characteristic similarity threshold tau is setf, τfIndicate that the similarity threshold of potential feature f, f are any one potential spy
Sign；
Based on SIMu,vAnd potential characteristic similarity threshold taufThe k feature neighbours for calculating user gather { Neibhgoru}。
According to user's similarity matrix of calculating and the k number of determination, similarity threshold is set, compares user to potential
The highest preceding k similarity value for meeting similarity threshold is put into arest neighbors set by the preference degree and similarity threshold of feature
In, the k feature neighbours for thus obtaining user gather { Neibhgoru}。
This is based partially on python realizations, and specific implementation is as follows：
The input of above procedure section is：User's similarity matrix SIMu,v, similarity threshold τf
Output is：The k feature neighbours of user gather { Neibhgoru}
The k feature neighbours set and the original rating matrix of the user for being preferably based on user calculate the pre- of every film
Test and appraisal point specific method include：
Based on formulaCalculate the deviation between arbitrary two films；
In formula, devm,nIndicate the deviation of film m and film n, film m and film n indicate in the portions M film arbitrary two not
Identical film, Sm,n(x) it indicates simultaneously to gather the user of film m and film n scorings, and Sm,n(x)∈{Neibhgoru,
Card () indicates Sm,n(x) number for the element for including in, umIndicate scorings of the user u for film m, unIndicate user u for
The scoring of film n；
Based on formulaCalculate the prediction scoring of every film；
In formula, wherein Nummn=Sm,n(x), PumIt scores for the prediction of film m, runIndicate scorings of the user u to film n,
IuIndicate the set of the film other than film m.
Calculate prediction scoring is based partially on python realizations, and specific implementation is as follows：
The input of above procedure section is：The k feature neighbours of user gather { Neibhgoru, the original rating matrix R of userum
Output is：To prediction scorings of the user u on film project m.
In conclusion the application has the following technical effects：
Overcome matrix Sparse Problems existing for film commending system：
It is one of the problem of long-standing problem commending system that matrix is sparse, recommends field same in film, slope
One algorithms are also more suitable for dense matrix.Therefore, the present invention calculates suitable decomposition dimension according to the data that experiment obtains
Z is reduced Time & Space Complexity, carried to matrix dimensionality reduction using matrix decomposition to preferably resolve matrix Sparse Problems
High commending system response speed.
The potential feature for excavating user in rating matrix, improves the precision of recommendation.
In the prior art, recommended using the slope one based on label, this method compensates for a to a certain extent
Property volume it is insufficient, but because it is a subjective process that user carries out scoring to film, these usual labels can not be complete
Representative user or film main feature, so using SVD decompose generate potential eigenmatrix can preferably represent
The potential feature vector of user, and the application obtains k arest neighbors also according to the potential characteristic similarity of user, recycles k neighbours meter
Film scoring is calculated, the personalization level of recommendation is improved.
Above-mentioned is only the preferred embodiment of the present invention, need to point out it is not depart from this skill for those skilled in the art
Under the premise of art scheme, several modifications and improvements can also be made, the technical solution of above-mentioned modification and improvement, which should equally be considered as, to be fallen
Enter this application claims range.
Claims (5)
1. associate(d) matrix decomposes and the film of collaborative filtering recommends method, which is characterized in that include the following steps：
The original rating matrix of user is obtained, the original rating matrix of user includes that N number of user believes the scoring of the portions M film
Breath；
User-eigenmatrix U is extracted using singular value decomposition based on the user original rating matrixZ；
Based on the user-eigenmatrix UZCalculate user's similarity matrix SIMu,v；
Based on preset k values and user's similarity matrix SIMu,vCalculate the k feature neighbours set of user；
K feature neighbours set and the original rating matrix of the user based on user calculate the prediction scoring of every film；
Prediction based on every film, which is scored, to be ranked up all films and is recommended by default rule.
2. associate(d) matrix as described in claim 1 decomposes and the film of collaborative filtering recommends method, which is characterized in that base
User-eigenmatrix U is extracted using singular value decomposition in the user original rating matrixZSpecific method include：
The original rating matrix of user is subjected to the matrix decomposition based on SVD, thenIn formula, SVD tables
Show singular value decomposition, RumFor the original rating matrix of the user, UZFor user-eigenmatrix, indicate user and potential feature it
Between matrix-vector description, SZFor diagonal matrix, indicate that the singular value matrix after dimensionality reduction indicates the singular value matrix (z* after dimensionality reduction
Z), z is dimensionality reduction dimension, VZFor film-eigenmatrix, indicate that film is described with latent matrix-vector between the features.
3. associate(d) matrix as described in claim 1 decomposes and the film of collaborative filtering recommends method, which is characterized in that institute
It states and is based on the user-eigenmatrix UZCalculate user's similarity matrix SIMu,vSpecific method include：
Extract user-eigenmatrix UZ, it is based on formulaIt calculates
User's similarity of potential feature；
Wherein UjkUser's set of potential feature j and k is indicated while possessing, j and k indicate the different potential spy of any two
Sign,Indicate that the user of potential feature j is averaged preference degree,Indicate that the user of potential feature k is averaged preference degree, ru,jIt is used with expression
Family u is to the preference degree of potential feature j, ru,kIndicate preference degrees of the user u to potential feature k；U is that any one in N number of user is used
Family；User-eigenmatrix UZIn element numerical value represent preference degree of the user to potential feature；
User's similarity matrix SIM is constituted by the set for the user's similarity being calculatedu,v。
4. associate(d) matrix as described in claim 1 decomposes and the film of collaborative filtering recommends method, which is characterized in that base
In preset k values and user's similarity matrix SIMu,vCalculate user k feature neighbours set specific method include：
Potential characteristic similarity threshold tau is setf, τfIndicate that the similarity threshold of potential feature f, f are any one potential feature；
Based on SIMu,vAnd potential characteristic similarity threshold taufThe k feature neighbours for calculating user gather { Neibhgoru}。
5. associate(d) matrix as described in claim 1 decomposes and the film of collaborative filtering recommends method, which is characterized in that base
The specific method packet of the prediction scoring of every film is calculated in the k feature neighbours set and the original rating matrix of the user of user
It includes：
Based on formulaCalculate the deviation between arbitrary two films；
In formula, devm,nIndicate that the deviation of film m and film n, film m and film n indicate that arbitrary two differ in the portions M film
Film, Sm,n(x) it indicates simultaneously to gather the user of film m and film n scorings, and Sm,n(x)∈{Neibhgoru, card
() indicates Sm,n(x) number for the element for including in, umIndicate scorings of the user u for film m, unIndicate user u for film
The scoring of n；
Based on formulaCalculate the prediction scoring of every film；
In formula, wherein Nummn=Sm,n(x), PumIt scores for the prediction of film m, runIndicate scorings of the user u to film n, IuTable
Show the set of the film other than film m.
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